spring 2012 quant lab manual_2
TRANSCRIPT
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TABLE of CONTENTS
Item Pg.
Course Syllabus… 3
Schedule of Events… 6
Safety, Policies, Procedures, and Grading… 8
Lab Report Format… 9
Grading Policy… 11
Quiz Topics… 12
Experiment 1 – Penny Pinching… 13
Supplement… 14
Experiment 2 – Memo from Corporate… 17
Experiment 3 – Calibration of Volumetric Glassware… 18
Supplement… 20
Experiment 4 – Sources of Variance… 22
Supplement… 26
Experiment 5 – Determination of Fe in Vitamin Tablets… 28
Supplement… 31
Experiment 6 – Simultaneous Analysis of a 2-Component Mixture… 34
Supplement… 36
Experiment 7 – Quantitative Determination of M&M Dyes… 39
Experiment 8 – Acid-Base Titrations… 43
Supplement… 47
Experiment 9 – Potentiometric Titration of Chloride and Iodide… 49
Supplement… 51
Appendix A – Prelab Briefing Materials
Overview of Measurements and Statistics… 53
Spectroscopy… 57
Overview of Equilibria and Titrations… 62
Appendix B – Statistical Tables… 66
Appendix C – Hazardous Waste Policy… 69
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CHEM 2285 QUANT LAB SYLLABUS
INSTRUCTORS: Dr. Richard Guan Office: CRB 103
Phone: 817-272-6086
Office Hours: 10AM - 11 AM MWF or by appt.
e-mail: [email protected]
TAs and Meeting Times
Section Meeting Time/Place TA Office/
Ofc hrs
Contact
001
MW pm
1 – 5 pm CPB 212 Jonathan Smuts CRB 315
TBA
002
TR pm
1– 5 pm CPB 212 Edra Dodbiba CRB 315
M, W 10 am – 12 pm
003
TR am
8 am – 12 pm CPB
212
Josh Crowell CRB 310
M, W 10 am – 12 pm
Text: Laboratory Manual, will be distributed electronically
Gary Christian, Analytical Chemistry, 6th Edition
Other materials: Scientific calculator, Laboratory notebook, USB portable
storage drive
Grading: Lab Reports (9) 400 pts. (8 x 50, one lab dropped)
Quizzes (4) 200 pts. (4 x 50)
Attendance/Lab Technique 40 pts.
-- Final Quiz on 4/11 (section 001) and 4/12 (sections 002 and 003) is Cumulative
--
Each student will be rated during the course of each experiment by the TA for
attendance (including punctuality and being on-task) and laboratory technique.
Description and Goals of the Course: Develop proficiency with both theoretical
basis and practical laboratory methods of quantitative chemical analysis
including the usage of computers for data analysis and presentation. The
techniques include: sampling, statistics, spectrophotometry, calibration, and
titrations.
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Recipe for success
1) Attendance is a must! Because most of the experiments build on one another,
missing one lab can mean the difference between success and failure in the
course.
2) Prior to lab, read the laboratory manual and suggested textbook chapters/sections
for the experiment which will be done that day.
3) Don’t procrastinate! You have to read and plan many days before for the
successful completion of each experiment.
4) Be able to communicate with your partner/partners and form a study group.
Mandatory Online Safety Training: Students registered for this course must complete the University’s required “Lab Safety Training”
prior to entering the lab and undertaking any activities. Students will be notified via MavMail
when their online training is available. Once notified, students should complete the required
module as soon as possible, but no later than their first lab meeting. Until all required Lab Safety
Training is completed, a student will not be given access to lab facilities, will not be able to
participate in any lab activities, and will earn a grade of zero for any uncompleted work.
1. You should have received an email from the UTA Compliance Department. Click on the
link in the email (or navigate to https://training.uta.edu for the login page)
2. Log on using your network log-on ID and password (what you use to access email). If
you do not know your NetID or need to reset your password, visit
http://oit.uta.edu/cs/accounts/student/netid/netid.html.
3. The available courses for completion will be listed. For Chemistry 1441, complete the
course entitled ‘Student Lab Safety Training’
4. Go to ‘Training I’ve Completed’, and print this displayed page for your TA. Verify that it
shows clearly your name, that the training is completed/passed and the date when the
training was completed. If you have just completed the training but it is not updated on
the ‘Training I’ve Completed’ page, try the training again (you should get to the
Certificate page). If this does not work, call the training helpline at 817-272-5100.
5. If you did not receive the training email and you have not already completed the training
you will need to contact the training helpline (817-272-5100) or email
6. Students who have not completed the training by census date may be dropped from the
lab (and consequently the lecture).
Once completed, Lab Safety Training is valid for the remainder of the same academic year (i.e.
through next August) for all courses that include a lab. If a student enrolls in a lab course in a
subsequent academic year, he/she must complete the required training again.
Use of a computer (spreadsheets and word processors) an essential component of this course. The
university provides numerous sites for free student computer usage with access to various
software. It is your responsibility to practice and familiarize yourself with the software. Ask your
TA if you need extra guidance.
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All questions/problems with online training should be directed to the University Compliance
Services Training Helpline at 817-272-5100 or by emailing [email protected].
Policies and Notes:
Dropping: When dropping the course, You are responsible to see that all the proper paperwork
is done by checking with the Chemistry Department office and, YOU MUST properly check out
of the lab, and account for any missing, broken, or dirty apparatus. Failure to follow these
instructions will result in a grade of ‘F’.
Drop for non-payment of tuition: If you are dropped from this class for non-payment of tuition,
you may secure an Enrollment Loan through the Bursar’s office. You may not continue to attend
class until your enrollment Loan has been applied to outstanding tuition fees.
Grade Replacement: Students enrolling in the course with the intention of replacing a previous
grade earned in the same course must declare their intention to do so at the registrar’s office by
Census Date of the same semester in which they are enrolled.
Pass/Fail: If P or F is a grade option in this class and you intend to take this class for a pass/fail
grade instead of a letter grade, you MUST inform me, through the necessary paperwork, BEFORE
the census date.
Americans with Disabilities Act: The University of Texas at Arlington in on record as being
committed to both the spirit and letter of federal equal opportunity legislation; reference Public
Law 93112-The Rehabilitation Act of 1973 as amended. With the passage of new federal
legislation entitled Americans with Disabilities Act-(ADA), pursuant to section 504 of The
rehabilitation Act, there is renewed focus on providing this population with the same
opportunities enjoyed by all citizens.
As a faculty member, I am required by law to provide “reasonable accommodation” to students
with disabilities, so as not to discriminate on the basis of that disability. Student responsibility
primarily rests with informing faculty at the beginning of the semester and in providing
authorized documentation through designated administrative channels.
Bomb Threat Policy: In the event of a bomb threat to a specific facility, University Police will
evaluate the threat. If required, exams may be moved to an alternate location, but they will not
be postponed. UT-Arlington will prosecute those phoning in bomb threats to the fullest extent of
the law.
Students with Pregnancies: For students who are pregnant, it is recommended by the Chemistry
and Biochemistry Department that you do not enroll into a chemistry lab at this time. If you
become pregnant during the semester, we recommend dropping the course as soon as possible
and special provisions will be made to assist you in finishing the course at later date. Please see
your faculty instructor for assistance.
IMPORTANT:
Academic Dishonesty: Enrollment in this course implies acceptance of the university policy as
outlined in the Regents’ Rules and Regulations and on this course syllabus.
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“Scholastic dishonesty includes but is not limited by cheating, plagiarism, collusion, the
submission for credit of any work or materials that are attributable in whole or in part to another
person, taking an examination for another person, any act designed to give unfair advantage to a
student or the attempt to commit such acts.” (Regents’ Rules and Regulations, Par One, Chapter
VI, Section e, subsection 3.2, Subdivision 3.22).
It is the students’ responsibility to be aware of what constitutes academic dishonesty.
Any and all accusations or situations which may involve academic dishonesty will be directed
to the Office of Judicial Affairs. No warnings will be given. Discipline may range from loss
of credit on an exam/quiz/assignment to expulsion from the university.
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Schedule of Events
Week starting Mon/Tues Wed/Thurs Friday
Mon, 1/16/12 No lab; Complete on-line safety training (see p. 7)
Mon, 1/23/12 No lab; Complete on-line safety training (see p. 7)
Mon, 1/30/12 Lab check-in; Group assignments
(CPB 212)
Lab check-in; Group assignments
(CPB 212)
Mon, 2/6/12 Chem 2335 Test 1 Problem Session Quiz 1: Measurement & Statistics
Begin Exp. 1 (CPB 212)
Mon, 2/13/12 Begin Exp. 2 (CPB 212) Begin Exp. 3 (CPB 212) Exp. 1
Report Due
Mon, 2/20/12 Begin Exp. 4 (CPB 212) Quiz 2: Spectroscopy
Begin Exp. 5 (CPB 212)
Exp. 2
Report Due
Mon, 2/27/12 Exp. 5 continued Overview of titrations (CPB 212) Exp. 3
Report Due
Mon, 3/5/12 CHEM 2335 Test 2 Problem Session Quiz 3: Equilibria & Titrations
Begin Exp. 6 (CPB 212) Exp. 4
Report Due
Mon, 3/12/12 -- Spring Break --
Mon, 3/19/12 Begin Exp. 7 (CPB 212) Exp. 7 continued Exp. 5
Report Due
Mon, 3/26/12 Begin Exp. 8 (CPB 212) Exp. 8 continued Exp. 6
Report Due
Mon, 4/2/12 CHEM 2335 Test 3 Problem Session Begin Exp. 9(CPB 212) Exp. 7
Report Due
Mon, 4/9/12 Exp. 9 continued Final Quiz Exp. 8
Report Due
Mon, 4/16/12 Make up Make up Exp. 9
Report Due
Mon, 4/23/12 CHEM 2335 Test 4 Problem Session
(CPB 212) Check out (CPB 212)
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Laboratory Exercises
Expt. No. Title # Lab Periods
1 Statistical Penny Pinching 1
2 Memo from Corporate 1
3 Calibration of Volumetric Glassware 1
4 Sources of Variance – The Weakest Link 1
5 Fe in Vitamin Tablets 2
6 Two Component Colorimetry 1
7 Quantitative Determination of M&M Dyes 2
8 Acid-Base Titrations 2
9 Potentiometric Titration of Chloride and Iodide 2
Mandatory Online Safety Training: Students registered for this course must complete the
University’s required “Lab Safety Training” prior to entering the lab and undertaking any
activities. Students will be notified via MavMail when their online training is available. Once
notified, students should complete the required module as soon as possible, but no later than their
first lab meeting. Until all required Lab Safety Training is completed, a student will not be given
access to lab facilities, will not be able to participate in any lab activities, and will earn a grade of
zero for any uncompleted work.
1. You should have received an email from the UTA Compliance Department. Click on the link in the
email (or navigate to https://training.uta.edu for the login page)
2. Log on using your network log-on ID and password (what you use to access email). If you do not know
your NetID or need to reset your password, visit http://oit.uta.edu/cs/accounts/student/netid/netid.html.
3. The available courses for completion will be listed. For Chemistry 1441, complete the course entitled
‘Student Lab Safety Training’
4. If you did not receive the training email and you have not already completed the training you will need
to contact the training helpline (817-272-5100) or email [email protected].
5. Students who have not completed the training by census date may be dropped from the lab (and
consequently the lecture).
Once completed, Lab Safety Training is valid for the remainder of the same academic year (i.e. through
next August) for all courses that include a lab. If a student enrolls in a lab course in a subsequent academic
year, he/she must complete the required training again.
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All questions/problems with online training should be directed to the University
Compliance Services Training Helpline at 817-272-5100 or by emailing
SAFETY
a. YOU MUST COMPLETE THE ON-LINE SAFETY BRIEFING PRIOR TO
BEGINNING THE EXPERIMENTS! (Ideally, during first week of classes)
https://training.uta.edu (For more details, please refer to page 7)
b. You must wear approved safety goggles at all times in the lab! Any student
not wearing safety goggles in lab when experiments are in progress will be
asked to leave the lab for the remainder of the period. Repeat offenders will
be denied access to the lab for the remainder of the semester.
c. No sandals! Lab aprons are recommended to protect clothing.
d. No Food in Lab - EVER!
e. Know where the showers, eye-wash fountains, and fire blankets are located.
f. Use the hoods when instructed or whenever in doubt.
g. NOTIFY THE LAB INSTRUCTOR OF ANY INJURIES.
h. For your safety, wash your hands after each lab.
EQUIPMENT
a. NEVER put spatulas, pipets or anything else into any community reagent
vessel. NEVER put any excess reagents back into these vessels. Take only
what you need.
b. Balances are sensitive and expensive. Treat them accordingly. Don’t touch
any knobs, switches, etc. until you know what you’re doing. An abused
balance will yield inaccurate results for everyone.
c. Hold your pipets correctly. Keep them clean by storing them filled with
distilled water. (No droplets should form during delivery.)
d. Use caution when pipetting. Many of the reagents you will use are highly
toxic. Use your pipet bulb.
e. Hold buret stopcocks properly. Buret stopcocks should not turn stiffly or
leak. Droplets should not form during delivery. Keep your buret filled with
distilled water when not in use.
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f. Treat the computer and hand-held data stations with care. YOU WILL BE
HELD FINANCIALLY RESPONSIBLE FOR DAMAGE TO COMPUTERS
AND HAND-HELD DEVICES (~$400) RESULTING FROM NEGLIGENCE!
g. RECORD THE NUMBER OF THE VERNIER HAND-HELD DEVICE YOU
USE (WITH THE T.A.) AND USE THE SAME DEVICE THROUGHOUT THE
SEMESTER.
PREPARATION
Read the experiment before it is to be done. Attend all pre-lab discussions and
ask about procedures you don’t understand. Preparing an outline of the
experimental procedures prior to the lab is a valuable way to avoid mistakes. Be
prepared to take a quiz on the dates indicated in the laboratory schedule.
DATA RECORDING
All data should be arranged in tables for ease of referencing and reporting. Data
can be recorded by the hand-held devices and transferred to an Excel sheet for
handling. In the end, all of the data collection is your responsibility. Be sure you
acquire all data, including temperatures, stock solution concentrations, etc.,
before leaving the lab.
STANDARD LAB REPORT FORMAT
Each lab report should begin with the following information: title of experiment,
name, date, and name of partner, if any. Each lab report is worth a total of 50
points. Do not wait to the last minute to write your lab report. The reports take
time to write and sometimes will be in excess of 10-15 pages. In addition, the
following sections should be included in each report (i.e. READ THIS
CAREFULLY AND FOLLOW INSTRUCTIONS):
1. Objective (5 pts): In this section, briefly state the main purpose of the lab,
which includes what you would be doing in the experiment and why are you
doing it. You should include the different analysis techniques that you will be
using, without explaining the relevant formulas; however, you should
mention the different tests you will be using. In the end include your
expectations of what the result of the lab will be.
2. Data (7 pts): In this section you must show all data collected during the
course of the lab experiment. The data needs to be organized and easy to read
(a separate grade will be assigned to clarity of presentation; see below). Each
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data set or data table should be accompanied by a caption (e.g. “Table 1. UV
absorbance values for Fe”) and appropriate text in the Summary of Results
section which describes its relevance. Number all tables and figures
sequentially (e.g. Table 1, Table 2,…; Figure 1., Figure 2.,…) and refer to them
as such in the Summary of Results section (e.g. “In Table 1 is shown the UV
absorbance values obtained for prepared standards and our unknown
sample”).
You should record all of the unknowns used, all stock solution
concentrations, and relevant temperatures. For each lab involving the use of
liquids, you should record and report the room temperature. This
information is your responsibility, and not your TA’s.
For experiments with class data and extremely large data sets (greater than
two pages worth of data), you may reference an appendix or attach an excel
sheet. However, you must show individual data for class data sets on your
lab report, and in cases the individual data is extremely large you may show
part of the data on the lab report and reference the rest as stated above.
Again, the placement of all data and its relevance to the experiment should be
explicitly written and referred to in the Summary of Results section.
3. Calculations & Graphs (8 pts): In this section you need to report the constants
used, calculations made, and graphs obtained during the lab experiment. You
should show formulas relevant to your calculations, define all variables, and
provide an example of how you would do the calculations. The equations
should be labeled to make them easier to reference to in your written text (e.g.
Equation 1., Equation 2.,…). Show the results of your calculations in tables,
and state or label what formulas were used for the calculations of each value.
Again, all exhibits (Tables, Equations, and Figures) should be explained with
appropriate accompanying text in the Summary of Results section, referring
directly to the exhibit of interest.
Be sure to properly label all Figures (plots, charts, etc.) in the lab report,
including axes and an appropriate caption (e.g. “Figure 3. Calibration plot for
UV determination of iron.”). Labels and captions for Figures should be placed
below the Figure. Labels and captions for Tables should be placed above the
Table. Specify data set used for each Figure; this is very important when
there is more than one data set in your experiment.
Be sure that all numerical values have the correct number of significant
figures, and make sure to include the appropriate units. This also applies to
all of your Figures and Tables.
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4. Summarized Results (15 pts): This section should be written in a manner that
guides the reader through the two sections above. Here, you will collect all of
your final results and succinctly summarize them in one place. Be sure to
refer to each Table, Figure, and Equation included above with appropriate
explanations of their relevance in the context of the experiment. Reserve
discussion of the results for the conclusion section. Unknowns (5/15 pts): In
the labs that involve an unknown, a clearly delineated entry into you lab
report stating the unknown used and its calculated value should be included
in this section. Point values will be assigned to based on the closeness of your
determined value with the “true” value of the unknown.
5. Conclusions (10 pts): This section should show that you have a good
understanding of what you did in the lab and why you did it. You should
discuss the results, what they mean, and how they relate to your objective.
Both expected and unexpected outcomes should be addressed. Unexpected
outcomes are not necessarily wrong if a good reason is given for obtaining
this result.
Make sure to support all comments with calculated values or data (be careful
to report the correct significant figures and uncertainties in reported values in
this section, also). Include discussion about your sources of error, and
speculate on their impact; your arguments must be reasonable. The reasoning
of your discussion about the errors has to be well-founded and reasonable.
If you get information outside the lab manual you must reference it.
** The overall clarity, readability, attention-to-detail, and presentation of your
lab report will also receive a score. To receive the maximum points (5 pts) for
this assessment, you should follow all of the instructions above, explicitly. **
GRADING POLICY
Laboratory write-ups will be due by 5 pm on the Friday of the week following
completion of the experiment, as indicated in the laboratory schedule on the
course syllabus. All lab reports should be submitted electronically to your TA
(Submit with file name: “2285_Lab#_LastName_First Initial.doc”) by 5 pm on
the date due. Lab write-ups turned in after 5 pm will be assessed a 10% penalty.
An additional 10% penalty will be assessed per day that the lab report is late.
Nine laboratory reports will be submitted and the lowest score will be dropped
in calculation of the final grade for the lab report portion (400/640 total points)
In addition to the lab reports, you will have four quizzes (50 points each) during
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the course of the semester. The quiz will cover relevant material presented in
pre-lab lectures, including procedural aspects of relevant experiments. A list of
quiz topics and relevant suggested reading are provided below. Three subject-
dependent quizzes and one cumulative final quiz will contribute 200/640 total
points toward your grade.
Finally, during each laboratory experiment, the TA will assign a grade for
attendance and good laboratory technique. Attendance marks (ranging from 1
to 5, with 5 being the highest) will be given based on presence in the lab,
punctuality, and consistently being on task. Marks for good laboratory
technique (ranging from 1 to 5, with 5 being the highest) will also be assessed by
the TA and instructor, based on cleanliness, care with handling equipment, and
conformance with other good laboratory practices. Deductions in either of these
categories is at the sole discretion of the TA and the instructors. This grade will
overall comprise 40 out of a total possible 640 points in the laboratory course.
LABORATORY MAKE-UP
An opportunity to make up labs missed for reasons of personal illness or trauma
(death in the family, etc.) will be given at the end of the semester. You must
provide some written documentation that you qualify for this opportunity.
Excuses/make-ups will not be granted for reasons of ran out of time,
oversleeping, tests to study for, didn’t feel like it, etc.
QUIZZES and QUIZ TOPICS
Quiz 1: Measurement and Statistics (50 points)
Sampling; Significant figures and scientific notation; Experimental error (types of
error); Accuracy and precision, Propagation of uncertainty (random error);
Gaussian distribution (mean and standard deviation); Q-test, t-test; Confidence
intervals
- Relevant concepts and procedures in Experiments 1, 2, 3, and 4
- Suggested Reading: Christian, 6th Ed. Ch. 2, 3, 5
Quiz 2: Spectroscopy (50 points)
Electromagnetic radiation and spectrum; absorbance vs. emission; Beer’s law;
Absorbance/transmittance calculation; Beer’s law plot and concentration of
unknown; Absorbance of a mixture.
- Relevant concepts and procedures in Experiments 4, 5, and 6
- Suggested Reading: Christian, 6th Ed. Ch. 16
Quiz 3: Equilibria, Titrations, and Chromatography (50 points)
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Solubility product, Titrations, Indicators, Primary standards, Titration
calculation, Charge balance, pKa values, Titration of weak acid with strong base,
ion selective electrode, Nernst equation, Basics of Chromatography, Paper
chromatography (including proposed methods of quantification from paper
chromatography, see Expt 7)
- Relevant concepts and procedures in Experiments 7, 8, and 9
- Suggested Reading: Christian, 6th Ed. Ch. 7, 8, 11, 14, 18, 19
Quiz 4: Cumulative Final Quiz (50 points)
All of the topics covered in Quizzes 1 – 3 and in the various experiments.
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EXPERIMENT 1
PENNY PINCHING: STATISTICAL TREATMENT OF DATA
Overview
As a scientist it is crucial for you to recognize that there is a vast difference between raw data and
final results. The insight provided by the data (i.e. results) almost always requires interpretation
by the scientist. Of course, this interpretive step can, without proper control, introduce
substantial individual bias. Even a well-intentioned scientist attempting to decide whether a
correlation exists between, for example, increased consumption of beer and increased risk of
falling down, may misinterpret the results without using appropriate statistical tools. The use of
statistical analysis tools allows us to decide in a less biased manner whether points can be
discarded, whether a trend exists, whether a correlation exists, etc., as well as the certainty with
which these correlations can be asserted. A vast array of statistical analysis methods have been
developed to aid in the interpretation of data. In this course we will use only the most
rudimentary of statistical analysis tools - the Q test (to determine if a value can be discarded) and
the Student’s t test (to determine the uncertainty and confidence associated with the assignment
of a value).
In this lab you will practice using some statistical analysis tools by measuring the distribution in
weights of a group of pennies. In order to have sufficient measurements with which to perform a
meaningful analysis you will also apply statistical analysis to the collected data from your entire
class.
Instructions
Read Christian 6th ed., Chapter 3
1. Obtain a sample of 10-20 pennies from the TA. Record the sample number in your notebook.
2. Carefully weigh each penny and record the mass and the date of the penny.
3. Submit your results to your TA for inclusion in the class data file. When all of the class
values are collected they will be sent to you as an MS Excel file for further analysis.
4. Return the pennies to your TA.
Data Analysis
1. Using your individual data set calculate the mean and standard deviation of the pennies’
weights. Check for outliers using the Q test at 90% confidence. Estimate a reasonable value
for Qcrit with N=20 and justify your estimate. If any values must be rejected, try to find a
physical reason for the outlying value, and recalculate the mean and standard deviation with
the outliers removed.
2. Divide the mass range between 2.30 grams and 3.30 grams into 40 equal intervals. Using the
class data set, construct a frequency table and a frequency histogram of the penny masses.
You should notice two distinct distributions in the penny masses. Are they Gaussian in
form?
3. Using the class data set calculate the mean and standard deviation for EACH
DISTRIBUTION of the pennies’ weights.
4. Use the Student’s t test to evaluate whether the two distributions of pennies truly represent
two distinct sets of pennies (99% confidence) or simply the random error associated with one
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set of penny weights. Justify your approach. You may find it helpful to review section 4-3,
especially case 2 on page 60 of the text. Is there a correlation between the identity of the
pennies and the apparent bimodal distribution of penny weights?
EXPERIMENT 1 Supplementary Material
PENNY PINCHING
Sample Data:
Individual
Pennies Year Mass (g)
1 1990 2.4715
2 2001 2.4777
3 1989 2.4789
4 2003 2.4830
5 1996 2.4878
6 2000 2.4895
7 1994 2.4903
8 1994 2.4964
9 1987 2.4996
10 2000 2.5034
11 1993 2.5119
12 1985 2.5126
13 1988 2.5164
14 1987 2.5227
15 1987 2.5231
16 1983 2.5645
17 1975 3.0727
18 1973 3.0819
19 1969 3.1078
20 1975 3.1241
Calculations & Graphs:
Constants Used in Calculations:
Qcrit (n=20) at 90% confidence = 0.300
- This value was found on “Q” test table provided by Dr. Schug. The table was
adapted from D.B. Rorabache, Anal. Chem., 63 (1981) 139.
ttable (DOF = ∞) at 99% confidence level = 2.576
- This value was found on Values of Student’s t Table provided by Dr. Schug.
The table was originally found in Quantitative Chemical Analysis, Seventh
Edition ©2007 W.H. Freeman and Company.
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Q-test Calculations for Individual Data:
Qcalc = _Gap_ Gap (low) = 2.4777 – 2.4715 = 0.0062g
Range Gap (high) = 3.1241 – 3.1078 = 0.0163g
Range (high-low) = 3.1241 – 2.4715 =
0.6526g
Qcalc(low) = 0.0062 = 0.0095 Qcalc(high) = 0.0163 = 0.0250
0.6526 0.6526
Qcalc(low) < Qcrit Qcalc(high) < Qcrit
Q calculated in both cases (high and low) is less than Q critical (table), so we retain
both values.
Mean and Standard Deviation for Individual Data:
Mean = ∑xi ∑ xi = sum of measured values
n n = number of measurements
Mean = 52.4158 = 2.6208g
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Standard Deviation (s) = ((∑( xi – mean)2)/(n-1))
1/2 ∑ xi = sum of measured
values
n = number of measurements
s = ((1.141910)/(19))1/2
= 0.2452g
Frequency Table for Class Data: Range (g) # of Pennies Range (g) # of Pennies
2.300 to 2.325 0 2.800 to 2.825 0
2.325 to 2.350 0 2.825 to 2.850 0
2.350 to 2.375 0 2.850 to 2.875 0
2.375 to 2.400 1 2.875 to 2.900 0
2.400 to 2.425 0 2.900 to 2.925 0
2.425 to 2.450 4 2.925 to 2.950 0
2.450 to 2.475 19 2.950 to 2.975 0
2.475 to 2.500 59 2.975 to 3.000 0
2.500 to 2.525 62 3.000 to 3.025 2
2.525 to 2.550 15 3.025 to 3.050 2
2.550 to 2.575 4 3.050 to 3.075 16
2.575 to 2.600 2 3.075 to 3.100 22
2.600 to 2.625 0 3.100 to 3.125 22
2.625 to 2.650 0 3.125 to 3.150 9
2.650 to 2.675 0 3.150 to 3.175 2
2.675 to 2.700 0 3.175 to 3.200 0
2.700 to 2.725 0 3.200 to 3.225 0
2.725 to 2.750 0 3.225 to 3.250 0
2.7250 to 2.775 0 3.250 to 3.275 0
2.775 to 2.800 0 3.275 to 3.300 0
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Mean and Standard Deviation for Low Distribution:
Mean = ∑xi ∑ xi = sum of measured values
n n = number of measurements
Mean = 2.5004g
Standard Deviation (s) = ((∑( xi – mean)2)/(n-1))
1/2 ∑ xi = sum of measured
values
n = number of
measurements
Standard Deviation = 0.0272g
Mean and Standard Deviation for High Distribution:
Mean = 3.0927g
Standard Deviation = 0.0301g
Student’s T-test:
Spooled = (((∑( xi – mean1)2)+( ∑( xj – mean2)
2)))
1/2
. Set 1 Set 2__________________
( n1 +n2 – 2)
Spooled = (((0.121888)+(0.067217))) 1/2
= 0.0281g
((166+75-2))
tcalc = |Mean1 – Mean2| ( (n1n2) ) 1/2
Spooled ((n1 + n2))
tcalc = |2.5004741 – 3.09268267| ( (12450) ) 1/2
= 151.3201
0.028129 ( (241) )
ttable < tcalc
Ttable is less than tcalc, therefore there are two distinct distributions of penny weights.
19
EXPERIMENT 2
A MEMO FROM CORPORATE:
ACCURACY AND PRECISION OF “VOLUMETRIC” GLASSWARE
Dear Staff Scientist:
As you know, our company manufactures glassware for scientists. As part of our marketing
program, we want to be able to indicate that the volumetric markings on our glassware are more
accurate than the competitors. In your laboratory, you have received the following pieces of
glassware from our top product line:
- 10 mL graduated pipet
- 50 mL graduated buret
- 10 mL graduate cylinder
- 50 mL graduated cylinder
Devise a protocol and evaluate the accuracy of delivering 5- and 10-mL volumes (and also, 25-mL
volumes for the larger pieces) of water from these glassware. Provide these data, along with a
quantitative comparison, which includes the precision of your measurements and interpretive
conclusions, in the form of a report for administrative review.
We thank you for your willingness to assist us in the important marketing venture.
Sincerely,
G. Ima Admin
V.P. for Marketing
Instructions
For this experiment, it is up to you devise an appropriate way to measure the accuracy of
delivering the indicated volumes using the indicated glassware. Be sure that your measurements
include sufficient replication for appropriate statistical evaluation of accuracy and precision of
your measurements.
Data Analysis Guidelines
Prepare a report which compares the ability of each type of glassware to deliver the indicated
volumes. Describe and defend the approach that you chose to perform the measurements. Use
appropriate statistical tests (especially, Student’s t test) to compare the different glassware. Be
sure to assess both your ability to make replicate measurements (precision) and the utility of each
glassware (accuracy) for volumetric measurements. Besides the potential inaccuracy of
graduations on the glassware, what other factors might be responsible for inaccuracies you
recorded? Find a source of published manufacturer glassware tolerances and compare these
values with your results.
20
EXPERIMENT 3
CALIBRATION OF VOLUMETRIC GLASSWARE
Overview
All pieces of laboratory equipment have an error and an uncertainty associated with the
measurement made using the equipment. Furthermore, the error can drift over the lifetime of the
equipment due to aging, abuse, etc. and must, therefore, be determined experimentally. This type
of error is “systematic” - it is a constant error relative to the indicated delivery volume. For
example, if the inside volume of our 10 ml graduated pipet has increased slightly over many years
of use, we will always be delivering some constant volume of water greater than the indicated 10
ml and the volume used for calculations must be adjusted for this error.
In reality, the act of measuring the systematic error in the delivery volume also introduces error
associated with YOUR ability to make the measurement. Generally, we operate on the
assumption that this error is “random”. Thus, in principle, the systematic error in the delivery
volume can be determined by making sufficient numbers of measurements so that the random
error introduced by you will be averaged out. Making multiple measurements also serves the
additional important function of allowing you to determine how random you are. In other words,
from the average spread in the volumes you deliver you can determine the uncertainty associated
with YOUR ability to deliver a given volume using a piece of equipment.
In this experiment you will calibrate your 10 ml graduated pipet and 50 ml graduated burets at
several different observed total volumes delivered. You will then generate a correction curve to
correct the systematic errors in delivery volumes to “true” volumes in future experiments. A plot
of the difference between the actual volume delivered and the observed volume delivered will
allow you to adjust for the systematic error in delivery volume when you use these volumetric
glassware in subsequent experiments. In addition, you will assess the error in your ability to
read the glassware accurately by calculating a pooled standard deviation of the delivered
volumes for each piece. Since the correction plots will be used in your subsequent quantitative
determinations, it is critical that you use good analytical technique in this experiment.
Read Christian 6th ed., Chapters 2 and 3
Instructions (Pipet)
1. Clean the pipet with soap and water (or a cleaning solution bath if necessary) and test it to be
sure that water drains uniformly without leaving streaks or droplets on the inside walls.
Measure the time required for the pipet to drain completely. The 10 ml graduated pipet
should require between 10 and 20 seconds for best results.
2. Accurately weigh an Erlenmeyer flask. This and all subsequent weighings should be to 0.1
mg. The vessel need not be dry on the inside.
3. Fill a beaker with water and record the temperature of the water. Use this water to fill the
graduated pipet.
4. Slowly drain the pipet into an unweighed beaker to within 0.02-0.03 ml of the zero mark and
then carefully adjust so the meniscus is just tangent to the zero mark. Record your starting
reading to the nearest 0.01 ml. Be careful to avoid parallax errors. Touch the tip of the pipet
to a moist glass surface to remove any hanging drops.
21
5. Drain water slowly into the weighed container until the meniscus is just above the 2.00 ml
mark. After a few seconds, adjust the meniscus to the unit mark. It is convenient to hit the
mark exactly, but not absolutely necessary as long as the reading is to the nearest 0.01 ml.
Touch the tip to the inside of the receiving flask. Again weigh the receiving vessel and
determine the mass of water delivered.
6. REFILL THE PIPET and repeat steps 2-5 two more times. Repeat the process for 4.00, 6.00,
8.00, and 10.00 ml volumes. A total of three readings should be recorded for each calibration
point.
Instructions (Burets)
1. Clean the buret and make sure it drains cleanly and uniformly. Test the stopcock for leakage
and ease of operation. Test the delivery time with the stopcock full open. For best results, this
should be about 90 seconds or more.
2. Fill a beaker with water and record the temperature of the water. Use this water to fill the
buret. Make sure no air bubbles remain around the stopcock or tip. If so, they can be
removed by opening the stopcock full and tapping as fluid flows.
3. Slowly drain the buret into an unweighed beaker to within ~0.5 ml of the zero mark. Then
carefully adjust the level of the water to the zero mark and record the initial reading to 0.01
ml.
4. Accurately weigh an Erlenmeyer flask. This and all subsequent weighings should be to 0.1
mg. The vessel need not be dry on the inside. Placed the weighed Erlenmeyer flask below the
buret.
5. Deliver 5.00 ml of water to the weighed Erlenmeyer flask and record the final buret reading to
0.01 ml. Again weigh the receiving vessel and determine the mass of water delivered.
6. REFILL THE BURET and repeat steps 3-6 two more times. Repeat the process for 10.00 ml,
15.00 ml, 20.00 ml and 25.00 ml. A total of three readings should be recorded at each
calibration point.
7. USE A STICKER AND MARK THE FIRST BURET AS BURET #1 AND INCLUDE YOUR
NAME. REPEAT STEPS 1-6 FOR YOUR 2ND BURET.
Data Analysis
Graduated pipet: Correct the mass of water to the desired constant volume (2.00, 4.00, 6.00, 8.00
or 10.00 ml). Find the average volume delivered and the average deviation of your three trials at
each pipet interval. Finally, make a plot of the pipet volume correction (delivered volume minus
indicated volume) versus indicated volume. Use this plot to correct to true volumes in future
standard solution preparations.
Burets: Correct the mass of water to the desired constant volume (5.00, 10.00, 15.00, 20.00 or 25.00
ml). Find the average volume delivered and the average deviation of your three trials at each
buret interval. Finally, make a plot of the buret volume correction (delivered volume minus
indicated volume) versus indicated volume. Use this plot to correct to true volumes in future
titration experiments. Repeat this analysis for your 2nd buret.
22
To get an idea of the uncertainty in your ability to deliver a volume using each piece of
glassware, calculate the pooled standard deviation of the delivered volumes. Also calculate the
error associated with the delivery of an individual volume from the errors associated with
reading the initial and final volumes on either of the burets. Which value is greater and which is
a better representation of the uncertainty in your ability to deliver a volume?
EXPERIMENT 3 Supplementary Material
CALIBRATION OF VOLUMETRIC GLASSWARE
Data: Temperature: 22.9°C
Density of water: 0.99762g/mL
Table1: Data set for Buret #1.
5.00mL(#1) weight (g) Actual Volume (mL)
Corrected Volume
5.00 4.71 4.72 -0.28
5.00 4.62 4.63 -0.37
5.02 4.81 4.82 -0.20
10.00mL(#1)
10.02 9.99 10.02 0.00
10.00 10.26 10.29 0.29
10.03 10.20 10.23 0.20
15.00mL(#1)
14.99 15.43 15.43 0.44
15.00 15.05 15.08 0.08
15.02 15.28 15.31 0.29
20.00mL(#1)
20.01 19.72 19.77 -0.24
19.99 19.70 19.75 -0.24
19.99 19.79 19.83 -0.16
25.00mL(#1)
25.02 24.94 25.00 -0.02
25.01 24.88 24.94 -0.07
24.99 24.77 24.82 -0.17
Calculations and Graphs:
1. Corrected Volume/ deviation= delivered volume – indicated volume
2. Mean /average ( x )= sum of volumes ÷ number of measurements
23
3. Standard Deviation (s) 1
)( 2
−
−=∑
n
xxs
i
xi= individual value; n= number of measurements; x = mean
4. Pooled Standard Deviation (spooled)=
( ) ( )( ) ( )
2
11
2 21
2
2
21
2
1
21
1 2
2
2
2
1
−+
−+−=
−+
−+−
=∑ ∑
nn
nsns
nn
xxxx
s set set
ii
pooled
s=standard deviation; n= number of measurements; xi= individual values; x =
mean
5. T-test for comparing to known value:
Confidence Interval n
tsx ±=µ
x = mean; t= student’s t; n= number of measurements; s= pooled standard deviation
(for this experiment)
6. Error Propagation (for reading error) = ± [(uncertainty1)2 + (uncertainty2)
2]0.5
24
EXPERIMENT 4
SOURCES OF VARIANCE – THE WEAKEST LINK
Overview
A chemical analysis generally consists of three steps: 1) obtaining a sample; 2) preparing the
sample for analysis; and 3) making appropriate measurements. Each step is subject to random
errors that are characterized by a standard deviation, σ, or variance, σ2; thus σ2samp is the variance
for obtaining a sample, σ2prep is the variance for preparing the sample, and σ2meas is the variance of
the measurements. Knowing the values for each of these variances is helpful if you wish to
improve an analytical method. The step with the largest variance is the weakest link. Improving
the weakest link improves the precision of the method; improving other steps without improving
the weakest link has little effect.
Determining values for these variances requires special consideration in the design of the
experiment. When you obtain, prepare, and analyze a sample, the total variance, σ2total, includes
contributions from each step. Furthermore, the components of the total variance can be further
partitioned into smaller parts. For spectrophotometric analysis, the measurement variance can be
partitioned into variance due to the spectrometer’s source, detector, and optics, σ2spect, and the
variance due to the positioning of the sample cell within the spectrometer, σ2pos. The total
variance can thus be represented as shown in Equation 1:
( )22222222
posspectprepsampmeasprepsamptotal σσσσσσσσ +++=++= (Eqn 1)
A simple determination of the total variance does not provide enough information to partition
the overall variance into its component parts. One approach to achieve this is to use an
experimental plan called a “nested design”. A nested design consists of several levels, with the
number of levels equal to the number of parameters you wish to evaluate. In this experiment,
you will determine the four sources of variance which give rise to total variance (contributions
from a) sampling, b) sample preparation, c) positioning of the sample cell, and d) the
spectrometer). Therefore, a four-level nested design, as shown in Figure 1, will be used.
25
Figure 1. Four-level nested experimental design for determination of four components of total
variance.
The first level consists of four samples collected randomly from the gross sample (identified
using Roman numerals I, II, III, and IV). Duplicate samples are obtained from each Level I
sample and prepared for analysis; these eight samples represent the second level and are
identified using the uppercase letters A and B. For the third level, each Level II sample is divided
in half before measuring its absorbance; these 16 samples are identified using the numbers 1 and
2. Finally, each Level III sample is placed in the spectrometer and its absorbance measured twice
without repositioning the sample, providing the 32 Level IV samples.
From this design, the components of the total variance can be determined. The variance at Level
IV, σ2IV, is influenced only by the spectrometer’s variance. Looking more closely at Level IV, note
that the difference between any two samples obtained from the same Level III sample is influenced
only by indeterminate errors in the spectrometer. The variance for Level IV, thus provides an
estimate for σ2spect. Because the variance is determined using differences, the normal standard
deviation equation is not used. Instead, the variance is calculated as:
( )
n
di
iIV
spectIV8
2
22∑
== σσ (Eqn 2)
where dIV is the difference between related level IV samples (e.g. IA1a and IA1b), and n is the
number of Level I samples (n = 4 in this case). The variance σ2IV has 4n degrees of freedom.
The variance for Level III, σ2III, includes contributions from the spectrometer and the positioning
of the sample cell; thus:
26
( )
n
di
iIIIspect
posIII42
2
2
22
∑=+=
σσσ (Eqn 3)
where dIII is the difference between related Level II samples (e.g. IA1 and IA2). The factor of 2 in
the term for spectrometer variance accounts for the two Level IV samples used to determine the
result for each Level III sample. The variance σ2III has 2n degrees of freedom.
The variance for the Level II samples, σ2II, includes contributions from the spectrometer, the
positioning of the sample cell, and sample preparation; thus:
( )
n
di
iIIspectpos
prepII242
2
22
22
∑=++=
σσσσ (Eqn 4)
where dII is the difference between related Level II samples (e.g. IA and IB). The factors of 2 and 4
in the term for the variances due to the sample cell positioning and the spectrometer,
respectively, account for the two Level III samples and four Level IV samples used to determine
the result for each level II sample. The variance σ2II has n degrees of freedom.
Finally, the variance for Level I, σ2I, is determined using the standard equation for variance, and
includes contributions from sampling, sample preparation, the positioning of the sample cell, and
the spectrometer:
( )
1842
2
222
22
−
−
=+++=∑
n
XXi
iispectposprep
sampI
σσσσσ (Eqn 5)
where Xi is the result for each Level I sample and X is the average result for all Level I samples.
The factors of 2, 4, and 8 in the terms for the variances due to sample preparation, the sample cell
positioning, and the spectrometer, respectively, account for the two Level II samples, four Level
III samples, and eight Level IV samples used to determine the result for each Level I sample. The
variance σ2I has n-1 degrees of freedom.
Instructions
Erythrosin B (EB), is a dye that has several analytical uses as a biological stain, as a
phosphorescent probe, and as an acid-base indicator. It is orange in strongly acidic solutions (pH
< 3), and it turns to red in aqueous solutions of pH > 3. EB is also known as Acid Red 51 and
FD&C red dye no. 3, and it has been used as a food coloring in maraschino cherries.
COONa
O
I
I
I
I
O ONa
Erythrosin B
The sample to be analyzed is a mixture of EB (tha analyte) and NaCl (the matrix). EB adheres to
the surface of salt crystals, imparting a pink color to NaCl. In fact, this is a common way to store
and dispense indictors that are unstable in solution. You will be provided with approximately 20
g of this mixture, which represents your gross sample.
27
1. For this lab experiment, you will work in groups of two (partner with your nearest neighbor).
Put your gross sample on a piece of paper, shape it into a flattened cone, and divide it into
quarters. Obtain an approximately 2-g sample from each quarter. These are your four Level I
samples.
2. Transfer each Level I sample into a clean glass or agate mortar and pestle. Grind each sample
for several minutes to reduce the particle size and further homogenize the sample. Divide each
of the processed samples in half and obtain an approximately 0.50-g sample from each half.
Weigh each sample as accurately as possible and record the mass.
3. Quantitatively transfer each sample to a 100-mL volumetric flask and dilute to volume with
distilled water. Be sure to thoroughly mix each solution. These are your eight Level II samples.
4. Fill two separate test tubes or vials (~5 mL minimum) from each volumetric flask. The
remaining portion of each Level II sample can be discarded (poured down the drain with water).
These are your 16 level III samples.
5. Adjust the spectrometer to a wavelength of 526 nm. Using distilled water as a reference,
measure the absorbance, A, of each Level III sample twice, without removing the sample cell
from the spectrometer between measurements. These 32 absorbance values are the results for
Level IV.
6. Calculate the concentration of EB in each Level IV sample using Beer’s Law (A = abC), where a
is the absorptivity of EB (a = 0.0916 cm-1 ppm-1 for EB at 526 nm), b is the pathlength (b = 1.00 cm),
and C is the concentration of EB in units of ppm (parts-per-million). Convert these values to %
w/w EB by accounting for the sample mass and its dilution.
7. To determine the % w/w EB for the Level III samples, average the associated results for Level
IV. For example, the % w/w EB for sample IA1 is the average result for samples IA1a and IA1b.
The results for the Level II and Level I samples are found in a similar manner; thus, the % w/w
EB for sample IA is the average result for samples IA1 and IA2, and the result for sample I is the
average result for IA and IB.
Data Analysis
Summarize your data using four tables. In the first table, report results for the Level IV samples
using the following headings: sample ID, mass of sample, absorbance, and % w/w EB. The
remaining tables report results for Level III, Level II, and Level I samples and include the
following headings: sample ID and % w/w EB.
Using your data and Equations 1 – 5, calculate values for σ2samp, σ2prep, σ2pos, σ2spect, and σ2total. In
addition, briefly answer the following questions in the course of your discussion:
- Are the differences between σ2samp, σ2prep, σ2pos, and σ2spect statistically significant? Use an
F-test to accomplish this (p. 63 – 64 in Harris, 7th Ed.)
- Based on your results, which step is the weakest link in this analysis?
- How might you go about improving the overall standard deviation for this analysis?
28
- Explain why the difference between the results for sample IA1a and IA1b are influenced
only by indeterminate errors. Is the same true for the difference between samples IA1
and IA2? How about for samples IA and IB, or for samples I and II?
- The data from your four-level nested design can also be used to evaluate the accuracy of
your analysis. The best estimate of the % w/w EB is the average result for your eight
Level II samples (why is this so?). Using the total variance for your analysis, determine
the 95% confidence interval for the % w/w EB and compare it to the expected value,
provided by your instructor. For this calculation, there are eight samples and seven
degrees of freedom.
When sampling is the weakest link, the sampling plan should be designed to minimize its
contribution to the overall variance. One approach is to find a way to increase the homogeneity
of the gross sample before collecting individual samples. For example, you could grind the gross
sample to decrease the average particle size. Another approach is to make a composite sample by
collecting several portions of the gross sample and mix them together before they are analyzed.
If the sampling variance for a particular sample size is σ2samp, and σ2meas is the variance due to the
spectroscopic analysis, then the total variance for the analysis of one sample is:
222
meassamptotal σσσ += (Eqn 6)
If we collect and analyze n separate samples of the same size, then the total variance is:
nn
meassamp
total
22
2 σσσ += (Eqn 7)
If, however, we form a composite sample by mixing together these n samples and removing k
identical samples for analysis, the total variance is:
nnk
meassamp
total
22
2 σσσ += (Eqn 8)
Using your results for σ2samp and σ2meas (σ2meas = σ2total - σ2samp), determine the total variance for (a)
the analysis of four separate samples taken from the gross sample, and (b) the analysis of two
portions of a composite sample formed by collecting and mixing four samples from the gross
sample. Finally, find a combination of n and k that will give you a total variance that is less than
that in (b), but that requires analysis of only one sample.
** The text of this experiment has been closely adopted from Harvey, D. J. Chem. Educ. 2002, 79,
360-363 and accompanying supporting information. The author also cites Anal. Chem. 1999, 71,
538A-540A. **
EXPERIMENT 4 Supplementary Material
SOURCES OF VARIANCE – THE WEAKEST LINK
29
30
31
EXPERIMENT 5
SPECTROPHOTOMETRIC DETERMINATION OF IRON IN VITAMIN TABLETS
Overview
Absorbance spectrophotometry is a powerful technique for the determination of the
concentration of species in solution which benefits from the simplicity, ruggedness and low cost
of the methodology and instrumentation. When properly performed, absorbance measurements
can be used to determine the concentrations of a wide range of inorganic and organic materials in
solution with good accuracy and good sensitivity.
Of course, the caveat “when properly performed” remains an important issue. First, it must be
recognized that the linear Beer’s law relation between absorbance and concentration only holds
across a limited range of analyte concentrations. At low analyte concentrations equilibrium shifts
can cause the chemical form of the absorbing species to change to a species having a different
molar absorptivity at the wavelength being used. At high analyte concentrations two effects may
occur. Light may be scattered by particulated analyte molecules in solution which will cause the
absorbance to appear artificially high and/or self-solvation of the analyte with itself can change
the electronic structure of the analyte leading to changes in the molar absorptivity at a given
wavelength. Frequently, initial experimental efforts must be directed at determining the analyte
concentration range which gives a linear absorbance response.
Second, care must always be exercised to confirm that the absorbance observed is genuinely due
to the species of interest. This requirement is often met in two ways. (1) Complexing agents are
added to both increase the strength of the absorbance of the analyte and to shift the absorption
bands to wavelengths where interfering absorbance by other species does not occur. (2) A
“blank” is prepared containing everything but the analyte of interest and used to set the “zero”
absorbance limit of the spectrophotometer.
In this procedure, Fe(III) is reduced to Fe(II) with hydroquinone, and complexed with o-
phenanthroline to form an intense red-orange colored complex, Fe(o-phenanthroline)32+. Initially,
this procedure is performed on several solutions having known concentrations of Fe(II) and the
absorbance is measured at 508 nm. A plot of absorbance vs. amount of Fe is then generated for
use as a standard calibration curve. Finally, a vitamin tablet containing iron is dissolved, diluted,
complexed with the o-phenanthroline and the absorbance measured at 508 nm. Using the
standard calibration curve, the amount of Fe in the vitamin tablet is determined.
Instructions
Read Christian 6th ed., Chapter 16
Preparation of standard curve:
1. Pipet 10.00 ml of standard Fe solution into a beaker and, using pH paper, measure the pH.
Record the concentration and temperature of the Fe solution. Add sodium citrate solution
one drop at a time until a pH of ~3.5 is reached as recorded using pH paper. Count the
drops needed (it should be around 10 ml).
2. Pipet a fresh 10.00 ml aliquot of Fe standard into a 100 ml volumetric flask and add the same
number of drops of citrate solution as required in step 1. Add 2 ml of hydroquinone
solution and 3 ml of o-phenanthroline solution, dilute to the mark with water, and mix well.
32
3. Prepare four more Fe solutions by pipetting 8.00, 6.00, 4.00 and 2.00 ml of Fe standard into
respective 100 ml volumetric flasks. Add sodium citrate solution to each 100 ml volumetric
flask in proportion to the volume of Fe solution. Also add to each 100 ml volumetric flask 2
ml of hydroquinone solution and 3 ml of o-phenanthroline solution. Dilute each solution to
the mark with water and mix well.
4. In a beaker prepare a Blank Solution containing all chemicals but the Fe solution (i.e.
approximately 10 ml of sodium citrate, 2 ml of hydroquinone solution, 3 ml of o-
phenanthroline solution and 85 ml of water).
5. Allow the solutions to stand for at least 10 min. Measure and record the temperature of
your solutions. Measure the absorbance of each solution at 508 nm using the Vernier device
and the UV-Vis spectrophotometer. (The color is stable so all solutions can be prepared at
once, if desired.) Use the blank solution as the reference solution to calibrate the
colorimeter.
Preparation and analysis of the unknown:
**Do not forget to measure and record the temperature of your unknown solutions in Step 7**
1. Place one tablet of the Fe containing vitamin and 25 ml of 6 M HCl in a 125 ml Erlenmeyer
flask. Boil gently in a fume hood for 15 min.
2. Filter the solution directly into a 100 ml volumetric flask. Wash the beaker and filter several
times with small portions of water to complete a quantitative transfer. Allow the solution to
cool, dilute to the mark with water, and mix well. Denote as Solution A.
3. First dilution: Pipet 5.00 ml of Solution A into a fresh 100 ml volumetric flask and fill to the
mark with water. (If the tablet contains <15 mg of Fe, use 10.00 ml instead of 5.00 ml.)
Denote as Solution B.
4. Deliver 10.00 ml of Solution B into a beaker and find out how many drops of sodium citrate
solution are needed to bring the solution to pH 3.5. This will require about 3.5 or 7 ml of
citrate, depending on whether 5 or 10 ml of unknown was diluted to form Solution B.
5. Second dilution: Pipet 10.00 ml of Solution B into a fresh 100 ml volumetric flask. Add the
required amount of citrate solution determined in (4.), 2 ml of hydroquinone solution, and 3
ml of o-phenanthroline solution. Dilute to the mark with water and mix well. Denote as
Solution C.
6. Prepare a Blank Solution containing all chemicals but the vitamin solution (i.e. the required
amount of sodium citrate, 2 ml of hydroquinone solution, 3 ml of o-phenanthroline solution
and water to make 100 ml of solution) in a beaker.
7. Allow the solutions to stand for at least 10 min. Measure and record the temperature of
your solutions. Measure the absorbance of three separate aliquots of Solution C at 508 nm
using the Vernier device and the UV-Vis spectrophotometer. Use the Blank Solution as the
reference solution to calibrate the colorimeter.
33
Data Analysis
1. Make a graph of absorbance versus μg/ml of Fe in the five calibration standards prepared.
Remember to correct the volumes of Fe solution for the delivery volume errors in the 10 ml
graduated pipet (you determined this in experiment 3) and for any temperature differential
between the temperature of the solution when it was made and the temperature at which it
was used. Use linear regression to find the slope and intercept of the calibration plot. (You
should include the point 0, 0 in your regression analysis, but do not force the regression to
go through this point.) Also calculate the standard deviations (uncertainties) in the slope
and intercept values.
2. Calculate the molarity of Fe (o-phenanthroline)32+ in each standard solution and find the
average molar absorptivity (ε in Beer’s law) from the five absorbance measurements.
Assume that all the iron has been converted to the phenanthroline complex and that the
pathlength is 1.0 cm for this calculation.
3. Calculate the average of the three absorbance values for the unknown and the standard
deviation of the three absorbance values. Using the Beer’s Law plot and the average
absorbance value, calculate the concentration of the Fe solution in μg/ml. Finally, correct for
dilutions and calculate the number of mg of Fe in the original vitamin tablet.
4. From the standard deviations of the slope and intercept of the calibration plot, and the
average deviation of the three unknown Fe absorbances, assign an error to the Fe
concentration in the unknown. Do this by propagating the errors in each of the values
through a Beer’s Law calculation. Propagate the error in the Fe concentration through the
dilution calculations and assign an error to the final calculated amount of Fe in the vitamin
tablet. (You may assume the error introduced by using the 100 ml volumetric flask is much
smaller than the error in your calibration plot and unknown absorbance measurements.)
EXPERIMENT 5 Supplementary Material
IRON IN VITAMIN TABLET
Table 1: Standard Iron Fe (II) solution absorptions.
Volume Fe Absorbance
Solution (mL) (A)
10.00 0.835
8.00 0.674
6.00 0.514
4.00 0.248
2.00 0.073
Blank 0
Table 2: Absorptions for Unknown Vitamin A.
34
Unknown Absorbance (A)
Vitamin A 0.179 0.165 0.197
Blank 0
Unknown Blank
Table 3: Volume Correction for Iron solution.
Volume Fe Average Corrected
Solution (mL) Correction (ml) Volume (ml)
10.00 -0.06 9.94
8.00 -0.02 7.98
6.00 -0.02 5.98
4.00 0.03 4.03
2.00 -0.03 1.97
Table 4: Calculations for Iron Fe(II) concentrations and absorptivity
Volume Fe Corrected Volume Absorance Concentration Molarity Molar
Solution (mL) (mL) (µg/ml) (mol/L) Absorptivity (ε)
10.00 9.94 0.835 28.4284 4.7662E-04 1.7519E+03
8.00 7.98 0.674 22.8228 3.8264E-04 1.7614E+03
6.00 5.98 0.514 17.1028 2.8674E-04 1.7926E+03
4.00 4.03 0.248 11.5258 1.9324E-04 1.2834E+03
2.00 1.97 0.073 5.6342 9.4461E-05 7.7280E+02
Table 5: Voume Correction for Unknown Vitamin A Volume Volume Indicated (ml) Correction (ml)
Vitamin A 5 5.005
Vit. A Solution 10 9.94
Table 6: Averages and Beer's Law calculations for unknown, and the data of the standard curve.
Avg Abs. (A) 0.180333333
avg. deviation (A) 0.016041613
Concentration (µg/ml) 8.686406795
Molarity (mol/L) 1.4563E-04
Mass of Fe (mg) 17.37281359
avg. (ε) 1.2383E+03
slope (m) 0.034274381
intercept (b) -0.117387882
Std dev of slope (sm) 0.001897731
Std dev of intercept (sb) 0.035868108
Std dev of slope and int (sy) 0.034139091
Error to Fe mass (mg) 0.3558
35
Figure 1: The standard curve; a graph of absorbance vs concentration (µg/ml) for Iron (Fe(II)) solutions.
Calculations for Table 3:
Corrected Volume (ml) = Volume Fe Solution (ml) + Average Correction (ml) (1)
Corrected Volume (ml) = 10.00 + (-0.06) = 9.94 ml
Calculations for Table 4:
Concentration (µg/ml) = Concentration of Fe stock solution * Corrected Volume * 1/(Volume of dilution)
(2)
Concentration (µg/ml) = 0.286 g/L * 9.94 ml * 1/100.00 ml * 1L/1000.00ml * 106µg/ml
= 28.4284µg/ml
Molarity (mol/L) = Concentration (µg/ml) / Molar mass Fe (0-phenanthroline) * (1/Volume of Dilution
(ml)) (3)
Molarity (mol/L) = (28.4284µg/ml) / (596.457g/mol) * (103ml/L) * (g/10
6µg) *(1/0.100L)
= 4.7662 * 10-4
mol/L
Beer’s Law: A = εbc (4)
Molar Absorptivity (ε) = A/bc (4’)
b = pathlength = 1.0cm, c = Concentration (M)
Molar Absorptivity (ε) = 0.835 / ((1cm)*(4.7662 * 10-4
mol/L)) = 1.7519*103
36
Calculation for Table 6:
Average Absorbance (A) = Σ(Absorbance of Unknown) / n (5)
Average Absorbance (A) = (0.179+0.165+0.197) / 3 = 0.18033 A
Average Deviation (A) = ((Σ(Absorbance – Average (Absorbance))2)/(n-1))
1/2 (6)
Average Deviation (A) = ((5.14667 * 10-4
) / (3-1))1/2
= 0.0160416 A
Concentration (µg/ml) = (Average Absorbance – Intercept (b) ) / Slope (m) (7)
= (0.1803333-(-0.1173878)) / 0.034274381 = 8.6864µg/ml
Molarity (mol/L) = Concentration (µg/ml) / Molar mass Fe (0-phenanthroline) * (1 / Dilution volume)
(8)
Molarity (mol/L) = (8.6864µg/ml) / (596.457g/mol) * (1/0.1000L) * (103mL/L) * (g/10
6µg)
= 1.4563 * 10-4
mol/L
Mass of Fe (mg) = Concentration (µg/ml) * Dilution Volume (9)
= (8.6864µg/ml) * (100.00 ml / 5.00ml) * (100.00ml/10.00ml) * 10.00 ml
* (mg/103µg) = 17.37 mg
37
EXPERIMENT 6
SIMULTANEOUS ANALYSIS OF A TWO-COMPONENT MIXTURE
Overview
Often, when a solution of two or more light-absorbing substances is prepared, the presence of
each component will not affect the light absorbing properties of the other components. With such
solutions, the absorption of light at a given wavelength λ is additive and the total absorbance will
be equal to the sum of the absorbances of the individual substances, 1 through n.
A(λ) = ε1bC1 + ε2bC2 + ε3bC3 + ... + εnbCn (at a given λ) (Eqn 1)
Satisfaction of these criteria can be confirmed by measurement of the absorbance of a mixture of
the substances and comparison of this value with the sum of the absorbances of pure solutions of
each substance where the concentrations of the pure solutions are identical to substance
concentration in the mixture.
If the above criterion is satisfied, spectrophotometric methods can be used to determine the
concentrations of each of the substances in an unknown mixture. To achieve this result both the
absorbance of the mixture and the molar absorptivities of each of the substances must be
determined at a minimum of as many wavelengths as there are substances. The results will
generate n equations with n unknowns which can be solved algebraically.
If only two substances are contained in a mixture, the absorbance of the mixture and the molar
absorptivity of the two substances must be determined at a minimum of two wavelengths.
However, a more accurate determination of the substance concentrations can be made by
measuring the absorbances of standard solutions of the two substances and of the unknown
mixture at many wavelengths. Manipulation of Beer’s law leads to the following relationship,
[ ][ ]
[ ][ ]
A
A
Y
Y
A
A
X
X
m
Xs s
Ys
Xs s
=
+ (Eqn 2)
Am = absorbance of unknown mixture
AXs = absorbance of standard solution of pure X
AYs = absorbance of standard solution of pure Y
[X]s = concentration of standard solution of pure X
[Y]s = concentration of standard solution of pure Y
[X] = concentration of component X in unknown mixture
[Y] = concentration of component Y in unknown mixture
A linear regression of a plot of Am/AXs vs. AYs/AXs will yield a straight line with a slope of [Y]/[Y]s
and an intercept of [X]/[X]s. A data point is obtained for each different wavelength used. Thus,
the concentrations of X and Y in the unknown mixture can be determined from the slope and
intercept values with the accuracy of the concentrations increasing as more measurements are
made at different wavelengths.
In this experiment, you will study absorption properties of a two-component mixture of
chromium (III) nitrate and cobalt (II) nitrate. Your first goal will be to show that the absorbance
of a standard mixture of Cr3+ and Co2+ reflects the additive absorbances of pure solutions of Cr3+
and Co2+. Subsequently, you will measure the absorbance of an unknown mixture of Cr3+ and
38
Co2+ and use the methods described above to determine the concentrations of the Cr3+and Co2+ in
the unknown.
Instructions
Read Christian 6th ed., Chapters 16
Additivity of the absorbances of Cr(III) and Co(II) nitrate solutions.
1. Using your graduated pipet deliver 10.00 ml of the standard Co2+ stock solution into a 250 ml
beaker. Add to this solution 10.00 ml of deionized water.
2. In a separate beaker repeat step 1 for the standard Cr3+ solution. Be sure to record the
standard stock solution concentrations.
3. In a third 250 ml beaker, deliver 10.00 ml of each of the standard Co2+ and Cr3+ solutions using
your graduated pipet.
4. Obtain an unknown mixture of Cr3+ and Co2+.
5. Determine the absorbance of each of the four solutions at 10 nm intervals between 400 nm and
600 nm using the Vernier hand-held device and the UV-Vis spectrophotometer. You will need
to re-zero the instrument at each wavelength using a deionized water blank.
Data Analysis 1. Plot the absorbance versus wavelength data for each of the three standard solutions (pure Co2+
solution, pure Cr3+ solution, and 50/50 mixture). Also plot the sum of the absorbance values
for the pure solutions of Cr3+ and Co2+ versus the wavelength. Does the absorbance sum
spectrum qualitatively match the absorbance spectrum for the mixture?
2. Make a plot of Am/ACr3+ vs. ACo2+/ACr3+ (one data point for each wavelength measured) and use
linear regression methods to determine the slope and intercept of the best fit line to this data.
Also determine the uncertainties in the slope and intercept values.
3. From the slope and intercept values and the concentrations of the standard solutions, calculate
the concentration of Cr3+ and Co2+ in the unknown mixture. Also estimate the uncertainty in
these values from the uncertainties in the slope and intercept values (you may assume the
concentrations of the standard solutions are much more accurate than your other
measurements).
EXPERIMENT 6 Supplementary Material
TWO-COMPONENT COLORIMETRY
Constants Used:
Initial Concentration of Cr3+
: 0.050 M
Initial Concentration of Co2+
: 0.18 M
Table 1: Measured absorbance values for various solutions.
39
Wavelength Chromium Cobalt Cr/Co
Mix Unknown
400 nm 0.155 0.0200 0.164 0.484
410 nm 0.155 0.0269 0.171 0.502
420 nm 0.143 0.0315 0.167 0.495
430 nm 0.119 0.0458 0.156 0.479
440 nm 0.101 0.0630 0.152 0.463
450 nm 0.0809 0.0752 0.149 0.466
460 nm 0.0650 0.0910 0.150 0.470
470 nm 0.0585 0.0975 0.155 0.483
480 nm 0.0487 0.105 0.148 0.510
490 nm 0.0511 0.123 0.169 0.556
500 nm 0.0545 0.128 0.181 0.600
510 nm 0.0615 0.136 0.194 0.646
520 nm 0.0737 0.125 0.193 0.660
530 nm 0.0910 0.107 0.194 0.640
540 nm 0.103 0.0835 0.188 0.602
550 nm 0.124 0.0650 0.180 0.654
560 nm 0.135 0.0453 0.173 0.523
570 nm 0.137 0.0315 0.161 0.495
580 nm 0.136 0.0205 0.153 0.456
590 nm 0.137 0.0173 0.148 0.432
600 nm 0.130 0.0137 0.135 0.399
The uncertainties in the slope and intercept values were calculated using standard
equations (e.g., use Excel (LINEST function, etc.))
Table 2: Values from data used to calculate the slope, intercept, and their respective
deviations.
Xi Yi XiYi Xi2 Di Di
2
0.129 3.126 0.40325 0.01664 -0.074759 0.00559
0.173 3.239 0.56035 0.02993 -0.114483 0.0131
0.221 3.469 0.76665 0.04884 -0.051091 0.00261
0.384 4.018 1.54291 0.14746 -0.067864 0.00461
0.622 4.576 2.84627 0.38688 -0.335962 0.113
0.929 5.758 5.34918 0.86304 -0.219559 0.0482
1.400 7.228 10.1192 1.96 -0.3844 0.148
1.666 8.255 13.7528 2.77556 -0.280686 0.0788
2.160 10.481 22.639 4.6656 0.23064 0.0532
2.400 10.880 26.112 5.76 -0.2034 0.0414
2.344 11.009 25.8051 5.49434 0.11998 0.0144
40
2.213 10.506 23.2498 4.89737 0.07168 0.00514
1.696 8.769 14.8722 2.87642 0.12918 0.0167
1.180 7.037 8.30366 1.3924 0.18822 0.0354
0.812 5.850 4.7502 0.65934 0.27855 0.0776
0.523 5.256 2.74889 0.27353 0.68767 0.473
0.336 3.876 1.30234 0.1129 -0.043256 0.00187
0.231 3.621 0.83645 0.05336 0.0662 0.00438
0.150 3.350 0.5025 0.0225 0.07635 0.00583
0.126 3.159 0.39803 0.01588 -0.031346 0.000983
0.106 3.079 0.32637 0.01124 -0.041926 0.00176
∑ 19.801 126.542 167.187 32.4632 1.145573
The equation for the plot is:
[ ] )08.0(75.2)07.0(47.3,
,
,
±+±=stdCr
stdCo
stdCr
unk
A
A
A
A
From this equation and the equation included in the objective, it can be determined
that:
)07.0(47.3][
][±=
std
unk
Co
Co
)08.0(75.2][
][±=
std
unk
Cr
Cr
The concentration of the standards when mixed can be determined using the equation:
2211 VCVC =
The concentrations of the standards were:
Initial
Concentration
(M)
Final
Concentration
(M)
Co2+
0.18 0.09
Cr3+
0.05 0.025
The concentrations of the unknowns in the mixture were:
41
)006.0(312.0)07.0(47.3)09.0(
][±=±=unkCo
)002.0(069.0)08.0(75.2)025.0(
][±=±=unkCr
Therefore, the concentrations for the unknowns in the mixture were
Co2+
= 0.312 (± 0.006) M
Cr3+
= 0.069 (± 0.002) M
Summarized Results:
Initial
Concentration
(M)
Final
Concentration
(M)
Co2+
0.18 0.09
Cr3+
0.05 0.025
[ ] )08.0(75.2)07.0(47.3,
,
,
±+±=stdCr
stdCo
stdCr
unk
A
A
A
A
)07.0(47.3][
][±=
std
unk
Co
Co )08.0(75.2
][
][±=
std
unk
Cr
Cr
The concentrations in Unknown were:
Co2+
= 0.312 (±0.006) M
Cr3+
= 0.069 (±0.002) M
42
EXPERIMENT 7
QUANTITATIVE DETERMINATION OF M&M DYES
Overview
The premise of this laboratory experiment is to develop a quantitative method for paper
chromatography of food dyes. As you will likely guess, this may not be the optimal way to make
such an analytical determination, given today’s range of analysis techniques available in the
modern chemical laboratory. To make it more interesting, you must devise the procedure for
quantitative determination (especially, how you will calibrate your chemical analysis technique)
on your own. However, some background and instructions are given below regarding how to
perform paper chromatography and qualitative analysis, which are necessary parts of the
experiment.
The following is taken directly from a Journal of Chemical Education publication (supplemental
information from Birdwhistell, K.R. and Spence, T.G. J. Chem Ed. 2002, 79(7), 847) and serves as
background for this experiment (note that the experiment you are being asked to perform,
though based on, is more extensive than the one published in this cited article):
“…separation methods rely on physical differences between the components of a mixture.
Undoubtedly, you are already familiar with several means chemists use to effect separations
based on physical differences. These techniques include: Filtration, where separation may be
effected because substances are present in different states (solid vs. liquid); Centrifugation, where
separation is effected by differences in density; and Distillation, where separation is effected by
taking advantage of differences in boiling temperatures of the various components. In this
laboratory exercise, we will effect a separation of a mixture of food dyes using paper
chromatography.
“All chromatography techniques have three important components: the analyte or mixture of
species being separated, a mobile phase, and a stationary phase. The mobile phase is a flowing
liquid or gas used to push the analyte over or through a stationary porous material (the
stationary phase). Because of physical interactions between the analyte and the stationary phase,
the analyte moves through or over the stationary phase more slowly than the mobile phase.
Furthermore, because physical interactions between the analyte and the stationary phase can be
different for each component of the mixture, the different components transit the stationary
phase at different speeds. Those that strongly interact with the stationary phase lag behind those
that interact only weakly. As a result, the components of the mixture may be separated.
“Paper chromatography is a form of liquid chromatography using a piece of paper as the stationary
phase rather than a packed chromatography column. In paper chromatography, analyte is applied
directly onto the bottom of the stationary phase (the chromatography paper) which is then placed
on edge in a developing tank containing the mobile phase so that the bottom edge of the paper is
submersed. Capillary action draws the mobile phase up the sheet of paper carrying along the
different components of the mixture. Due to physical interactions between the different
components and the stationary phase, the components move up the paper at different speeds.
The paper is removed from the tank before the solvent front reaches the top of the paper and the
position of each component of the mixture is marked as well as the position of the solvent front
itself. Unlike in liquid column chromatography, the components of the mixture are not allowed
to elute off of the top of the stationary phase. Rather, each component is characterized by the
43
distance it traveled up the paper. The ratio of this distance to the distance the solvent front
traveled, denoted Rf, is characteristic of a particular substance and remains constant regardless of
the other components present in the mixture and, therefore, can be used to qualitatively identify
the substance. The Rf of each component is dependent on the type of stationary phase used and
the composition of the mobile phase.”
Instructions
Read Christian, 6th ed., Chapter 19 for background on chromatography theory and principles.
Part 1. Preparing your developing tank and qualitative analysis (J. Chem. Ed. 2002, 79, 847)
1. Prepare a developing tank by pouring 10 mL of the mobile phase (0.10% wt/v solution of
NaCl in H2O) into a 400 mL beaker and covering the beaker with Parafilm. It is important
that the air above the mobile phase become saturated with solvent vapor so that solvent
does not evaporate from the stationary phase as the chromatogram develops. Therefore, be
sure to keep the developing tank covered at all times.
2. With a pencil, draw a horizontal line 1.5 cm from the bottom edge of the chromatography
paper. Draw vertical tick marks along this line every 2 cm (see Figure 1a). Using a capillary
and one of the standard dye solutions, make a spot on the chromatography paper at one of
the marks. Try to keep your spots less than 4 mm in diameter. Allow the dye to dry and
reapply the same dye in the same spot 1 or 2 times or until a sufficiently dark spot has been
achieved. With a pencil, note the name of the dye below the spot.
3. Repeat steps 2 and 3 for the remaining dyes across the bottom of the chromatogram.
4. When the spots have been applied, form the chromatography paper into a cylinder, and
staple the edges of the paper together making sure to leave a gap between the edges as
shown in Figure 1b. If the edges come into contact, solvent will not travel at a uniform speed
up the chromatography paper and the components of the mixture will not move in a straight
line.
5. Place the chromatography paper into the developing tank, do not let it touch the sides of the
tank and quickly replace the Parafilm cover. Make sure the level of the mobile phase is
below the line of dyes on your paper. Allow the chromatogram to develop.
6. When the solvent front is approximately 1 cm from the top of the chromatography paper,
remove the chromatogram and lay it flat on a paper towel. Immediately mark the position of
the solvent front with a pencil. The front will continue to move as the paper dries so it is
important that you mark this position now. Measure and note the distance the solvent front
traveled (Dsolvent, see Figure 2).
44
7. Draw an ellipse around each spot on the developed chromatogram and draw a horizontal
line through the center of each spot. If a spot shows significant “tailing” make your
horizontal line through the darkest part of the spot (see Figure 2). Use the distance from the
starting line (not the bottom of the paper!) to these horizontal lines to determine Ddye for
each dye. Record distances and Rf values in your notebook (Rf = Ddye/Dsolvent).
8. Place the chromatogram on edge, in the drying oven for 5 min or until dry. Take your dry
chromatogram and observe the spots under illumination with a hand-held UV lamp on
long-wavelength irradiation. Note the color of the spot under normal visible light and the
color if there is any observed fluorescence (if any).
WARNING: UV light can damage your eyes. Always point lamps away from you. Do not look
into the UV lamps
1.5 cm
2 cmsample spot
a) b)
1.5 cm
2 cmsample spot
1.5 cm
2 cmsample spot
a) b)
Figure 1. Preparation and spotting of chromatography paper.
Dsolvent
solvent front
initial solvent levelDdye,1
Ddye,2
“peak tailing”
Dsolvent
solvent front
initial solvent levelDdye,1
Ddye,2
“peak tailing”
Figure 2. Developed chromatogram. Immediately mark the solvent front with a pencil when the
paper is removed from the developing tank. The spot on the right exhibits significant peak tailing.
The distance the spot has traveled should be indicated on the point of maximum spot density.
45
Part 2. Extraction and determination of M&M dye
1. Develop a method for removing the M&M shell (containing the dye) from the chocolate
center. Consider using multiple candy shells and consider weighing a) the M&M(s) prior to
removal of the shell and b) the shell(s) that have been removed. In your report, you will be
asked to provide your determination for a) the amount of dye per gram of shell, b) the
amount of shell per gram of M&M, and c) the amount of dye per gram of M&M. You
should dissolve your shell (and dye) completely in a precise volume of 50/50 ethanol/water.
2. Prepare a second piece of chromatography paper. Make at least three spots from your
sample dye solution on the paper. You may need to apply your sample to the spot from the
capillary more than once. During this portion of the experiment, you will be asked to
determine which standard dye is contained in your sample. You may use additional spaces
on your chromatogram to re-run any dyes from part 1 that you feel might match your
unknown dye. In this case, qualitative identification of your sample dye is based on
matching Rf values to your pure dye standards run in part 1.
3. Once you have determined which standard dye is contained in your unknown sample,
devise a means to calibrate your determination, in order to quantify the amount of dye in
your unknown sample. There are many ways that this could be done. Give it some
thought, and keep in mind that every step you make has to be precise and quantitative, so
that in your final determination, you can provide the requested values (i.e. those w/w
concentrations listed in (1.) above). In some fashion, you will need to correlate the density
of the spot for each standard with the amount of dye applied, so that you can construct a
calibration curve, perform a linear regression, and assign a value to your unknown. Be sure
to include sufficient replication in your scheme so that you can perform satisfactory error
analysis for your unknown determination. (Note: Whatever technique you decide on
(cutting out and weighing spots doesn’t really work), it is likely to have a high degree of
error associated with it. This is okay, as long as you properly determine and report the
associated error.)
Reporting your findings
Prepare a report of your experiment. Be certain to include the following items (in appropriate
section of the lab report document):
• Table of Rf values you determined for the dye standards and your unknown sample
(qualitative analysis). Include supporting text.
• A detailed description of the procedure used to prepare the candy shell (and dye) in a
reproducible fashion.
• A detailed description of the procedure/experimental design used to prepare the
calibration.
• The results of your calibration (i.e. your calibration plot).
• The results of your quantitative determination, including a) the amount of dye per gram
of shell, b) the amount of shell per gram of M&M, and c) the amount of dye per gram of
M&M.
• Proper statistical analysis for your determination.
46
EXPERIMENT 8
ACID-BASE TITRATIONS
Overview
A titration is an experiment in which a solution having a known concentration of a reactant (the
titrant) is mixed with a solution having an unknown concentration of a second reactant. The
“equivalence point” is the point at which the volume of added titrant contains exactly the
number of moles of the reactant of known concentration required to react stoichiometrically with
all of the reactant of unknown concentration. If the volume of the titrant required to reach the
equivalence point can be accurately determined, the concentration of the titrant is known and the
stoichiometry of the reaction is known, then the number of moles of the unknown in the sample
can be determined. Finally, if the initial volume of the unknown was accurately defined, then the
initial concentration of the unknown is also easily calculated. This simple, inexpensive
titrametric approach is widely used to determine the concentrations of a variety of compounds,
including cations, anions, acids, bases, etc.
Of particular importance in any titrametric experiment is the method used to indicate when the
equivalence point is reached. Typically some parameter must be monitored which changes
dramatically when all of the unknown concentration reactant is used up. Sophisticated
instrumentation can be used to monitor the concentration of any of the reactants or products and
the systematic changes in these concentrations can indicate when the equivalence point is
reached. More commonly the reaction between the titrant and the unknown is designed to yield
a visible color change when the equivalence point is reached. Alternatively, an indicator is added
to the reaction which changes color as a function of the relative concentration of one of the
reactants or products. Of course, this latter method of defining the equivalence point is
dependent on the user, i.e. a color change might be visible to one person and not to another. As
such, the observed color change is typically referred to as the “endpoint” to distinguish this user
defined volume from the true equivalence point of the titration.
The titration of a polyprotic acid is somewhat more complicated than the titration of a simple
monoprotic acid due to the different forms the polyprotic acid can have in solution and the
different Ka’s of each of these forms. For example, a triprotic acid can exist in solution in any of
four forms, H3A, H2A-, HA2- or A3- and, in fact, DOES exist in solution in all four forms at any
given time. Of course the relative amounts of the different forms of H3A can vary dramatically
depending on the pH of the solution and the Ka’s for each of the acid dissociation reactions. For
example, in a very basic solution the A3- will be the dominant specie in solution while in an acidic
solution the H3A will be the dominant specie in solution. If you were to start with a solution of
H3A and begin to titrate the solution with a strong base you would find that there are very
distinct pH ranges where each of the four forms of the triprotic acid are in greater concentration
than any of the other three. With a little logic you can qualitatively understand how and when
these different ranges occur.
Let us assume that the first acid dissociation constant is relatively small and that each subsequent
Ka becomes progressively smaller. Up until the first half equivalence point the H3A is the
dominant species in solution. At the first half equivalence point the [H3A] is exactly equal to the
[H2A-] (neglecting the small error due to the equilibrium dissociation of the acid). At any point
beyond the first half equivalence point the H2A- species dominates and is the major specie in
solution at the first equivalence point. As we titrate beyond the first equivalence point, however,
we begin to produce the HA2- and [HA2-] equals the [H2A-] at the second half equivalence point.
47
Beyond the second half equivalence point the HA2- dominates and is the major species in solution
at the second equivalence point. Beyond the second equivalence point we begin to produce
substantial amounts of A3- until the third half equivalence point where [HA2-] equals [A3-].
Beyond this point A3- is the dominant species in solution and is the major species in solution at
and beyond the third equivalence point. Beyond this point the dominant equilibrium in solution
is that of the A3- conjugate base.
Range Dominant Equilibrium
start → 1st eq. pt. H3A <==> H2A- + H+
1st eq. pt. → 2nd eq. pt. H2A- <==> HA2- + H+
2nd eq. pt. → 3rd eq. pt. HA2- <==> A3- + H+
> 3rd eq. pt A3- + H2O <==> HA2- + OH-
All of these changes in relative concentration of the various forms of the H3A can be monitored
by determining the pH of the solution as the titration is performed. Since we know which forms
of the acid are dominant in the various ranges of the titration (start → 1st eq. pt., 1st eq. pt. → 2nd
eq. pt., 2nd eq. pt. → 3rd eq. pt., > 3rd eq. pt.) we can establish which acid equilibrium expression is
most important in determining the solution pH in each range. Basing our calculations on the
dominant equilibrium, although sometimes prone to error, allows us to substantially simplify the
mathematical demands of determining the concentrations of all species in solution.
Instructions
Read Christian 6th ed.: Chapters 6, 7, 8
Note: Perform Steps 1 and 2 during the first laboratory period. If time permits you may also
perform the determination of the Ash Unknowns during the first laboratory period, but
otherwise leave subsequent steps for subsequent lab periods.
Note 2: Be sure to rinse the drop counters and pH electrodes thoroughly with deionized water
at the end of each lab period.
During the 1st period provide your TA with (2) sample vials for your unknowns.
Step 1. Preparation of Standard NaOH
1. Obtain 1 L of degassed water from your TA and place the water into a capped bottle. Using a
graduated cylinder, add 10 mL of 30% (wt/wt) NaOH to the water to produce a ~0.1 M
NaOH solution. Keep this bottle capped during storage to prevent CO2 from being absorbed
by the solution.
2. Accurately weigh four samples of solid KHP (~0.30 g) into four 100 mL beakers. Using a
graduated cylinder, add 25 mL of distilled water to each flask and swirl until the KHP is
dissolved. Also add 3 drops of phenolphthalein indicator to each flask.
3. Measure the temperature of your NaOH solution and fill a buret with the solution. Place a
cap loosely over the top of the buret to minimize the entry of CO2. Make sure no bubbles are
left in the buret tip and adjust the volume of the NaOH so the bottom of the meniscus is at
the 0.0 ml mark on the buret. Titrate one of the KHP samples by slowly dripping (about 1
drop per second) the NaOH titrant into the KHP sample while stirring with a stirbar.
Monitor the pH of the solution using the Vernier LabQuest PDA, drop counter attachment,
48
and pH probe attachment. Note the approximate buret volume at which a large change in
the pH of the solution occurs.
4. Refill the buret and repeat the titration accurately for the three remaining KHP samples. Do
this by introducing 2-3 drops/second of the titrant until you are within several of the
previously noted endpoint volume. At this point begin adding the titrant at a slower rate
(e.g., < 1 drop/sec) while recording both the buret volume and the pH. Keep adding the
titrant dropwise until you have gone well past the endpoint of the titration. Also, carefully
note the buret volume (or number of drops) at which the indicator permanently changes
from its initial clear color to a faint pink color that does not fade. Again, constant agitation of
the reaction vessel is necessary.
Step 2. Preparation of Standard HCl
1. Place approximately 1 L of water in a tightly capped bottle. Using a graduated cylinder add
8.5 mL of 37% (wt/wt) HCl into the bottle and mix the solution well to produce an ~0.1 M
HCl solution.
2. Accurately weigh four samples of solid Na2CO3 (~0.13 g) into four 100 ml beakers. Using a
graduated cylinder, add 25 mL of distilled water to each flask and swirl until the Na2CO3 is
dissolved. Also add 3 drops of bromcresol green indicator to each flask.
3. Measure the temperature of your HCl solution and fill a buret with the solution. Make sure
no bubbles are left in the buret tip and adjust the volume of the HCl so the bottom of the
meniscus is at the 0.0 ml mark on the buret. Warm one of the Na2CO3 samples to about 60-70 0C under the hood and then, at your bench, titrate the sample by slowly dripping (about 1
drop per second) the HCl titrant into the sample solution while stirring with a stir bar.
Monitor the pH of the solution and drop count using the Vernier LabQuest PDA, drop
counter attachment, and pH probe attachment. Note the approximate buret volume at which
a large change in the pH of the solution occurs.
4. Refill the buret and repeat the titration accurately for the three remaining Na2CO3 samples.
Do this by introducing 2-3 drops/second of the titrant until you are within several drops of
the previously noted endpoint volume. At this point begin adding the titrant at a slower rate
(< 1 drop/sec), while recording the buret volume and the pH. Keep adding the titrant
dropwise until you have gone well past the endpoint of the titration. Also, carefully note the
buret volume at which the indicator permanently changes from its initial green color to a
blue color which does not fade.
Step 3. Analysis of Unknowns
1. Accurately weigh four samples of KHP unknown (~ 0.5 g each) into four 100 ml beakers.
Dissolve each sample in 25 mL of distilled water and add three drops of phenolphthalein to
each flask. Measure the temperature of the NaOH solution. Titrate each of the four samples
using the procedure described (one may be used as a test run) while monitoring the pH, drop
count, and the buret volume, as before. Note, you need at least three accurate experimental
determinations.
2. Accurately weigh four samples of Ash unknown (containing Na2CO3) (~ 0.3 g each) into four
100 ml beakers. Dissolve each sample in 25 mL of distilled water and add three drops of
49
bromcresol green to each flask. Measure the temperature of the HCl solution. Titrate each of
the four samples using the procedure described (one may be used as a test run) while
monitoring the pH, drop count, and the buret volume, as before. Note, you need at least three
accurate experimental determinations.
Step 4. Titration of a Triprotic Acid
1. Accurately deliver 10.00 mL of ~0.1 F H3PO4 stock solution into a 100 mL beaker using your
graduated pipet. Add 10 - 20 ml of water to this solution using your graduated cylinder.
2. Titrate the sample of H3PO4 with your standardized (~0.1 M) NaOH solution. In the initial
titration, slowly add (about 1 drop per second) the NaOH titrant into the sample while
stirring. Monitor the pH and drop count for the titration using the Vernier LabQuest PDA,
drop counter attachment, and pH probe attachment. Note the volume(s) added at which
there are large changes in the solution pH.
3. Carefully repeat steps 1 and 2 in a more precise fashion. Monitor the pH and drop count for
the titration using the Vernier LabQuest PDA, drop counter attachment, and pH probe
attachment. Add the NaOH titrant at a faster rate until you are within 1.0 ml of each of the
three ½ endpoints and within 1.0 ml of each of the three endpoints Then add the titrant at a
slower rate until you are just past each of these points. Continue the titration until you add 6
ml (many drops) of NaOH beyond the third endpoint.
Note: Do not forget to determine the volume associated with each drop for each solution
dispensed from the buret. This will allow you to equate drop count with volume dispensed.
This is a simple procedure, but ask your TA if you need help.
Data Analysis
1. For the accurate titrations using the NaOH standard solution, calculate the molarity of the
NaOH solution. Remember to correct the volume of the NaOH titrant required to reach the
endpoint using the results from Experiment 3. From the results, calculate the average and
average deviation of the NaOH molarity at the temperature at which you performed the
standardization.
2. For the accurate titrations using the HCl standard solution calculate the molarity of the HCl
solution. Remember to correct the volume of HCl titrant required to reach the endpoint using
the results from Experiment 3. From the results, calculate the average and average deviation of
the HCl molarity at the temperature at which you performed the standardization.
3. From the endpoint volumes in the titrations of each of the three KHP unknowns and the
molarity of your NaOH standard solution, calculate the mass of KHP in the unknown
samples and the weight percent of KHP in the sample. Remember to correct the
concentration of the titrant for any changes in temperature from the temperature at which it
was standardized and the buret volume for the systematic error determined in Experiment 3.
From the calculated results determine the average and average deviation of the weight
percent of KHP. Repeat these calculations and determine the average and average deviation
of the weight percent for the Na2CO3 in the ash unknowns.
50
4. Calculate the error associated with the final weight percent of KHP and Na2CO3. You should
do this by evaluating the various errors associated with the standard solution concentrations,
volumes used, etc. and either propagating these errors through the calculation of the weight
% of KHP and Na2CO3 OR by making a logical argument why a given error can be viewed as
the dominant source of error in the experiment.
5. For the accurate titration of the H3PO4 solution, plot the titration curve (pH vs. V). Also plot
∆pH / ∆V vs. V. This second plot is essentially the first derivative plot of your titration curve
and will allow you to easily determine the end points of the titration. From your first
derivative plot calculate the average concentration of the H3PO4 solution from the NaOH
volumes required to reach the first and second endpoints. The third endpoint is difficult to
observe. Speculate why this may be so. Also, from the titration curve, estimate values of Ka1,
Ka2, and, if possible, Ka3. Estimate these equilibrium constants first by assuming all activity
coefficients are unity, and second by using the extended Debye-Hückel equation to estimate
activity coefficients, γ. How do your values compare to the tabulated values in the book?
6. Explain how an indicator works. Why are you using the specified pH indicators for this
experiment. Suggest indicators which could be used to visualize each equivalence point for
titration of the triprotic acid.
7. Determine the titration error for you different titration set-ups.
EXPERIMENT 8 Supplementary Material
ACID-BASE TITRATIONS
DATA Table 1: Titration of KHP standard with NaOH. Temperature was 23˚C
NaOH Standard Mass (g) Titrated amount (mL)
Buret Correction (mL) True Volume(mL)
Sample 2 0.30 16.62 -0.02 16.60
Sample 3 0.30 16.20 -0.02 16.18
Sample 4 0.30 16.84 -0.02 16.82
Table 2: Titration of Unknown KHP #465 with NaOH standard. Temperature was 23 ˚C Unknown KHP #465 Mass (g)
Titrated amount (mL)
Buret Correction (mL)
True Volume (mL)
Sample 1 0.50 16.15 -0.02 16.13
Sample 2 0.50 16.75 -0.02 16.73
Sample 3 0.50 17.31 -0.02 17.29
Table 3: Titration of Soda Ash with HCl standard at 60˚C
HCl Standard Mass (g) Titrated amount (mL)
Buret Correction (mL)
True Volume (mL)
Sample 1 0.13 24.95 -0.02 24.93
Sample 2 0.13 25.05 -0.02 25.03
Sample 3 0.13 24.40 -0.02 24.38
Temperature C 60 61 63 60
51
Table 4: Titration of Unknown Soda Ash #241 with HCl standard. Temperature was 23˚C Unknown ASH #241 Mass (g)
Titrated amount (mL)
Buret Correction (mL)
True Volume (mL)
Sample 2 0.31 16.20 -0.02 16.18
Sample 3 0.30 16.82 -0.02 16.80
Sample 4 0.30 15.80 -0.02 15.78
Calculations:
1. number Moles of NaOH and HCl
Corrected mass / molecular weight
2. Molarity of NaOH HCl
Number of moles solute/ total volume (liters)
3. Average Molarity
(trial 1 + trial 2 + trial 3) / 3
4. Deviation of Molarity
5. Weight Percent
(Weight of solute (g) / total unknown sample)* 100
6. Average Percent
(percent 1 + percent 2 + percent 3…+percent n) / n of percents
7. Mass of Unknown KHP and Ash from volumes titrated
(Average M KHP)(Volume titrated)(1/1000mL)(Molar mass of KHP)
52
EXPERIMENT 9
POTENTIOMETRIC TITRATIONS OF CHLORIDE AND IODIDE
Overview
In this experiment, you will perform a potentiometric titration of a mixture of chloride and iodide
using a standard solution of silver nitrate. Using this approach, the concentrations of chloride
and iodide in an unknown solution can be determined. The potential of a silver electrode
immersed in the solution is measured with respect to a reference electrode. Since pH does not
change during the titration, a glass electrode will be used as the reference electrode. The
experimental set-up will look as follows:
Fig. 1. Titration setup
The data obtained also allow the calculation of the solubility product (Ksp) of AgI and AgCl.
Silver iodide (Ksp ~ 10-16) precipitates first, since it is less soluble than silver chloride (Ksp ~ 10-10).
AgCl starts precipitation near the equivalence point of the iodide titration. The change in
potential of the iodide titration curve will level off at the point when the chloride starts
precipitating, near the iodide equivalence point inflection. This will be followed by a typical S-
shaped chloride potentiometric end-point. The error in determining the iodide end point is small
if it is taken at the point at which the potential levels off. (See Figure 7-8 and accompanying text
on page 131-132 in Harris 7th ed.)
Overall, silver ions precipitate with chloride and iodide, each with a 1:1 stoichiometry:
Ag+ + Cl- � AgCl(s) Ag+ + I- � AgI(s)
Throughout the titration, the potential of the cell (the potential between the glass and silver
electrodes) should conform to the Nernst Equation (at 25 °C):
[ ]( )+′+=−= AgEEEE refAg log0591.00
(Eqn 1)
53
where 0′
E incorporates the potential of the reference electrode and any liquid junction potentials.
Prior to the first break in the titration curve (the equivalence point corresponding to complete
precipitation of silver iodide), the cell potential is governed by the iodide concentration. After
this, but prior to the second break (the equivalence point for precipitation of silver chloride), the
cell potential is governed by the chloride concentration. Beyond the second break, the silver ion
concentration is in excess and can be readily calculated from the Nernst equation and free silver
ion concentration.
We will use a salt bridge in this experiment. The salt bridge consists of a U-shaped glass tube
filled with potassium nitrate which is an relatively inert electrolyte. The salt bridge allows the
flow of ions to maintain a balance in charge between the oxidation and reduction vessels while
keeping the contents of each separate. With the charge difference balanced, electrons can flow
once again, and the reduction and oxidation reactions can proceed.
Instructions
Read Harris, 7th ed.: 6-3; Chapter 7 (especially 7-5); 15-1; and 15-2.
1. Obtain ~0.1 g of unknown (solid sample) which contains a mixture of KI and KCl. Pour your
unknown carefully into a 50- or 100-mL beaker. Dissolve the sample in approximately 20 mL of
water and transfer it quantitatively into a 100-mL volumetric flask. Dilute to the mark.
2. Weigh accurately approximately 0.17 g of dry, room temperature AgNO3, and dissolve it in a
100-mL volumetric flask. The AgNO3 should have been previously dried for 1 hour at 105°C, and
then cooled for at least 30 minutes in a dessicator, shielded from light.
3. Pipette a 25 mL aliquot of the unknown into a 100-mL beaker. Add 25 mL of distilled water.
Add a stir bar and stir constantly, during the titration.
4. Pour 50 ml buffer solution into a 100 mL beaker. Use a KNO3 U shape salt bridge to connect the
unknown and the buffer (see Fig. 1). Make sure there is no air bubble trapped at the two ends of
the salt bridge. Ask your TA how to get rid of the air bubble.
5. Load your AgNO3 standard solution into a buret. Using the Vernier LabQuest PDA, drop
counter, and electrodes, set up a titration arrangement. Titrate the unknown with standard
AgNO3 using 1-mL increments up to near the first end point (“break”), then use 0.10-mL
increments, as required, until the E values become nearly constant past the first end point. Then
add 1-mL increments again until the second endpoint is close, followed by 0.10-mL increments.
Continue the titration past the second endpoint by a few milliliters.
6. Repeat the titration two more times (steps 3 and 4, above). Be sure to rinse the electrodes
between titrations with distilled water.
Note: Do not forget to determine the volume associated with each drop for each solution
dispensed from the buret. This will allow you to equate drop count with volume dispensed.
This is a simple procedure, but ask your TA if you need help.
Note 2: Be sure to rinse the drop counters and electrodes thoroughly with deionized water at
the end of each lab period.
Data Analysis
54
Calculate and report the percent of iodide and chloride in your sample (calculated for the dry
sample). Include the error based on the three repetitions.
Calculate the ratio of Ksp of AgI and AgCl from the measured potentials of the titration curve
equivalence points.
EXPERIMENT 9 Supplementary Material
POTENTIOMETRIC TITRATIONS OF CHLORIDE AND IODIDE
Example Data:
Volume (mL)
Potential at Ag
electrode (V)
Potential at pH
probe (mV) E (mV) Volume (mL)
Potential at
Ag electrode
(V)
Potential at pH
probe (mV) E (mV)
0 0.005 247.3 -242.3 8.522 0.285 262.3 22.7
0.046 0.005 247.8 -242.8 8.569 0.28 262.6 17.4
0.093 0 247 -247 8.615 0.285 262.6 22.4
0.139 0 246.7 -246.7 8.661 0.285 262.6 22.4
0.185 0 247.5 -247.5 8.708 0.285 262.6 22.4
0.232 0.005 247.5 -242.5 8.754 0.29 262.9 27.1
(Partial Data Set)
55
I- Cl-
Volume of Titrant (mL) 7.47 13.46
Corrected Volume (mL) 7.41 13.07
Number of moles 0.000742 0.001308
Number of grams 0.094105 0.046367
Mass percent 67.0% 33.0%
Error ± 0.2% ± 0.4%
]][[
]][[
)(
)(
−+
−+
=ClAg
IAg
K
K
AgClsp
AgIsp
567.0)(
)(=
AgClsp
AgIsp
K
K
Molarity of Ag+ stock = 0.100074 M
56
OVERVIEW OF MEASUREMENTS & STATISTICS
Safety and Waste Disposal
• Goggles and closed-toe shoes mandatory
• Gloves and aprons highly recommended
• No chemicals should go down the drain
• Know your safety symbols…
Laboratory Notebooks
• Write everything in your notebook
• Record what you did and what you observed
• Record computer file names, stock concentrations, temperatures, chemical
reactions, etc.
Experiment 1 – Penny Pinching
• Use the analytical balance correctly
o Never place chemicals directly onto the weighing pan.
o “Tare” the instrument before weighing.
o Record your data to the highest sensitivity possible
o Use all digits
o Recognize the uncertainty in the last digit
o Leave the balance clean and free of debris, chemicals, etc.
• Use the Q-test to retain and discard values (Harris, 7th ed. P. 65, section 4-6)
57
o range
gapQcalc =
o If Qcalc > Qcrit, then the value should be discarded
o Appendix B contains statistical tables
• Analyze statistical distributions (Normal, Gaussian distributions) (Harris, 7th ed.
P. 53, section 4-1)
o Note: The standard deviation (reported with only one significant figure)
defines how many significant figures the mean can have (e.g. 3.43 ± 0.02).
• Use the Student’s t test to compare two sets of data with each other to see if the
same or different (Harris, 7th ed. P. 53, section 4-3)
o For 2 sets of data consisting of n1 and n2 measurements, we calculate a
value of t as…
21
2121
nn
nn
s
xxt
pooled
calc+
−=
where spooled is:
2
)1()1(
2
)()(
21
2
2
21
2
1
21
1 2
2
2
2
1
−+
−+−=
−+
−+−
=∑ ∑
nn
nsns
nn
xxxx
s set set
ji
pooled
o Compare tcalc with ttable for (n1 + n2 – 2) degrees of freedom. If tcalc > ttable,
then difference is significant.
o Appendix B contains statistical tables
n
x
x i
i∑=Mean (µ)
Standard deviation
(σ)
( )
1
2
−
−
=∑
n
xx
s i
i
x
n
x
x i
i∑=Mean (µ)
Standard deviation
(σ)
( )
1
2
−
−
=∑
n
xx
s i
i
x
58
Experiment 2 – A Letter from Corporate
• Which piece of graduated (“volumetric”) glassware can be used to deliver the
most accurate and precise values of the specified volumes?
• You will test: 10 mL graduated pipet; 50 mL graduated buret; 10 mL graduated
cylinder; 50 mL graduated cylinder
• It is up to you to decide how best to do this, but think about: Density; Analytical
balances; Repetitive measurements; Averages and std deviations; Accuracy and
precision; t-test, F-test for comparison
• Accuracy – nearness of measured value to “true” value
• Precision – how reproducible the measurement is.
Experiment 3 – Calibration of Volumetric Glassware
• Calibration of a 10-mL graduated pipet and a 50-mL graduated buret
o Generate a correction curve to account for “systematic error”
o Assess your ability to deliver volumes by determining “random” error.
• Systematic Error (determinate error) – constant error inherent to a piece of
equipment being used
o Can be determined experimentally and corrected for
o Will be consistently positive or negative
• Random Error (indeterminate error) – error that arises from an unknown source
and cannot be controlled
o Always present and cannot be corrected for
o Has an equal chance of being positive or negative
• Making Measurements
o Clean and rinse all glassware thoroughly; no soap bubbles
o Check for leaky stopcocks (buret)
o No air bubbles
o Eye level at reading level to avoid “parallax error”
o Record your data to the nearest 0.01 mL (graduations to 0.1 mL)
• Propagation of Error (Harris, 7th ed. P. 44, section 3-4)
o For Addition and Subtraction, use absolute error
( ) ( ) ( ) ( )44332211 exexexex ±=±+±+±
3214 xxxx ++= 2
3
2
2
2
14 eeee ++=
o For Multiplication and Division, use relative error
( ) ( ) ( )432211 eyeyey ±=±×±
59
213 yyy ×= 1
11
y
ere = 2
2
2
13 rerere +=
• Correction curves
o A larger range of values will be used for calibration of the buret
2 4 6 8 10
volume correction
(mL)
+
-
delivered volume (mL)
Experiment 4 – Sources of Variance
• Various steps in a chemical analysis introduce additional error into the overall
final result.
• Each step is subject to random error and introduces variance (s2).
• The total variance is the sum of the variance of the steps.
• Determining individual variances requires special consideration for experimental
design
60
2
samps
2
poss
2
preps
2
specs
SUMMARY OF CHEM 2285 LAB BRIEFING
SPECTROSCOPY
61
Electromagnetic spectrum encompasses an enormous range of wavelengths and
frequencies (or energies). UV-visible molecular absorption spectrometry
involves absorption of ultraviolet and visible radiation, and is a powerful
technique for the determination of the concentration of species in solution due to
the simplicity, ruggedness and low cost of the methodology and
instrumentation. In UV-Vis spectrometry, absorption commonly occurs with
many organic molecules, metals, and metal-organic complexes, and involves
bonding (outer valence) electrons.
Electromagnetic radiation (e.g. light) is a form of energy with both wave and
particle properties. What can happen to the light intensity as it passes through a
medium? It slows down in media other than vacuum because electric vector
interacts with electric fields in the medium.
Absorption and emission are two most interesting and most useful processes
when electromagnetic radiation interacts with matter. When a molecule absorbs
a photon, the molecule gains energy. On the other hand, when a molecule emits
a photon, the molecule loses energy.
62
Based on quantum mechanics, the energy of a photon depends on its frequency
(v):
Ephoton = hv, where
h = Planck’s constant
h = 6.63 x 10-27 erg sec or 6.63 x 10-34 Js
Postulates of Quantum theory include:
1. Atoms, ions and molecules exist only in discrete energy states
E0 = ground state
E1, E2, E3 ... = excited states
− Excitation can be electronic, vibrational or rotational.
− Energy levels for atoms, ions or molecules are different.
− Measuring energy levels gives means of identification – spectroscopy.
2. When an atom, ion or molecule changes energy state, it absorbs or emits
energy equal to the energy difference.
ΔEtransition = E1 - E0 = hv = hc/λ
Absorption and Emission
Absorption involves transitions from
ground state to excited states. For
absorption to occur, the energy of the
photon must exactly match the energy
difference between the ground state and
one of the excited states of the absorbing species. On the other hand, emission of
electromagnetic radiation occurs when excited particles (atoms or molecules)
return to ground state by giving up excess energy.
Atomic Absorption and Molecular Absorption
In atomic absorption, only a few well-defined frequencies are observed in the
spectrum, since for absorption of radiation to occur, the energy of the exciting
63
photon must exactly match the energy difference between the ground state and
one of the excited states of the absorbing species. Compared with atomic
absorption, molecular absorption is more complex because many more potential
transitions exist, i.e., electronic energy level, vibrational energy level, and
rotational energy level transitions. The energy of a molecule is made up of three
components: Emolecule = Eelectronic + Evibrational + Erotational (note that Eelectronic > Evibrational >
Erotational). Eelectronic represents the electric energy of the molecule that arises from
the energy states of its several bonding electrons; Evibrational describes the energy
associated with the interatomic vibrations that are present in molecular species;
while Erotational is the energy caused by various rotational motions within a
molecule. It should be mentioned that the number of rotational states is much
larger that that of vibrational states, and the number of vibrational states is much
larger than that of electric states.
Beer-Lambert Law (Beer’s Law)
Beer’s Law is a fundamental law governing molecular and atomic absorption
spectroscopy. Let’s consider a beam of light with an initial radiant intensity P0
pass through a layer of solution (with a thickness of b and concentration of c).
The intensity of the light after passage through the solution is P.
E0
E1
En
……
.
E0
E1
En
……
.
E0
E1
En
……
.
E0
E1
vibrational level
rotational level
E2
E0
E1
vibrational level
rotational level
E2
Energy Levels - Molecular Absorption Energy Levels - Atomic Absorption
64
According to Beer’s law, there is a linear relationship between absorbance and
concentration of the solution:
A = -log (T) = log (P0/P) = εbc, where
Transmittance (T) = P/P0, Absorbance (A) = -log (T), b = thickness (in cm); c =
concentration of the solution (in M); and ε = molar absorptivity (L mol-1 cm-1).
The linear relationship between absorbance and concentration of the solution is
the basis of the quantitative detection employed by molecular and atomic
absorption spectroscopy.
Simultaneous Analysis of a Two-Component Mixture
Beer’s law also applies to a mixture of solutions since absorbance is additive.
Atotal = A1 + A2 +…+An= ε1bc1 + ε2bc2 + … + εnbcn
Take a solution which contains two substances for example, if the absorbance of
the mixture and the molar absorptivities of the two substances are known at two
Concentration (c)
Ab
sorb
ance
(a)
Incident light P0
hv Emerging light P
b
Absorbing Soln. (C)
65
wavelengths, the concentrations of the two
substances could be calculated from 2
equations with 2 unknowns.
Aλ1 = εx_λ1b[x] + εy_λ1b[y]
Aλ2 = εx_λ2b[x] + εy_λ2b[y]
where Aλ1, Aλ2, εx_λ1, εx_λ2, εy_λ1, εy_λ2, and b
are known or could be determined.
OVERVIEW OF EQUILIBRIA &
TITRATIONS
When we write a balanced equation (doing stoichiometry calculations), we assume that
all the reactants are quantitatively converted to products irreversible reactions. For
example,
2H2(g) + O2(g) → 2H2O (g)
C (s) + O2 (g) → CO2 (g)
However, irreversible reactions are rare, and most reactions do not proceed to completion
as products since reverse reaction starts.
2NO2(g) ⇔ N2O4(g)
3H2 (g) + N2 (g) ⇔ NH3 (g)
Where reactants continuously form products and products continuously produce
reactants. After some time, the forward reaction and reverse reaction rate become equal,
and the concentrations stop changing. At that point, the system reaches a dynamic
equilibrium.
Chemical equilibrium is the state where the concentrations of all reactants and products
remain constant with time. On the molecular level, there is frantic activity. Equilibrium
is not static, but is a highly dynamic situation.
For the reaction
aA + bB ↔ cC + dD
we write the equilibrium constant, K, in the form
ba
dc
BA
DCK][][
][][=
66
where the lowercase superscript letters stand for stoichiometry coefficients and each
capital letters represents a chemical species. The symbols [A], [B], [C], [D] stand for the
concentrations of species A, B, C, and D, respectively. Note that, in the thermodynamic
derivation of the equilibrium constant, each quantity in the above equation is expressed as
the ratio of the concentration of a species to its concentration in its standard state. For
solutes, the standard state is 1 M; for gases, the standard state is 1 bar; while for solids
and liquids, the standard state is pure solid or liquid.
Solubility product is the equilibrium constant for the reaction in which a solid salt
dissolves to give its constituent ions in solution. Solid is omitted from the equilibrium
constant because it is in its standard state. Take the following reaction for example:
Hg2Cl2(s) ↔Hg22+
+ 2Cl-
The solubility product Ksp is
Ksp = [Hg22+
][Cl-]
2 = 1.2 × 10
-18
Acid Dissociation Constant (Ka)
When an acid is dissolved in water, we have the following general acid dissociation
reaction:
HA + H2O ⇔ H3O+ + A
- ⇔ H
+ + A
-
The acid dissociation Constant, Ka, is defined as follows:
Note that it is a common practice to omit H2O from equation.
HA ⇔ H+ + A
-
Strong Acid and Weak Acid
The strength of an acid is defined by the equilibrium position of its dissociation reaction.
Strong Acid:
� Its equilibrium position lies far to the right. (e.g., HNO3)
� Yields a weak conjugate base. (e.g., NO3−)
� Very large Ka
Weak Acid:
][
]][[
][
]][[ 3
HA
AH
HA
AOH
aK−+−+
==
67
� Its equilibrium lies far to the left. (e.g., CH3COOH)
� Yields a much stronger (it is relatively strong) conjugate base than water (e.g.,
CH3COO-)
� A small Ka
The pH Scale
pH scale provides a very convenient way to express [H+]:
pH ≈ −log[H+], and [H
+] = antilog(-pH) = 10
-pH
Note that 1 pH unit equals10× concentration.
• pH in water ranges from 0 to 14.
Kw = 1.00 × 10−14
= [H+] [OH
−]
pKw = 14.00 = pH + pOH
• pH of pure water = 7.00
Strong Bases and Weak Bases
“Strong” and “weak” are used in the same sense for bases as for acids.
• Strong means “complete dissociation” (hydroxide ion supplied to solution). For
example,
NaOH → Na+ + OH
-
1M NaOH solution contains 1M Na+ and 1M OH
-, and no undissociated NaOH.
• Weak means “very little dissociation” (or reaction with water). Note that many of
these weak bases do not contain OH- ions. However, when dissolved in water,
they increase [OH-]. For example,
H3CNH2 + H2O ↔ H3CNH3+ + OH
−
Polyprotic Acids
Polyprotic acids can provide more than one proton (H+) to the solution (e.g., H2SO4,
H2CO3, H3PO4, etc.). Note that they dissociate in a stepwise manner.
e.g., H2SO4 (aq) → H+(aq) + HSO4
-(aq)
68
large Ka1, strong acid
HSO4-(aq) ⇔ H
+(aq) + SO4
2-(aq)
small Ka2, weak acid
• Example of a triprotic acid
H3PO4 (aq) ⇔ H+(aq) + H2PO4
-(aq)
H2PO4-(aq) ⇔ H
+(aq) + HPO4
2-(aq)
HPO42-
(aq) ⇔ H+(aq) + PO4
3-(aq)
Note that for typical weak polyprotic acids, Ka1> Ka2 >Ka3 indicating that the loss
of a second or third proton occurs less easily than loss of the first proton (because the
negative charge on the acid increase, it becomes more difficult to remove the
positively charged proton.
Titration: a common laboratory method of quantitative chemical analysis that is used to
determine the concentration of a substance in solution by adding to it a standard reagent
of known concentration in carefully measured amounts until a reaction of definite and
known proportion is completed, as shown by a color change or by electrical
measurement, and then calculating the unknown concentration.
Equivalence point: the point when the quantity of added titrant is the exact amount
necessary for stoichiometric reaction with the analyte.
End point: the point when you think this is true, and is subject to experimental error.
Indicator: a substance that undergoes a change in color when the end-point of a titration
is reached.
Back titration: a quantitative chemical analysis technique that allows to find the
concentration of a reactant of unknown concentration by reacting it with an excess
volume of another reactant of known concentration. The resulting mixture is then
titrated, taking into account the molarity of the excess that was added. This is used as
opposed to standard volumetric titration when the substance being analyzed is either too
slow or too weak to give a valid reaction.
Reference electrode: an electrode which has a fixed composition and a constant
potential.
Indicator electrode: the electrode used with reference electrode to measure potential of
unknown solution. The potential of the indicator electrode is proportional to the activity
of the analyte (e.g., ion) in question.
69
Ion-selective electrode: an electrode which generates an electric potential based on the
selective binding of one type of ion to a membrane.
Nernst Equation
For the half-reaction aA + ne- ⇔ bB, the Nernst equation giving the half-cell potential is
where E0 is the standard reduction potential (AA = AB =1); R is the gas constant; T is
temperature; n is the number of electrons in the half-reaction; F is the Faraday constant;
and Ai is the activity of species i.
Appendix C Hazardous Waste Policy
The following procedure details the hazardous waste policy for teaching labs.
1. Students must dispose of all waste in the appropriate 4 L glass waste bottle
found in the hood. There are three glass bottles in the hood. They are labeled
“Non-Halogenated Waste,” “Halogenated Waste,” and “Heavy Metals Waste.”
It is critical that you teach students how to determine which waste bottle is the
correct one.
a. All waste containing any metal atom heavier than calcium is considered
heavy metal waste and should be disposed of as Heavy Metals
Hazardous Waste.
b. All waste containing halogen atoms (but not containing heavy metal
atoms) should be treated as Halogenated Hazardous Waste.
c. All other waste generated in the teaching laboratories should be disposed
of as Non-Halogenated Hazardous Waste.
d. Crystalline waste should be dissolved in a small amount of an
appropriate solvent (usually water or acetone) and disposed of as
described in a, b, or c above. Do not leave any unlabeled waste in the
hood! For example, an organic lab student who synthesizes 4-
bromonitrobenzene (s) in a lab should dissolve this product in a few mL
of acetone and place it in the 4 L bottle for Halogenated Waste.
e. Solid Waste: Some experiments have solids that cannot be dissolved
(polymers, celite, filterpaper, etc…). In these cases a Solid Waste container
will be available for collection of this waste.
2. At the end of each lab period, you need to record the identity and quantity of the
waste generated by your lab. Have the students record what they dispose on the
white board in the room or you can make a sheet with the class roll listed down
the left side of the paper. The paper should have one of three headings: non-
aA
bB
nFRTEE
Α
Α−°= ln
70
halogenated, halogenated or heavy metals. Tape these sheets to the front of the
hood.
3. At the end of each lab period, you, the TA, need to:
a. Fill out the Daily Hazardous Waste forms located on the side of the hood.
Use the student sheets described in (3) as a guide, but be sure that the
total volume that you report is equal to the actual volume disposed of.
Write out the full proper chemical names-DO NOT abbreviate. Include
concentrations when possible.
b. Empty the 4 L glass bottles into the appropriate 10 L Nalgene near the
hood. After filling, be sure to replace the cap loosely. This must be done
at the end of every lab period!
4. When a 10 L container is full, take the Daily Hazardous Waste form for the full
container (completely filled out!) to the stockroom. The stockroom will provide
an empty 10 L Nalgene container with a new Daily Hazardous Waste form. Do
not continue writing on the Daily Form for the full Nalgene container. This
procedure is very important.