pottitrsp05

Chemistry 135 Clark College

Potentiometric Titrations Revised Spring 2005 NF Page 1 of 14

POTENTIOMETRIC TITRATION OF A WEAK ACID A Weak Acid/Strong Base Titration

For this experiment: 1. Complete the Prelab and obtain a stamp before you begin the experiment. 2. Write your lab notebook prelab and get it initialed/signed before you begin the experiment. 3. Obtain an unknown organic acid and record the unknown code in your notebook and on the

data report sheet. Look for the unknown assignments taped to the wall near the Instructors Station in the lab.

4. Titrate a preliminary sample of your unknown roughly with phenolphthalein to determine approximate equivalence point.

5. Perform two trials of your titration using the LoggerPro interfaces and the same batch of NaOH that you standardized.

6. Determine the identity of your unknown from the calculated equivalent weight and estimated pKa.

Turn in your Data Report Sheet, Stamped Prelab, notebook pages and the following (labeled and organized graphs for each equivalence point in each titration: pH vs VNaOH, 1st derivative curve, 2nd derivative curve, and a blow-up of the pKa/buffer region. Introduction

In a potentiometric titration one makes a graph of the volume of titrant delivered from a buret against the voltage (or some function directly related to the voltage, such as pH) produced by two electrodes in the solution being titrated. Provided the equilibrium of the analytical reaction is favorable and one chooses the right combination of electrodes there will be a sharp change in voltage at the equivalence point. This change in voltage can be used in place of a color indicator to locate the equivalence point. This is obviously a very useful technique if one is dealing with a colored solution in which an indicator would be useless or in a system for which a suitable indicator does not exist.

Although the present experiment deals with an acid-base reaction, potentiometric titrations can also be used with redox reactions, precipitation reactions and complex formation reactions, as well as titrations in non-aqueous systems. Furthermore, although the present experiment may give the impression that the technique is slow, it can, in routine work, be made just as rapid as titrations using visual indicators, and often gives more accurate results.

The choice of electrodes is critical. One electrode, called the reference electrode, must hold a constant potential throughout the titration, regardless of the concentration of various reagents in the solution. The other electrode, called the indicator electrode, must have a potential that depends directly on one of the reactants or products in the analytical reaction. The electrodes used in acid-base titrations are almost always a calomel reference electrode and a glass indicator electrode. The potential of the glass electrode depends directly on the hydrogen ion activity in solution, whereas the potential of the calomel electrode is constant because it is isolated from the solution being titrated by a salt bridge.

A pH meter, or pH amplifier, such as the one used in this experiment, is essentially an electronic voltmeter. However, through calibration, its output reads directly in pH units instead of volts. The apparatus is sketched in Figure 1. One performs the titration by adding increments of titrant from the buret and reading the pH of the solution after each addition.



Figure 1 Treatment of Potentiometric Data

For each trial set of data, plot the entire titration curve as in Figure 2. The equivalence point is the point of maximum slope. You will notice, however, that the volume scale of such a graph is too compressed to read the equivalence point to 0.02 mL as required in order to obtain part-per-thousand accuracy. One may prepare a second graph in which one plots the region from about 1-2 mL before the equivalence point to 1-2 mL beyond, as illustrated in Figure 3. The operator must judge the inflection point. The volume scale is now large enough that the volume at the inflection point can be read to the nearest 0.02 mL. The main sources of error are the failure to draw a smooth curve through the data points and in judging the location of the inflection point. The latter error is somewhat analogous to a titration using a color indicator in which the main source of error is the operator's judgment as to the color at the end point. We will also use other mathematical methods to help determine the equivalence point.

TABLE 1 Sample Titration Data

Corrected Volume NaOH pH



0.00 3.86 24.00 5.20 36.20 9.29 2.03 4.02 26.00 5.32 36.40 9.84 4.00 4.14 28.00 5.44 36.60 10.17 6.00 4.28 30.00 5.60 37.00 10.50 8.00 4.40 32.00 5.80 38.00 10.87

10.00 4.51 34.00 6.13 40.03 11.23 12.00 4.61 35.00 6.43 42.00 11.40 14.02 4.71 35.21 6.53 44.00 11.53 16.00 4.81 35.39 6.64 46.00 11.63 18.00 4.90 35.60 6.79 48.00 11.70 20.00 5.01 35.79 6.98 50.01 11.77 22.00 5.09 36.00 7.35



Weak Acid Titration

Volume of NaOH

pH

2.00

4.00

6.00

8.00

10.00

12.00

0.00 20.00 40.00 60.00

Figure 2 Estimation of pKa at the Half-titration Point

After you have located the equivalence point in the first titration curve, you can calculate the volume of sodium hydroxide at the equivalence point in the titration and therefore the volume at which exactly half of the acid will be neutralized. This is called the buffer point, half-titration point or half-equivalence point. This point is particularly significant because it provides an estimate of the acid dissociation constant of the acid being titrated.

In general, for any weak acid we have the following equilibrium:

HA (aq) + H2O (l) H3O+ (aq) + A- (aq) Ka = [H+] [A-]

[HA]

Now, at the half-titration point, exactly half of the acid, HA, has been converted into its conjugate base. That is, the solution can be considered to be one containing equal concentrations of HA and A-. Thus, it should be clear that at this particular point in the titration [HA] = [A-]. Therefore, Ka = [H+], or pKa = pH.

Some typical data at the half-equivalence point are presented in Table 2. These data are for the same titration as the data in Figures 2 and 3. Thus, the equivalence point occurs at 36.11 mL, the half-equivalence point at 18.05 mL, and the pKa is approximately 4.90, as determined from Figure 4. Some disagreement in pKa from handbook is typical, and is a result of the use of molar concentrations in place of activities in the expression for the equilibrium constant. Nevertheless, it is valuable information when seeking to identify unknown acids.

Table 2 Half-Equivalence Data

Vol NaOH mL pH

12.00 4.61

14.02 4.71

16.00 4.81

18.00 4.90

20.00 5.01

22.00 5.09

24.00 5.20

Expansion of Half- Equivalence pt.

Volume of NaOH

pH

4.60

4.80

5.00

5.20

13.00 15.00 17.00 19.00 21.00 23.00 25.00

Figure 3



First Derivative Plot We noted above that at the equivalence point, the slope of the titration curve is at a maximum. In

other words, the rate of change of pH with addition of titrant is at its highest at the equivalence point. So, if we could plot the rate of change of pH with change in volume (pH/V) against volume, then a "spiked" curve should result and the peak of this spike should occur at the equivalence point. This is conveniently done by adding equal increments of titrant near the equivalence point. Consider the data collected during a titration, as shown in Table 3. We want to plot pH/V against the volume to get the first derivative. Such a plot is shown in Figure 4. The volume used is the average of the two volumes used to calculate pH. So, the volume for pH/V = 0.71 is 35.50 mL, and so on. The equivalence point is the maximum of this plot, which, when extrapolated, occurs at 36.10 mL. This extrapolation leads to an uncertainty that can be partially avoided by a second derivative plot (see below).

Note that we have used equal volume increments here ( 0.20 mL), and so pH could have been plotted in place of pH/V. These equal increments are not necessary but do shorten the calculations. Although the average volume may be calculated to 0.001 mL for plotting, experimentally, we are not justified in reporting the equivalence point to more than 0.01 mL.

Table 3

First Derivative Data Volume NaOH pH pH V Vol. Avg. pH/V

35.39 6.64 35.60 6.79 0.15 0.21 35.50 0.71 35.79 6.98 0.19 0.19 35.70 1.00 36.00 7.35 0.37 0.21 35.90 1.76 36.20 9.29 1.94 0.20 36.10 9.70 36.40 9.84 0.55 0.20 36.30 2.75 36.60 10.17 0.33 0.20 36.50 1.65

First Derivative Plot

Avg. Vol. NaOH

dp

H/d

V

0.00

2.00

4.00

6.00

8.00

10.00

35

.50

35

.70

35

.90

36

.10

36

.30

36

.50

Figure 4



Second Derivative Plot Mathematically, the second derivative of a titration curve should pass through zero at the

equivalence point. The last four columns in Table 3 illustrate how such a plot can be accomplished. The second derivative is the rate of change of the first derivative with respect to the change in the average volume. The average of the two successive volumes used for the first derivative plot is also used for the second derivative plot (Figure 5). Again, there is some extrapolation, but it is less significant than in the first derivative plot. The equivalence point is taken as 36.11 mL. As before, we are experimentally justified in reporting it to the nearest 0.01 mL.

In using derivative methods, the volume increment should not be too large or there will not be sufficient points near the equivalence point.

Caution should be used with derivative methods. Derivatives tend to emphasize noise or scatter in the data points, being worse for the second derivative. Therefore, if a particular titration is subject to noise, a direct plot (pH versus Volume) may be preferred.

Table 4

Second Derivative Data Vol. Avg. pH/V (V) (pH/V) V avg (pH/V)/V

35.50 0.71 35.70 1.00 0.20 0.29 35.60 1.43 35.90 1.76 0.20 0.76 35.80 3.81 36.10 9.70 0.20 7.94 36.00 38.72 36.30 2.75 0.20 -6.95 36.20 -34.75 36.50 1.65 0.20 -1.10 36.40 -5.50

Second Derivative Curve

Vol. NaOH

d2

pH

/d

V2

-40.00

-20.00

0.00

20.00

40.00

35.40 35.60 35.80 36.00 36.20 36.40

Figure 5

Assembling the Data Once you have obtained the equivalence volumes and pKas, you can use that information to

determine the identity of your unknown acid. The molecular weight can be determined from the equivalence point data. The pKa values can be determined from the half-equivalence points. Your unknown acid can be either monoprotic or diprotic. Although this is often readily seen in the titration curve, some diprotic acids appear to have only one equivalence point, if the two pKa values are less



than 2 pH units apart. However, the resulting calculated molecular weight will be the equivalent weight, and thus will be one-half the molecular weight. It is a match (or near-match) of both the pKa and molecular weight data that determines the identity of your unknown acid. Table 5 gives a list of possible organic acids for this experiment.

Table 5 Selected Physical Data for Organic Acids

Acid Molar mass(g/mol) pKa1 pKa2 Benzoic acid 122.1 4.20

2 Chlorobenzoic acid 157.58 2.94

4 Chlorobenzoic acid 157.58 3.99

trans Crotonic acid 86.09 4.69

Maleic acid 116.04 1.92 6.23

Malonic acid 104.06 2.83 5.69

Potassium hydrogen phthalate 204.23 5.41

Succinic acid 118.1 4.19 5.57

Sodium hydrogen sulfite 104.06 7.21

d -Tartaric acid 150.09 3.04 4.37

m Toluic acid 128.85 4.27 Reference Table taken from Langes Handbook of Chemistry, McGraw-Hill Book. Co. 1979.



NOTES Note 1: Buret readings must be made to the nearest 0.01 mL and the pH meter should be

read to the nearest 0.01 pH unit.

Note 2: After you have located the equivalence point in the first titration curve, it is a simple matter to calculate from the sample weights the location of the equivalence point in the second sample.

EXPERIMENTAL PROCEDURE Equivalent Weight Estimate Mass approximately 0.5 grams into a 250 mL Erlenmeyer flask (don't use the analytical balance, this is for a trial run!), add 100 mL of distilled water and cover with a watch glass. Do a phenolphthalein titration and calculate the approximate equivalent weight of your unknown organic acid. Determine the mass of unknown acid needed for a 35-40 mL titration.

Potentiometric Titration You may work with someone else to help obtain data. Each person must obtain their own sample of an unknown acid. Assume the samples have a 100.0% purity. One person may operate the buret while the other records the data. Exchange roles with each person's sample. If you have a diprotic acid, do the calculations and graph for the 2nd equivalence point. Technique note: To rinse the electrode, use your waste beaker and hold it under the electrode then rinse the electrode thoroughly with distilled water, collecting the waste.

1. Using the analytical balance, mass two samples of the unknown acid as calculated above into two 250-mL beakers. Record the mass to the nearest 0.0001 g. Dissolve each in about 100 mL of distilled water and cover each with a watch glass.

2. Prepare the computer for data collection by opening Experiment 24 from the Chemistry with Computers experiment files of Logger Pro. You should see a blank data table and graph. The vertical axis has pH scaled from 0 to 14 pH units. The horizontal axis has volume scaled from 0 to 25 mL. Change the maximum volume to 50 mL by clicking once on the 25 and typing in 50.

3. Calibrate your pH electrode using buffers pH 4 and 7. Find the Collect item in the menu bar and open Calibrate... Follow directions to calibrate your pH probe using the two buffers. You will have to type in the appropriate pH values when the voltage values stabilize. Re-check your calibration with one of the buffers and make sure it is stable. Remember to rinse the pH probe between solutions, and be sure to Save your calibration.

4. Obtain a clean 50-mL buret and rinse the buret with a few mL of the ~0.1 M NaOH solution you have standardized in the last experiment. Dispose of the rinse solution into your waste beaker. Use a buret clamp to attach the buret to the ring stand as shown in Figure 1. Fill the buret above the 0.00-mL level of the buret with the ~0.1 M NaOH solution. Drain a small amount of NaOH solution into the waste beaker so it fills the buret tip and leaves the NaOH at the 0.00 mL level of the buret. Be sure to record the precise concentration of the NaOH solution in your data table.

5. Prepare your experimental set-up as shown in Figure 1. Use a utility clamp to suspend a pH electrode on a ring stand, and a buret clamp to attach the buret to the ring stand. Place a stir bar in one of your acid solutions to use a magnetic stirplate. Position the pH electrode in the acid solution and adjust its position so that it is not struck by the stir bar. Do not place the magnetic stirrer close to a computer, the magnet interferes with the monitor!

6. Before adding NaOH titrant, click on the Collect button and monitor pH for 5-10 seconds. Once the pH has stabilized, click on the Keep button. The computer will hold this pH value and wait for you to type in the buret reading. Enter the current buret reading (should be 0.00 mL). You have now saved the first data pair for this experiment.



7. You are now ready to continue the titration. This process goes faster if one person manipulates and reads the buret while another person operates the computer and enters volumes.

8. Add the next increment of NaOH titrant (enough to raise the pH about 0.30 units). Again click on the Keep button and enter in the volume.

9. Continue adding NaOH solution in increments that raise the pH by about 0.30 units (constant pH increments) and enter the buret reading after each increment. Near the equivalence point, when the curve starts to rise sharply, change to intervals of 0.20 mL units (or less). Note this is a change to constant volume increments. This eases the treatment of the data later.

10. After the curve flattens again, you may add NaOH solution in larger increments (going back to changes of 0.30 pH units) until all 50 mL have been added, or the pH becomes relatively constant.

11. Dispose of any waste beaker contents into the appropriate product collection container.

Treatment of Potentiometric Data Part of your grade will be determined by your manipulation of the data so that the graphs and tables are appropriate.

1. Save your data on the desktop in the folder labeled 135. You files should be titled with your initials and whether this is the first or second titration, e.g. NFacid1. Be sure you save with your initials or other notation so that you (and I) can keep the different trials separate.

NOTE: You may save your data in the Chem 135 folder on the desktop of the computer if you want to do so, then you may come back and manipulate the data later. In Logger Pro there are various ways to accomplish each task and to make the graphs look correct. Please be sure to save your raw data and to practice a little.

2. The titration curve you have obtained should have a shape similar to the one shown in Figure 2. Print both the data table and the graph window separately.

3. View the first derivative curve by clicking the y-axis title (pH) and selecting the first derivative (d1).

4. Change the scales on the x- and y- axes to give an expanded graph in the window.

5. Record the equivalence point, which is the peak on the graph, by using the Analyze menu to find the maximum point for your graph. Print the graph with that point indicated by the analysis bar.

6. Follow the same process to view the 2nd derivative curve. The equivalence point is where the second derivative equals zero. Change the scales on the x- and y- axes to give an expanded graph in the window and find the point where the line crosses the x-axis using the Analyze menu. Then print the graph.

7. Now that you have the equivalence pt. volume of NaOH, go back to the original titration curve and expand the region about the half-equivalence pt. You may use the Analyze menu to find the pH at the half-equivalence pt. Print this graph as well.

8. Repeat the procedure with the second sample, and be sure to change units, axis titles on the computer screen as needed.

NOTE: Expand axes as necessary to provide good-looking, useful results. It is sometimes advantageous to have the pH, 1st, and 2nd derivative graphs expanded about the equivalence point using the same scale for the x-axes.



Processing the Data 1. Calculate the equivalent weight of your unknown using your equivalence point.

2. Find the pKa for your unknown acid from the half-equivalence point and identify the acid using the table attached.

3. Staple together the report forms, data tables, and the required graphs. Print your name and date on each graph. A portion of your grade will depend upon the presentation of your data and graphs. Graphs include:

Complete titration curves based on the data for both titrations.

The first derivative graph showing the equivalence point region on an expanded volume scale (see Figure 3). You should be able to read volumes to 0.01 mL.

The second derivative graph showing the equivalence point region on an expanded volume scale (see Figure 4). You should be able to read volumes to 0.01 mL.

Expanded half equivalence pt region for each titration.

NOTE: If you have a diprotic acid, you will actually turn in 14 graphs: you will need to treat each equivalence point and half-equivalence point separately.

APPENDIX

Concentration Units Normality vs. Molarity. Most titration calculations can be carried out using either concentration units, N or M. Remember that normality is the number of equivalents per liter of solution, where an equivalent is the number of active units per mole of compound. Active units can be H+ or OH for acid/base reactions or electrons for redox reactions.

Example: A 1.5 M H2SO4 solution is 3.0 N, because there are 2 equivalents of H+ in every mole of H2SO4.

1.5 mol H2SO4

L x

2 eq H+

mol H2SO4 =

3.0 eq

L = 3.0 N

Equivalent Weight: The equivalent weight of a compound is the mass of compound that can supply one mole of active units (H+, OH, es)

Example: Determine the equivalent weight of barium hydroxide. The formula Ba(OH)2 has a mass of 171.35 g/mol. Since barium hydroxide has 2 equivalents of OH per mole, the equivalent weight is 1/2 the molecular weight.

171.35g

mol x

1 mol Ba(OH)2

2 eq OH-

= 85.675 g

eq



SAMPLE CALCULATIONS

A. Weak Acid Strong Base Titrations The equivalence point of the titration occurs when the milliequivalents of base added exactly equals the milliequivalents of acid in the flask or when millimoles of base units added exactly equals the millimoles of acid units in the flask.

meq acid = (mL acid)(N acid) meq base = (mL base)(N base)

The usefulness of normality in volumetric analysis is demonstrated with following: at the equivalence point

NAcidVAcid = NBaseVBase

To calculate the number of equivalents contained in a known acid sample, one needs the sample mass, its purity, and its equivalent weight.

equiv acid =

sample wt.(g) x purity factor

equiv. wt. (g/eq.)

or in more familiar form/path: g sample g acid eq. acid

equiv acid = g sample x

g acid

100 g sample x

eq acid

g acid

Calculations in this experiment are the same as those in the Standarization of NaOH experiment please review them. Example 1: Determine the equivalents of acid in a 0.4567 g sample of citric acid which is 92.15%

pure. Citric acid is a triprotic organic acid, C6H8O7.

equiv acid = 0.4567 g sample x

92.15 g acid

100 g sample x

1 eq acid

64.05 g acid = 0.0006571 equiv acid

Example 2: A 0.8676 gram sample of a pure organic acid required 38.69 mL (corrected) of 0.1042 N

NaOH for to reach the equivalence point. Calculate the equivalent weight of the acid, and report with a relative error of 1 part per 1000. Assume a purity of 100% or 1.

Equiv Wt = 0.8676g acid x 1 equiv NaOH

1 equiv acid x

1L

0.1042equiv NaOH x

1

0.03869L

Equiv Wt = 215.2 g/equiv (ppth precision)



Chem 135 Potentiometric Titration of a Weak Acid DATA REPORT SHEET Name ________________________

Unknown Identification ________ Normality of NaOH _________ Approximate Equivalent Weight Data (Indicator Titration)

Sample Mass = VNaOH =

Equiv. Weight =

Potentiometric Titration Data. Enter your data in to the appropriate spreadsheet in the lab. Show Sample Calculations on the back of this page.

Trial 1 Trial 2 Average

Sample Mass (g)

VNaOH, 1st Equiv. pt.

VNaOH, 2nd Equiv pt.

Equiv. Wt.

Molar Mass

pKa1

pKa2

Identity of Unknown acid

Show sample calculations for Equiv. Wt and Molar Mass on the back.



Sample calculations for Equiv. Wt. and Molar Mass



Chem 135 Potentiometric Titration of a Weak Acid PRELAB Name ________________________

You may use this experiment handout, your textbook or any other resources you can find to answer these questions.

1. Distinguish between the terms endpoint and equivalence point. 2. Draw the correct Lewis structures for phosphoric acid and phosphorus acid and thoroughly explain

why one of these is a triprotic acid and the other is diprotic.

3. Write chemical reactions which represent a. Ka for benzoic acid.

b. Kb for aniline.

- over -



4. A 0.0450 M solution of benzoic acid has a pH of 2.78. Determine pKa for this acid.

pKa =

5. A 0.535 M solution of an unknown acid HA is 65% dissociated. Determine the pKa.

pKa =

pottitrsp05

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