Chemistry 153
Clark College
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. Each student will receive a different unknown! You may pick your own number,
don’t forget to record the number in your lab notebook and on the Data Report Sheet. Store your
unknown in your lab drawer.
4. Whenever you handle unknown organic compounds, WEAR GLOVES!!!
5. Titrate a preliminary sample of your unknown roughly with phenolphthalein to determine
approximate equivalence point.
6. Perform two trials of your titration using the LoggerPro interfaces and the same batch of NaOH
that you standardized.
7. 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 blowup 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.
Potentiometric Titrations
Revised Spring 2008 NF
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Chemistry 153
Clark College
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
0.00
2.03
4.00
6.00
8.00
10.00
12.00
14.02
16.00
18.00
20.00
22.00
Potentiometric Titrations
pH
3.86
4.02
4.14
4.28
4.40
4.51
4.61
4.71
4.81
4.90
5.01
5.09
Corrected
Volume NaOH
24.00
26.00
28.00
30.00
32.00
34.00
35.00
35.21
35.39
35.60
35.79
36.00
pH
5.20
5.32
5.44
5.60
5.80
6.13
6.43
6.53
6.64
6.79
6.98
7.35
Revised Spring 2008 NF
Corrected
Volume NaOH
36.20
36.40
36.60
37.00
38.00
40.03
42.00
44.00
46.00
48.00
50.01
pH
9.29
9.84
10.17
10.50
10.87
11.23
11.40
11.53
11.63
11.70
11.77
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Chemistry 153
Clark College
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 halfequivalence 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)
H3
O+
(aq) + A- (aq)
 H+   A - 
Ka =
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 halfequivalence 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.
Figure 3 
Potentiometric Titrations
Expansion of the Half-Equivalence Point
5.30
5.20
5.10
pH
Table 2
Half-Equivalence Data
Vol NaOH mL
pH
14.02
4.71
16.00
4.81
18.00
4.90
20.00
5.01
22.00
5.09
24.00
5.20
5.00
4.90
4.80
4.70
4.60
13.00
15.00
17.00
19.00
21.00
23.00
25.00
Volume of NaOH (mL)
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Chemistry 153
Clark College
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
Volume NaOH
35.39
35.60
35.79
36.00
36.20
36.40
36.60
pH
6.64
6.79
6.98
7.35
9.29
9.84
10.17
First Derivative Data
∆pH
∆V
Vol. Avg.
0.15
0.19
0.37
1.94
0.55
0.33
0.21
0.19
0.21
0.20
0.20
0.20
∆pH/∆V
35.50
35.70
35.90
36.10
36.30
36.50
0.71
1.00
1.76
9.70
2.75
1.65
First Derivative Plot
12.00
10.00
²pH/²V
8.00
6.00
4.00
2.00
0.00
35.40
35.60
35.80
36.00
36.20
36.40
36.60
Average Volume NaOH (mL)
Figure 4
Potentiometric Titrations
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Chemistry 153
Clark College
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.
35.50
35.70
35.90
36.10
36.30
36.50
∆pH/∆
V
0.71
1.00
1.76
9.70
2.75
1.65
∆(∆V)
∆(∆pH/∆V)
V avg
∆(∆pH/∆V)/∆V
0.20
0.20
0.20
0.20
0.20
0.29
0.76
7.94
-6.95
-1.10
35.60
35.80
36.00
36.20
36.40
1.43
3.81
38.72
-34.75
-5.50
Second Derivative Curve
50
40
d2pH/dV2
30
20
10
0
35.4
-10
35.6
35.8
36
36.2
36.4
36.6
-20
-30
-40
Average Volume NaOH (mL)
Figure 5
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Chemistry 153
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Fortunately for us, LoggerPro generates the first and second derivative data automatically, so it is simply
a matter of plotting and analyzing the curves!
Assembling the Data
Once you have obtained the equivalence volumes and pKa’s, 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
Benzoic acid
Molar mass(g/mol)
122.1
pKa1
4.20
pKa2
Butanoic acid
88.10
4.83
3 – Chlorobenzoic acid
157.58
3.82
Maleic acid
116.04
1.92
6.23
Malonic acid
104.06
2.83
5.69
Oxalic acid
90.03
1.27
4.28
Phenoxyacetic acid
152.15
2.99
Potassium hydrogen phthalate
204.23
5.41
Succinic acid
118.1
4.19
Sodium hydrogen sulfite
104.06
7.21
d -Tartaric acid
150.09
3.04
m – Toluic acid
128.85
4.27
5.57
4.37
Reference Table taken from Lange’s Handbook of Chemistry, McGraw-Hill Book. Co. 1979, and
http://www.zirchrom.com/organic.htm (accessed April 9, 2008).
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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.
SAFETY INFORMATION: Use gloves whenever you are handling the solid unknown organic acid!
EXPERIMENTAL PROCEDURE
Obtain an unknown acid sample, and record the unknown number in your notebook. On each vial of
unknown 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 the
analytical balance, this is for a trial run!), and add 100 mL of distilled water. Do a phenolphthalein
titration 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 rinse
the electrode thoroughly with distilled water, collecting the waste.
1. Using the analytical balance, mass two samples of the unknown acid 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  Chemistry with Computers 
25 Titration dip acid. Make sure the vertical axis of the graph is pH scaled from 0 to 14 pH units
and 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 are
reused by other students. Place the electrode into the first buffer solution. Go to the menu and under
the Experiment open Calibrate. Click Calibrate now. The electrode will be reading a voltage–
when this has stabilized, type in the pH of your buffer into the “Enter Value” box under Reading 1
and then click Keep. Rinse your electrode and place it into the second buffer solution. When the
voltage has stabilized again, enter that pH value in the box under Reading 2 and click keep. Click
done to return to the graph and data table screen. Rinse the electrode and check your calibration 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 lower number,
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 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 0.00mL 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.
Potentiometric Titrations
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Chemistry 153
Clark College
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. You are now ready to continue the titration.
7. Add the next increment of NaOH titrant (enough to raise the pH about 0.20 units). Again click on
the Keep button and enter in the volume. You MUST wait for the pH to stabilize before clicking
Keep and 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 the pH is
constant or fluctuates between 2 numbers.
8. Continue adding NaOH solution in increments that raise the pH by about 0.20 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 less than 0.20 pH units. This will be increasingly
smaller volume increments.
9. After the curve flattens again, you may add NaOH solution in larger increments (going back to
changes of 0.20 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 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 your jump drive. 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 (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 the
data in APH 102, or install LoggerPro on your personal computer (contact me for this one). 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.
Potentiometric Titrations
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Chemistry 153
Clark College
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 need to generate graphs for each equivalence point and
analyze each equivalence (and half-equivalence) point.
Potentiometric Titrations
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Chemistry 153
Clark College
SAMPLE CALCULATIONS
Calculations in this experiment are the same as those in the Standardization of NaOH experiment
– please review them!
A. Weak Acid — Strong Base Titrations
The equivalence point of the titration occurs when the milliequivalents (meq) 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 weight (in g) x purity factor
equiv. weight (g/eq)
or, in a more familiar form
equiv. acid = g sample x
g acid
equiv acid
x
100 g sample
g acid
Example 1: A 0.8676 gram sample of a pure organic acid required 38.69 mL 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 = 0.8676 g acid x
1 equiv NaOH
1L
1
x
x
1 equiv acid
0.1042 equiv NaOH 0.03869L
Equiv Wt = 215.2 g/equiv (ppth precision)
Potentiometric Titrations
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Chemistry 153
Chem 135
Clark College
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.
(If applicable)
Equiv. Wt.
Molar Mass
pKa1
pKa2
Identity of
Unknown acid
Show sample calculations for Equiv. Wt and Molar Mass on the back.
Potentiometric Titrations
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Chemistry 153
Clark College
SHOW!! Sample calculations for Equiv. Wt. and Molar Mass
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Chemistry 153
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Chem 153
Potentiometric Titration of a Weak Acid
PRELAB
Name ________________________
Stamp here
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 a chemical reaction that represents the acid dissociation of benzoic acid in water and write the
equilibrium expression.
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 Potentiometric Titrations
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Chemistry 153
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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 of
NaOH is required to reach the equivalence point. What is the molar mass of this acid? (Use reg. sig
fig rules)
Molar Mass =
6. Look up the structures of the following acids and provide structural or line formulas for them.
Maleic Acid
Malonic Acid
Phenoxyacetic Acid
Succinic Acid
d-Tartaric Acid
m-Toluic Acid
Potentiometric Titrations
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