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Chemistry 135 Clark College

Potentiometric Titrations Revised Spring 2007 NF Page 1 of 14

POTENTIOMETRIC TITRATION OF A WEAK ACIDA 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 beforeyou begin the experiment.3. Obtain an unknown organic acid and record the unknown code in your notebook and on the data

report sheet. Each student will receive a different unknown! You may pick your own number,dont forget to record the number in your lab notebook and on the Data Report Sheet. Store yourunknown in your lab drawer.

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

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

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

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 blowup of the pKa/buffer region.

Introduction

In a potentiometric titration one makes a graph of the volume of titrant delivered from a buretagainst the voltage (or some function directly related to the voltage, such as pH) produced by twoelectrodes in the solution being titrated. Provided the equilibrium of the analytical reaction is favorableand 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 theequivalence point. This is obviously a very useful technique if one is dealing with a colored solution inwhich 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 alsobe used with redox reactions, precipitation reactions and complex formation reactions, as well astitrations in non-aqueous systems. Furthermore, although the present experiment may give theimpression that the technique is slow, it can, in routine work, be made just as rapid as titrations usingvisual indicators, and often gives more accurate results.

The choice of electrodes is critical. One electrode, called the reference electrode, must hold aconstant potential throughout the titration, regardless of the concentration of various reagents in thesolution. 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 titrationsare almost always a calomel reference electrode and a glass indicator electrode. The potential of theglass electrode depends directly on the hydrogen ion activity in solution, whereas the potential of thecalomel electrode is constant because it is isolated from the solution being titrated by a salt bridge.


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A pH meter, or pH amplifier, such as the one used in this experiment, is essentially an electronicvoltmeter. However, through calibration, its output reads directly in pH units instead of volts. Theapparatus is sketched in Figure 1. One performs the titration by adding increments of titrant from theburet 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 thepoint of maximum slope. You will notice, however, that the volume scale of such a graph is toocompressed to read the equivalence point to 0.02 mL as required in order to obtain part-per-thousandaccuracy. One may prepare a second graph in which one plots the region from about 1-2 mL before theequivalence point to 1-2 mL beyond, as illustrated in Figure 3. The operator must judge the inflectionpoint. The volume scale is now large enough that the volume at the inflection point can be read to thenearest 0.02 mL. The main sources of error are the failure to draw a smooth curve through the datapoints and in judging the location of the inflection point. The latter error is somewhat analogous to atitration using a color indicator in which the main source of error is the operator's judgment as to thecolor at the end point. We will also use other mathematical methods to help determine the equivalencepoint.

TABLE 1 Sample Titration Data

CorrectedVolume NaOH pH CorrectedVolume NaOH pH CorrectedVolume NaOHpH0.00 3.86 24.00 5.20 36.20 9.292.03 4.02 26.00 5.32 36.40 9.844.00 4.14 28.00 5.44 36.60 10.176.00 4.28 30.00 5.60 37.00 10.508.00 4.40 32.00 5.80 38.00 10.8710.00 4.51 34.00 6.13 40.03 11.2312.00 4.61 35.00 6.43 42.00 11.4014.02 4.71 35.21 6.53 44.00 11.5316.00 4.81 35.39 6.64 46.00 11.6318.00 4.90 35.60 6.79 48.00 11.7020.00 5.01 35.79 6.98 50.01 11.7722.00 5.09 36.00 7.35


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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 volumeof 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 aciddissociation 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 conjugatebase. 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 sametitration 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. Somedisagreement in pKa from handbook is typical, and is a result of the use of molar concentrations in placeof activities in the expression for the equilibrium constant. Nevertheless, it is valuable informationwhen seeking to identify unknown acids.

Table 2Half-Equivalence Data

Vol NaOH mL pH14.02 4.7116.00 4.8118.00 4.9020.00 5.0122.00 5.0924.00 5.20

Figure 3


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First Derivative Plot

We noted above that at the equivalence point, the slope of the titration curve is at a maximum. Inother 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 isconveniently done by adding equal increments of titrant near the equivalence point. Consider the datacollected during a titration, as shown in Table 3. We want to plot pH/V against the volume to get thefirst derivative. Such a plot is shown in Figure 4. The volume used is the average of the two volumesused to calculate pH. So, the volume forpH/V = 0.71 is 35.50 mL, and so on. The equivalencepoint is the maximum of this plot, which, when extrapolated, occurs at 36.10 mL. This extrapolationleads 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 beenplotted in place ofpH/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 notjustified in reporting the equivalence point to more than 0.01 mL.

Table 3

First Derivative DataVolume NaOH pH pH V Vol. Avg. pH/V

35.39 6.6435.60 6.79 0.15 0.21 35.50 0.7135.79 6.98 0.19 0.19 35.70 1.0036.00 7.35 0.37 0.21 35.90 1.7636.20 9.29 1.94 0.20 36.10 9.7036.40 9.84 0.55 0.20 36.30 2.7536.60 10.17 0.33 0.20 36.50 1.65

Figure 4


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Second Derivative Plot

Mathematically, the second derivative of a titration curve should pass through zero at theequivalence 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 theaverage volume. The average of the two successive volumes used for the first derivative plot is alsoused for the second derivative plot (Figure 5). Again, there is some extrapolation, but it is lesssignificant than in the first derivative plot. The equivalence point is taken as 36.11 mL. As before, weare 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 besufficient points near the equivalence point.

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

Table 4

Second Derivative DataVol. Avg.

pH/V (V) (pH/V) V avg (pH/V)/V

35.50 0.7135.70 1.00 0.20 0.29 35.60 1.4335.90 1.76 0.20 0.76 35.80 3.8136.10 9.70 0.20 7.94 36.00 38.7236.30 2.75 0.20 -6.95 36.20 -34.7536.50 1.65 0.20 -1.10 36.40 -5.50

Figure 5


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Fortunately for us, LoggerPro generates the first and second derivative data automatically, so it is simplya matter of plotting and analyzing the curves!

Assembling the Data

Once you have obtained the equivalence volumes and pKas, you can use that information todetermine the identity of your unknown acid. The molecular weight can be determined from theequivalence 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 titrationcurve, some diprotic acids appear to have only one equivalence point, if the two pKa values are less than2 pH units apart. However, the resulting calculated molecular weight will be the equivalent weight, andthus will be one-half the molecular weight. It is a match (or near-match) of both the pKa and molecularweight data that determines the identity of your unknown acid. Table 5 gives a list of possible organicacids for this experiment.

Table 5 Selected Physical Data for Organic Acids

Acid Molar mass(g/mol) pKa1 pKa2Benzoic acid 122.1 4.202 Chlorobenzoic acid 157.58 2.944 Chlorobenzoic acid 157.58 3.99trans Crotonic acid 86.09 4.69Maleic acid 116.04 1.92 6.23Malonic acid 104.06 2.83 5.69Potassium hydrogen phthalate 204.23 5.41Succinic acid 118.1 4.19 5.57Sodium hydrogen sulfite 104.06 7.21d-Tartaric acid 150.09 3.04 4.37m Toluic acid 128.85 4.27

Reference Table taken fromLanges Handbook of Chemistry, McGraw-Hill Book. Co. 1979.


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NOTES

Note 1: Buret readings must be made to the nearest 0.01 mL and the pH meter should be readto 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 tocalculate from the sample weights the location of the equivalence point in the second sample.

EXPERIMENTAL PROCEDURE

Obtain an unknown acid sample, and record the unknown number in your notebook. On each vial ofunknown acid, a mass range is listed. Use this amount for each titration you perform.

Equivalent Weight Estimate

Weight out an appropriate of acid (as listed on your vial) into a 250 mL Erlenmeyer flask (don't use theanalytical balance, this is for a trial run!), and add 100 mL of distilled water. Do a phenolphthaleintitration and calculate the approximate equivalent weight of your unknown organic acid.

Potentiometric Titration

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 rinsethe electrode thoroughly with distilled water, collecting the waste.

1. Using the analytical balance, mass two samples of the unknown acid as calculated above into two250-mL beakers. Record the mass to the nearest 0.0001 g. Dissolve each in about 100 mL ofdistilled water and cover each with a watch glass.

2. Prepare the computer for data collection by opening ExperimentChemistry with Computers25 Titration dip acid. Make sure the vertical axis of the graph is pH scaled from 0 to 14 pH unitsand the horizontal axis reads 0 to 50mL. Change the axes as necessary.

3. Do not start to calibrate without having the buffers ready to use. Obtain two buffer solutions,one each of buffer pH 4 and buffer pH 7. Do not contaminate or dilute these solutions! They canbe reused by other groups. Place the electrode into the first buffer solution. Go to the menu andunder the Experiment open Calibrate. Click Calibrate now. The electrode will be reading avoltage when this has stabilized, type in the pH of your buffer into the Enter Value box underReading 1 and then clickKeep. Rinse your electrode and place it into the second buffer solution.When the voltage has stabilized again, enter that pH value in the box underReading 2 and clickkeep. Click done to return to the graph and data table screen. Rinse the electrode and check yourcalibration with the other buffer and make sure it is stable. If your pH value is significantly different(0.05 pH units) than the buffer you are checking, or if the value drifts slowly to a higher or lowernumber, contact your lab instructor.

4. Obtain a clean 50-mL buret and rinse the buret with a few mL of the ~0.1 M NaOH solution youhave standardized in the last experiment. Dispose of the rinse solution into your waste beaker. Use aburet 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 intothe waste beaker so it fills the buret tip and leaves the NaOH at the 0.00 mL level of the buret. Besure 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 pHelectrode on a ring stand, and a buret clamp to attach the buret to the ring stand. Place a stir bar inone of your acid solutions to use a magnetic stirplate. Position the pH electrode in the acid solutionand adjust its position so that it is not struck by the stir bar. Do not place the magnetic stirrer closeto a computer, the magnet interferes with the monitor!


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

7. Add the next increment of NaOH titrant (enough to raise the pH about 0.30 units). Again click onthe Keep button and enter in the volume. You MUST wait for the pH to stabilize before clicking

Keepand entering your NaOH volume there is a delay between when the NaOH is added and

when the solution is properly stirred and the pH stabilizes. You should wait until the last digit of thepH is constant or fluctuates between 2 numbers.

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

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

10.Dispose of any waste beaker contents into the appropriate product collection container.Treatment of Potentiometric DataPart of your grade will be determined by your manipulation of the data so that the graphs and tables areappropriate.

1. Save your data on your jump drive. You files should be titled with your initials and whether this isthe first or second titration, e.g. NFacid1. Be sure you save with your initials or other notation sothat you (and I) can keep the different trials separate (if you need to e-mail me your data).

NOTE: You may save your data, then you may come back and manipulate the data later, work on thedata in APH 102, or install LoggerPro on your personal computer (contact me for this one). InLogger 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 thesecond derivative equals zero. Change the scales on the x- and y- axes to give an expanded graph inthe window and find the point where the line crosses the x-axis using the Analyze menu. Then printthe graph.

7. Now that you have the equivalence pt. volume of NaOH, go back to the original titration curve andexpand the region about the half-equivalence pt. You may use the Analyze menu to find the pH atthe 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 thecomputer screen as needed.

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


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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 oneach 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 analyze derivative curves only for the second equivalence

point (and half-equiv point): However, you will need to treat each equivalence point and half-equivalence point separately for calculations.


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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. ShowSample Calculations on the back of this page!

Trial 1 Trial 2 AverageSample Mass (g)VNaOH, 1

st Equiv. pt.VNaOH, 2

ndEquiv pt.

(If applicable)Equiv. Wt.Molar MasspKa1pKa2Identity ofUnknown acid

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


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Sample calculations for Equiv. Wt. and Molar Mass


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

3. Write a chemical equation which represents the acid dissociation constant for benzoic acid.

4. For a weak acid titrated with a strong base, where does the pH = pKa?a) At the equivalence point.

b) At the half-equivalence point.

c) At the beginning of the titration.

- over -


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5. A 0.2292 g sample of an unknown monoprotic acid is titrated with 0.1124 N NaOH. 24.79 mL ofNaOH is required to reach the equivalence point. What is the molar mass of this acid?

Molar Mass =

6. Look up the structures of the following acids and provide structural formulas for them.

trans-Crotonic acid Maleic Acid Malonic Acid

Succinic Acid d-Tartaric Acid m-Toluic Acid

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