instru compensate

8/3/2019 Instru Compensate

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I. About Graphs

What is a graph?In mathematics, a graph is an abstract representation of a set of objects where some

pairs of the objects are connected by links. The interconnected objects are represented by

mathematical abstractions called vertices, and the links that connect some pairs of

vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of

dots for the vertices, joined by lines or curves for the edges.[1]

What are the types of graphs?There are many types of graphs and charts that are commonly used for showing

different reports. These are listed as follows.

Bar Graphs Line Graphs Scatter Plot Graphs Pie Charts

Bar GraphsThese are one of the most common types of graph used to display data.

Sometimes known as "column charts", bar graphs are most often used to show amounts

or the number of times a value occurs. The amounts are displayed using a vertical bar

or rectangle. The taller the bar, the greater number of times the value occurs. Bar

graphs make it easy to see the differences in the data being compared.[2]


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Figure 1.1 A Bar Graph [3]

Line GraphsThese are often used to plot changes in data over time, such as monthly

temperature changes. They can also be used to plot data recorded from scientific

experiments, such as how a chemical reacts to changing temperature or atmospheric

pressure.

Similar to most other graphs, line graphs have a vertical axis and a horizontal axis.

If you are plotting changes in data over time, time is plotted along the horizontal or x-

axis and your other data. When the individual data points are connected by lines, they

clearly show changes in your data and you can use these changes to predict future

results.[2]


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Pie Charts or Circle GraphsThese graphs are a little different from the other three types of graphs discussed. For

one, pie charts do not use horizontal and vertical axes to plot points like the others. They

also differ in that they are used to chart only one variable at a time. As a result, it can

only be used to show percentages.

The circle of pie charts represents 100%. The circle is subdivided into slices

representing data values. The size of each slice shows what part of the 100% it

represents.[2]

Figure 1.4 A Circle Graph[4]


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II. Line Graphs Importance of constructing and interpreting line graphs

Line Graphs play an important role in the modeling and understanding data in

analytical chemistry. Graphs are visual representations of numerical systems and

equations. Graphs help us to visualize the relationship of one bit of data to another. The

relationship can also be translated into a mathematically meaningful equation. The

equation for a line (y = mx + b) is one such equation.

In constructing a line graph, plotting known data can help us to visualize the

behavior of systems in situations that have not been measured. Thus, we can predict

whether the data gathered are decreasing or increasing with respect to its variables.

Graph Variables Independent and Dependent variables

DefinitionsIndependent Variables these variables are ones that are more or less controlled.

Scientists manipulate these variables as they see fit. They still vary, but the variation isrelatively known or taken into account.

Dependent Variables these not controlled or manipulated in any way, but

instead are simply measured or registered. These vary in relation to the independent

variables, and while results can be predicted, the data is always measured. There can be

any number of dependent variables, but usually there is one to isolate reason for variation.


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y vs. x Convention in plotting variablesBy convention, the independent variable is plotted along the horizontal (x) axis

and the dependent variable is plotted up the vertical (y) axis. To plot a point, you simply

move along thex axis to the point that corresponds to the value of your independent

variable, then find the point up the y that corresponds to your dependent variable's score,

and mark a spot on the graph where lines from these points meet.

When choosing a title for a chart, say y plotted againstx. That is, 'dependent

variable' plotted against 'independent variable'.

Equation of a Line Mathematical equation

The equation of a line with a given slope m and the y-intercept b is

y = mx + b

This is obtained from the point-slope equation by setting a = 0. It must be

understood that the point-slope equation can be written for any point on the line, meaning

that the equation in this form is not unique. The slope-intercept equation is unique

because if the uniqueness for the line of the two parameters: slope and y-intercept.[5]

Parameters: slope and y-interceptThe slope of a line is a number that measures its "steepness", usually denoted by

the letterm. It is the change in y for a unit change in x along the line.[6]

The y-intercept of a line is the point at which is crosses either the y axis. If we do

not specify which one, the y-axis is assumed. It is usually designated by the letterb.

Unless that line is exactly vertical, it will always cross the y-axis somewhere, even if it is

way off the top or bottom of the chart.[7]


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Plotting data of a linear curve ProcedureA standard linear curve is a graph relating a measured quantity (radioactivity,

fluorescence, or optical density, for example) to concentration of the substance of interest

in "known" samples. You prepare and assay "known" samples containing the substance in

amounts chosen to span the range of concentrations that you expect to find in the

"unknown" samples. You then draw the standard curve by plotting assayed quantity (on

the Y axis) vs. concentration (on the X axis). Such a curve can be used to determine

concentrations of the substance in "unknown" samples.

Line of best fitA straight line drawn through the center of a group of data points plotted on a

scatter plot. Scatter plots depict the results of gathering data on two variables; the line of

best fit shows whether these two variables appear to be correlated.

A more precise method for determining the line of best fit is a mathematical

calculation called the least squares method. The line of best fit is used in regression

analysis, and is a key input in statistical calculations such as the sum of squares.[19]

Method ofLeast Squares (Linear Regression)The method of least squares is a standard approach to the approximate solution

of overdetermined systems, i.e., sets of equations in which there are more equations than

unknowns. "Least squares" means that the overall solution minimizes the sum of the

squares of the errors made in solving every single equation.

[8]


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Using Linear Regression (LR) function of a scientific calculatoro Procedure of encoding/key-in of data

1. Clear all the data firstPress SHIFT > Press CLR > Press 3(ALL) > Display: Reset All > Press

= > Press AC.

2. Set calculator to Linear Regression modePress MODE twice > Press 2 (REG) > Press 1 (Lin)

3. Entry of dataDo data entry one by one with x comma y format

Time (min) Distance (m)

1 3.5

3 5.6

5 7.4

Then do entry of data:

Press 1 > Press , > Press 3.5 > Press M+ > Display n=1



o Determination of linearity of data (linearity check)Press SHIFT > Press "2" > Press >" (next button) twice >>> Press "3" (r) >

Press "=" > Display (for the above example: r = 0.998

). If you need R square, just use thesquare button.


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o Determination of slope and y-interceptFor slope (B)

Press "S" > Press "2" > Press ">" (next button) twice > Press "2" (B) >>> Press "=" >Display (for the above example: B =0.975)

Fory- intercept (A)

Press "SHIFT" > Press "2" > Press ">" (next button) twice > Press "1" (A) >>> Press "="

> Display (for the above example: A=2.575)

Now, you get the equation: y = Bx+A

y = 0.975x +2.575 ( r = 0.988)

o Calculating value of x for a given value of yGiven that y = 5.0, x can be calculated using the equation y = 0.975x +2.575 that was

made earlier. Substitute y from the equation and find x;

y = 0.975x +2.575

x = 5.0 2.575 / 0.975

x = 2.49

o Calculating value of y given the value of xGiven that x = 4.0, y can be calculated using the equation y = 0.975x +2.575 that was

made earlier. Substitute x from the equation and find y;

y = 0.975x +2.575

y = 0.975(4.0)+2.575 = 6.475


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III. Calibration Curve Definition (what is a calibration curve?)

In analytical chemistry, a calibration curve is a general method for determining

the concentration of a substance in an unknown sample by comparing the unknown to a

set of standard samples of known concentration. A calibration curve is one approach to

the problem of instrument calibration; other approaches may mix the standard into the

unknown, giving an internal standard.

The calibration curve is a plot of how the instrumental response, the so-

called analytical signal, changes with the concentration of the analyte (the substance to

be measured).[9]

Procedure (how to prepare a calibration curve?)A calibration curve is prepared by plotting the data or by fitting them to a suitable

mathematical equation, such as the linear relationship used in the method of least squares.

The operator prepares a series of standards across a range of concentrations near the

expected concentration of analyte in the unknown. Analyzing each of these standards

using the chosen technique will produce a series of measurements. For most analyses a

plot of instrument response vs. analyte concentration will show a linear relationship. The

operator can measure the response of the unknown and, using the calibration curve,

can interpolate to find the concentration of analyte.[9]


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Determination of value of unknown concentration of an analyte from a calibrationcurve

One of the most common applications of spectrophotometry is to determine the

concentration of an analyte in a solution. The experimental approach exploits Beer's Law,

which predicts a linear relationship between the absorbance of the solution and the

concentration of the analyte (assuming all other experimental parameters do not vary).

In practice, a series of standard solutions are prepared. A standard solution is a

solution in which the analyte concentration is accurately known. The absorbances of the

standard solutions are measured and used to prepare a calibration curve, which is a graph

showing how the experimental observable varies with the concentration. Thus, the points

on the calibration curve should yield a straight line (Beer's Law). The slope and intercept

of that line provide a relationship between absorbance and concentration:

A = slope c + intercept

The unknown solution is then analyzed. The absorbance of the unknown

solution,Au, is then used with the slope and intercept from the calibration curve to

calculate the concentration of the unknown solution, cu.[10]

cu =

Au- intercept

slope


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Illustration (graph)

Figure 3.1 A Calibration Curve

Sample problems Applications to Spectroscopy

Standard solutions of iron complex were prepared and the absorbances of

these solutions were measured by spectronic 21. The results are presented in table

3.1

Table 3.1 Absorbance reading of iron complex

Solutions Concentration (ppm) Absorbance

Blank 0.00 0.00

1 1.00 0.21

2 3.00 0.433 5.00 0.59

4 7.00 0.70

5 9.00 0.89

Unknown ? 0.46


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Applications to ElectrochemistryStandard solutions of AR grade sodium chloride were prepared and the conductance

of each solution was measured. The gathered data were presented in table 3.2.

Table 3.2 Measured conductances of various solutions with respect to its concentration

Concentration (ppm) Conductance (mS/cm)

0.00 0.00

10.0 356

20.0 663

30.0 955

40.0 1265

Unknown 781

a. Construct a calibration curve of conductance versus concentration.b. From the calibration curve, calculate the concentration of the unknown solution.

Solution:

Figure 3.3 Calibration curve of AR grade NaCl standard solutions

y = 31.29x + 22

R = 0.9987

0

200

400

600

800

1000

1200

1400

0 10 20 30 40 50

Conductance(mS/cm)

Concentration (ppm)


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The equation of the line was found to be y = 31.29x + 22, let x = unknown

concentration. To solve for x:

y = 31.29x + 22

x= 781 22/31.29

x = 24.26ppm

Applications to ChromatographyStandard solutions of AR graded CCl4 of known concentration were prepared

(0.00, 20.00, 40.00, 60.00 and 80.0) and each concentration gave a peak area of (0.00,

325, 635, 910 and 1230). Construct a calibration curve of peak versus concentration and

calculate for the concentration of the unknown if its peak area is 721.

Solution:

Figure 3.4 Calibration curve of AR graded cyclohexane

y = 15.225x + 11

R = 0.9993

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100

Peakarea

Concentration


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Standard Addition Curve Procedure (how to prepare a standard addition curve)

The instrument response is then measured for all of the diluted solutions and the

data is plotted with volume standard added in the x-axis and instrument response in the y-

axis. Linear regression is performed and the slope (m) and y-intercept (b) of the

calibration curve are used to calculate the concentration of analyte in the sample.[11]

Interpretation of data (how to determine the unknown concentration of ananalyte from a standard addition curve)

If the response is linear, then when the total analyte concentration is 0, the

response is 0. We can extrapolate the line back to a point at which Response = 0 (as

presented in figure 2.2). The Concentration value at which Response = 0 is the x-intercept

of the regression line. Here it happens to be at 0.0015 units of added analyte. What does

this mean in the context of the analysis? In order to have a total of 0 analyte causing 0

response, we would have to add 0.0015 units analyte, or remove 0.0015 units. Why?

Because the sample of unknown that was placed in every container has 0.0015

concentration units. Remember, [Analyte]total = [added] + [unknown]. So, 0 = -0.0015added

+ [unknown], and thus 1.7 = [unknown].[13]

Another approach is possible using the linear regression to determine the

unknown concentration of the analyte,

S = mVS+ b [Equation 1]

Where: S = instrument response (signal)

VS = volume of standard

Conceptually, if the curve started where the instrument response is zero, the volume of

standard [(Vs)0] from that point to the point of the first solution on the curve (x = 0)

contains the same amount of analyte as the sample. So:

Vxcx = |(VS)0|cS [Equation 2]


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Where: Vx = volume of the sample aliquot

cx = concentration of the sample

cs = concentration of the standard

Combining Equation 1 and Equation 2 and solving for cx results in:

Cx = bCs/mVx [Equation 3]

And one can then calculate the concentration of analyte in the sample from the slope and

intercept of the standard addition calibration curve.[12]

Illustration (graph)

Figure 2.1 Standard Addition Method Plot (absorbance vs. concentration of standard)


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Multiple Addition Method (multiple data)

o Identify variables in equationWhere,


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Sample problems Application to spectroscopy

The single-point standard addition method was used in the determination of

phosphate by the molybdenum blue method. A 2.00-mL urine sample was treated with

molybdenum blue reagents to produce a species absorbing at 820 nm, after which the

sample was diluted to 100-mL. A 25.00-mL aliquot of this solution gave an absorbance

of 0.428 (solution 1). Addition of 1.00-mL of a solution containing 0.0500 mg of

phosphate to a second 25.0-mL aliquot gave an absorbance of 0.517 (solution 2). Use

these data to calculate the concentration of phosphate in milligrams per millilitre of the

specimen.

Solution:

C = A1c1Vs / A2Vt A1Vx [eq. 4.2]

Here we substitute into eq. 4.2, and obtain

= 0.00780 mg PO43-

mL

This is the concentration of the diluted sample. To obtain the concentration of the

original urine sample, we need to multiply by 100.00/2.00. Thus,

[PO43-]= 0.390 mg/mL


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Application to electrochemistryA cell containing of a saturated calomel electrode and a silver ion developed a

potential of -0.4706 V when immersed in 50.00-mL of a sample. A 5.00-mL addition of

standard 0.02000 M silver solution caused the potential to shift to -0.4490 V. Calculate

the molar concentration of lead in the sample.

Solution:

[eq. 4.1]We shall assume that the activity of Pb

2+is approximately equal to [Pb

2+] and

apply eq. 4.1. Thus,

whereEcell is the initial measured potential (-0.4706 V).

After the standard addition is added, the potential becomes Ecell(-0.4490 V), and

Subtracting this equation from the first leads to

= 0.7297

[Ag+]= 4.08 x 10

-3


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Figure 5.1 A Continuous Variation Plot (Absorbance vs. Mole fraction)

Sample ProblemA series of Ni2+ and dimethylglyoxime (DMG) solutions of equal volume was

prepared to determine the stoichiometry of the complex.The absorbance of each solution

was measured.

Table 5.1 Absorbance reading of nickel complex solution

Sample 0.0050M

Ni2+

(mL)

0.0050M

DMG

(mL)

X Ni2+

X DMG Absorbance

1 1.0 9.0 0.1 0.9 0.65

2 2.0 8.0 0.2 0.8 1.25

3 3.0 7.0 0.3 0.7 1.39

4 4.5 5.5 0.45 0.55 1.19

5 5.5 4.5 0.55 0.45 1.07


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Solution:

Figure 5.2 Plot Continuous Variation

Beer-Lambert's law states that the absorbance is proportional to the concentration

of the absorbing species. Since the sum, nM+ nL, is kept constant, the maximum amount

of complex is formed when the ratio nM/nL corresponds to the stoichiometry of the

complex.

Maximum absorbance is observed when the x/y =XNi2+

/XDMG. The maximum

occurs at aroundXNi2+ = 0.3. Thus x/y = 0.3/0.70 = 2/4.7 = 2/5.

Mole-Ratio Method Description ofMethod

In the mole-ratio method, a series of solutions is prepared in which the analytical

concentrations of one reactant (usually the cation) is held constant while that of the other

is varied. A plot of absorbance versus mole-ratio of the reactants is then made. If the

formation constant is reasonably favourable, we obtain two straight lines of different

slopes that intersect at a mole ratio corresponding to the combining ratio in the

complex.[14]


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GraphTypical mole-ratio plot is shown in figure 5.2. Formation constants can be

evaluated from the data in the curved portion of mole-ratio plot where the reaction is least

complete.[14]

Figure 5.2 Mole-ratio Method Plot (1:1)

Sample ProblemThe accompanying data were obtained on a slope ratio investigation of the

complex formed between NH4 and Quinol. The measurements were made at 420nm

wavelength.


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Slope-Ratio Method Description of the Method

This approach is particularly is useful for weak complexes but is applicable only

to systems in which a single complex is formed. The method assumes (1) that the

complex-formation reaction can be forced to completion by a large excess of either

reactant, (2) that Beers Law is followed under these circumstances, and (3) that only the

complex absorbs at the wavelength chosen for the experiment.[14]

Consider the reaction in which the complex MxLy is formed by the reaction ofx

moles of the cation M withy moles the ligand.

xM+yL = MxLy

Mass-balance expressions for this system are

cM= [M] +x[MxLy]

cL = [L] +y[MxLy]

where cM and cL are the molar analytical concentrations of the two reactants. We now

assume that at very high analytical concentration ofL, the equilibrium is shifted far to the


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right and [M]


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Graph

Figure 5.3 A Plot of Slope-ratio Method

Sample Problem


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VI. SpectrophotometricTitration Description

In analytical chemistry, Spectrophotometric titration is an analytical method in

which the radiant-energy absorption of a solution is measured spectrophotometrically

after each increment of titrant is added.[15]

Procedure Techniques forEnd-point determination

The spectrophotometer is an optical device that responds only to radiation within

a selected very narrow band of wavelengths in the visual, ultraviolet, or infrared regions

of the spectrum. The response can be made both quantitatively and linearly related to the

concentration of a species that absorbs radiation within this band. Titrations at

wavelengths within the visual region are by far the most common.

An example is the titration of iron(II) in dilute sulfuric acid solution with a

standard solution of potassium permanganate. The spectrophotometer is adjusted to

measure the absorbance of the highly colored titrant. Very little absorbance is observed

until the end point is reached; iron(II) and the reaction products are essentially colorless

and are not seen by the spectrophotometer. However, the absorbance rises as titration is

continued beyond the end point because the titrant is no longer being destroyed.[16]

The

titration curve is shown in figure 6.1.


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Graph

Figure 6.1 Spectrophotometric titration curve of iron(II) in dilute sulfuric acid solution

with potassium permanganate as the titrant. The curve shows the response when the

titrant absorbs beyond the end point.

Sample Problem

The concentrations of Fe3+ and Cu2+ in a mixture can be determined following their

reaction with hexacyanoruthenate (II), Ru(CN)64, which forms a purple-blue complex

with Fe3+ (max = 550 nm), and a pale green complex with Cu2+ (max = 396 nm) . The

mo l a r absorptivities (M 1

cm 1) for the metal complexes at the two wavelengths are

summarized in the following table.

Table 6.1 Molar absorptivities of Copper andIron

550 396

Fe3+

9970 84

Cu2+

34 856


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When a sample containing Fe3+ and Cu2+ is analyzed in a cell with a pathlength

of 1.00 cm, the absorbance at 550 nm is 0.183, and the absorbance at 396 nm is 0.109.

What are the molar concentrations of Fe3+ and Cu2+ in the sample?

Solution:

(Am)1 = (X)1bCX+ (Y)1bCY [eq. 6.1]

(Am)2 = (X)2bCX+ (Y)2bCY [eq. 6.2]

Substituting known values into equations 6.1 and 6.2 gives

A550 = 0.183 = 9970CFe + 34CCu

A396 = 0.109 = 84CFe + 856CCu

To determine the CFe and CCu we solve the first equation for CCu

and substitute the result into the second equation.

Solving for [Fe] gives the concentration of Fe3+

as 1.80 105

M. Substituting this

concentration back into the equation for the mixtures absorbance at a wavelength of 396

nm gives the concentration of[Cu] as 1.26 104

M.


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VII. PotentiometricTitration Description

In analytical chemistry, potentiometric titration is a titration in which an electrode

reversible to one of the ionic components of the analyte or titrant is immersed in the

analyte solution and the electric potential of the electrode (relative to that of an inert

reference electrode) is measured during addition of titrant. Because the potential of an

electrode is a logarithmic function of the activity of the ion to which the electrode is

reversible, an abrupt change in its potential is observable as an equivalence point is

approached.[17]

Procedure Techniques forEnd-point determination

If a pH meter is used, acid-base titration curves can be plotted or recorded. The

meter and its associated electrodes are first standardized by use of a buffer solution of

known pH. The electrodes are then immersed in the well-stirred solution to be titrated,

and the titration is begun. For routine purposes, interest is in rapid and reasonably close

end-point location. Titration is first carried out quite quickly until the meter shows signs

of rapid response, and then is slowed so that it can be stopped at the pH jump or fall that

marks the end point. Obviously, potentiometric titration can be used for a highly colored

titrand solution, in which the response of a color-change indicator could not be seen.

There are two approaches to higher precision. In the first the pH at which the

desired end point occurs is determined, and the titration of the actual sample is then

arrested exactly at, or very close to, this pH value. The other approach is to stop at the

point of steepest slope of the titration curve. This can be done by plotting (or, with

suitable instrumentation, sensing) the first derivative (pH/V) or the second derivative

(2pH/V

2) against the volume Vof titrant added. In theory this method is applicable to

any potentiometric titration, without the need to predetermine the end-point conditions.


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By suitable choice of electrodes, these potentiometric methods can also be applied

to combination titrations and to oxidation-reduction titrations. The advent of modern ion-

selective electrodes has greatly extended the scope of potentiometric titration and other

branches of titrimetry.[16]

Graph

Figure 7.1 Measurements, first and second derivative in a potentiometric titration.


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Sample ProblemCalculate the titration curve for the titration of 50.0 mL of 0.0500 MSn2+ with

0.100 M Tl3+

Both the titrand and the titrant are 1.0 M in .HCl. The titration reaction is

Sn2+

(aq)+ Tl3+

(aq) Sn4+

(aq) + Tl+(aq)

Solution:


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VIII. Molecular Weight Determination using HPLC Description ofLiquid Chromatographic Methods employed in molecular weight

determination

High-performance liquid chromatography, HPLC, is a chromatographic

technique that can separate a mixture of compounds and is used in biochemistry and

analytical chemistry to identify, quantify and purify the individual components of the

mixture. HPLC typically utilizes different types of stationary phases, a pump that moves

the mobile phase(s) and analyte through the column, and a detector to provide a

characteristic retention time for the analyte. Analyte retention time varies depending on

the strength of its interactions with the stationary phase, the ratio/composition of

solvent(s) used, and the flow rate of the mobile phase.

The widely used technique for the molecular weight determination (usually

polysaccharides) is the Size-exclusion chromatography (SEC), also known as gel


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permeation chromatography or gel filtration chromatography. It separates particles on

the basis of size. It is generally a low resolution chromatography and thus it is often

reserved for the final, "polishing" step of purification. SEC is used primarily for the

analysis of large molecules such as proteins or polymers. SEC works by trapping these

smaller molecules in the pores of a particle. The larger molecules simply pass by the

pores as they are too large to enter the pores. Larger molecules therefore flow through the

column quicker than smaller molecules, that is, the smaller the molecule, the longer the

retention time.[19]

ProcedureThe sample to be analyzed is introduced, in small volumes, into the stream of

mobile phase. The solution moved through the column is slowed by specific chemical or

physical interactions with the stationary phase present within the column. The velocity of

the solution depends on the nature of the sample and on the compositions of the

stationary (column) phase. The time at which a specific sample elutes (comes out of the

end of the column) is called the retention time; the retention time under particular

conditions is considered an identifying characteristic of a given sample. The use of

smaller particle size column packing (which creates higher backpressure) increases the

linear velocity giving the components less time to diffuse within the column, improving

the chromatogram resolution. Common solvents used include any miscible combination

of water or various organic liquids (the most common are methanol and acetonitrile).

Water may contain buffers or salts to assist in the separation of the sample components,

or compounds such as trifluoroacetic acid which acts as an ion pairing agent.

A further refinement ofHPLC is to vary the mobile phase composition during theanalysis; gradient elution. A normal gradient for reversed phase chromatography might

start at 5% methanol and progress linearly to 50% methanol over 25 minutes; the gradient

depends on how hydrophobic the sample is. The gradient separates the sample mixtures

as a function of the affinity. This partitioning process is similar to that which occurs

during a liquid-liquid extraction but is continuous, not step-wise. In this example, using a


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water/methanol gradient, more hydrophobic components will elute (come off the column)

when the mobile phase consists mostly of methanol (giving a relatively hydrophobic

mobile phase).

The choice of solvents, additives and gradient depend on the nature of the column

and sample. Often a series of tests are performed on the sample together with a number of

trial runs in order to find the HPLC method which gives the best peak separation.[19]

Graph

Figure 8.1 An example of a Plot of log mol. wt. versus Ve/Vo of a series of molecular

weight standards

Sample ProblemStandard solutions of polystyrene of known molecular weight were prepared and

the retention time of each solution was measured using size exclusion chromatography.

Prepare a plot of log MW versus retention time. Find the molecular weight of the

unknown with a retention time of 14.55.


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Table 8.1 Retention time of Polystyrene

MW Log MW Retention time (min)

6.75x106

6.829 12.78

5.99 x106 6.777 13.28

5.04 x106

6.702 13.77

4.27 x106

6.630 14.20

3.55 x106

6.550 14.76

Solution:

Figure 8.2

The equation of the line was found to be y = -0.1443x + 8.6836, let y = unknown

molecular weight. To solve for y:

y = -0.1443x + 8.6836

y = -0.1443(14.55)+ 8.6836

y = 6.5840

y = 106.5840

y = 3.84x106

y = -0.1443x + 8.6836

R = 0.9944

6.5

6.55

6.6

6.65

6.7

6.75

6.8

6.856.9

12.5 13 13.5 14 14.5 15

logMW

Retention time (tR)


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LIST OF REFERENCES

[1] http://en.wikipedia.org/wiki/Graph_%28mathematics%29

[2] http://spreadsheets.about.com/od/spreadsheetlessons/ss/excel_graph_use.htm

[3] http://www.ncsu.edu/scivis/chemistry.html

[4] http://www.ground-water-

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[5] http://www.cut-the-knot.org/Curriculum/Calculus/StraightLine.shtml

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[7] http://www.mathopenref.com/coordintercept.html

[8] http://en.wikipedia.org/wiki/Least_squares

[9] http://en.wikipedia.org/wiki/Calibration_curve

[10] http://www.chm.davidson.edu/vce/spectrophotometry/unknownsolution.html

[11] http://docs.google.com/viewer?a=v&q=cache:scrY_M8zXxkJ:www.asi-

sensors.com/ASI/learning/standard_addition.pdf+Standard+Addition+Method&hl=tl&gl

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o_xrOg8DvKxHpc-F9KB-wFlyKWo4cowgtHTLmgF02P6CaoHt6vGHuSvpXopPjRB9qT9-

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[12] http://en.wikipedia.org/wiki/Standard_addition

[13]http://www.google.com.ph/url?sa=t&rct=j&q=how%2Bto%2Bprepare%2Ba%2Bstan

dard%2BADDITION%2Bcurve&source=web&cd=4&ved=0CDMQFjAD&url=http%3A

%2F%2Fwww.asdlib.org%2FonlineArticles%2Fecourseware%2FAnalytical%2520Chem

istry%25202.0%2FText_Files_files%2FChapter5.pdf&ei=roStTuroDof9iQLZprWICw&

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[14] Fundamentals of Analytical Chemistry, 8th

ed., D. A. Skoog, D. M. West, F. J.

Holler, and S. R. Crouch. Brooks/cole, a division of Thomson Learning, 2004.

[15] http://www.answers.com/topic/spectrophotometric-titration

[16] http://accessscience.com/content/Titration/699100


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[17] http://www.answers.com/topic/potentiometric-titration-1

[18] http://en.wikipedia.org/wiki/High-performance_liquid_chromatography#Size-

exclusion_chromatography

[19] http://www.investopedia.com/terms/l/line-of-best-fit.asp#ixzz1cLBcCTQD

instru compensate

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