Determination of the First Dissociation Constant of Weak Acids
SCHA-266
Experiment 1
Apparatus: pH meter with electrode sodium hydroxide solution, about 0.1 M (standardized) unknown solution of a weak acid (100mL of approx. solution)
25-mL pipet buret, buret clamp, and ring stand
150-mL beaker
250-mL beakers (3) standard buffer solutions, pH 4, 7 and 10
General Theory
According to the Brønsted-Lowry acid-base theory, the strength of an acid is related to its ability to donate protons. All acid-base reactions are then competitions between bases of various strengths for these protons. For example, the strong acid HCl reacts with water according to Equation [1]:
HCl
( aq )
+ H
2
O
( l )

H
3
O
+
( aq )
+ Cl
-
( aq )
[1]
This is a strong acid and is completely dissociated (in other words, 100 percent dissociated) in dilute aqueous solution. Consequently, the [H
3
O
+
] concentration of a 0.1 M HCl solution is 0.1 M . Thus HCl is a stronger acid than water and completely donates a proton to water to form H
3
O
+
.
By contrast, acetic acid, HC
2
H
3
O
2
(abbreviated HOAc), is a weak acid and is only slightly dissociated, as shown in Equation [2]:
H
2
O( l ) + HOAc( aq ) H
3
O
+
( aq ) + OAc
-
( aq ) [2]
Its acid dissociation constant, as shown by Equation [3], is therefore small:
K a
=
[ H
3
O

][ OAc

]
[ HOAc ]
= 1.8 x 10
-5
[3]
Acetic acid only partially dissociates in aqueous solution, and an appreciable quantity of undissociated acetic acid remains in solution.
For the general weak acid HA the dissociation reaction and dissociation expression are:
[4] HA( aq ) + H
2
O( l ) H
3
O + ( aq ) + A
K a
=
[ H
3
O

][
[ HA ]
A

]
( aq )
[5]
SCHA-266 Page 1 Weak Monoprotic Acid

Recall that pH is defined as:
–log [H
3
O
+
] = pH [6]
Solving Equation [5] for [H
3
O
+
] and substituting this quantity into Equation [6] yields:
[H
3
O
+
] = K a
[ HA ]
[ A

]
[7]
–log [H
3
O
+
] = –log K a
– log
[ HA ]
[ A

]
[8] pH = p K a
– log
[ HA ]
[ A

]
[9] where p K a
= –log K a
If we titrate the weak acid HA with a base, there will be a point in the titration at which the number of equivalents of base is just one-half the number of equivalents of acid present (at ½ V e
). This is the point at which 50 percent of the acid has been titrated to produce A
-
and 50 percent remains as HA. At this point
[HA] = [A
-
], the ratio [HA]/[A
-
] = 1, and log [HA]/[A
-
] = 0. Hence, at this point in a titration, that is, at one-half the equivalence point, Equation [9] becomes pH = p K a
@ ½ V e
[10]
By titrating a weak acid with a strong base and recording the pH versus the volume of base added, one can determine the dissociation constant, K a
, of the weak acid. From the resultant titration curve we obtain the dissociation constant, as explained in the following paragraph.
From the titration curve (Figure 1), we see that at the point denoted as half the equivalence point, where
[HA] = [A ], the pH is 4.3. Thus, from Equation [10], at this point pH = p K a
, or p K a
= 4.30
–log K a
= 4.30 log
K a
K a
= – 4.30
= 5.0 x 10
-5
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12
8
pK a
= 4.30
6
4
2
½ equivalence point
Equivalence point
3.7 mL 7.4 mL
0
0 2 4 6
Volume of base added, mL

8 10 12
Figure 1.
Titration curve for the titration of the weak acid HA with a base.
(Your instructor will show you a graphical method for locating the equivalence point on your titration curves.)
Operation of the pH Meter
In order to measure the pH during the course of the titration, we shall use an electronic instrument called a pH meter. This device consists of a meter and two electrodes.
The main variations among different pH meters involve the positions of the control knobs and the types of electrodes and electrode-mounting devices. The measurement of pH requires two electrodes: a sensing electrode that is sensitive to [H
3
O
+
] concentrations, and a reference electrode. This is because the pH meter is really just a voltmeter that measures the electrical potential of a solution.
The reference electrode is just an electrode that develops a known potential that is essentially independent of the contents of the solution into which it is placed. The glass membrane electrode is sensitive to the H
3
O
+
concentration of the solution into which it is placed; its potential is a function of
[H
3
O
+
]. It operates by mobility of H
3
O
+
ions in the glass membrane. This can be more precisely described, but for our purposes here it is sufficient for you to understand that two electrodes are required.
These two electrodes are sometimes combined into an electrode called a combination electrode, which appears to be a single electrode. The combination electrode, however, does contain both a reference and a sensing electrode.
SCHA-266 Page 3 Weak Monoprotic Acid

Preliminary Operations with the pH meter
1. Obtain standard buffer solutions of known pH. (Try to conserve these. Use scintillation vials to hold these solutions.)
2. Plug in the pH meter to line current. Our meter will not require a warm up time. It should be left plugged in until you are completely finished with it however.
3. The meters used in the lab can read in units of mV or pH. Select the pH mode.
4. Prepare the electrodes . Make certain that the solution in the reference electrode extends well above the internal electrode. If it does not, ask your instructor to fill it with saturated KCl solution. Slide down the rubber collar on the reference electrode. Rinse the outsides well with distilled water. (Our electrodes now are gel filled and require no maintenance but your solution should be up to the white line which marks the reference junction)
5. Standardize the pH meter . Set the pH meter control to correct room temperature. Carefully immerse the electrodes into the first buffer solution in a small beaker. You should select the two buffers that will come close to the values you will measure (4 and 7 are a good starting pair).
Remember that the glass electrode is very fragile; it breaks easily!
Don’t touch the bottom of the beaker with the electrode surface!!
Set the function to “read” or “pH”. The meter will adjust itself to the value of the buffer you have placed it in. When the meter indicates ready then hit yes, rinse the electrode with distilled water and move it to the next buffer. When this value is obtained enter yes. Record the slope that is briefly displayed. . The pH meter is now ready to measure pH.
RECORD ALL DATA DIRECTLY INTO YOUR NOTEBOOK!
Procedure
A. Determination of pK a
of Unknown Acid.
With the aid of a pipet bulb, pipet a 25.00 mL aliquot of your unknown acid solution into a 250-mL beaker and carefully immerse the previously rinsed electrode into this solution. Measure the pH of this solution. Record the pH in your notebook. Begin your titration by adding 1 mL of your standardized base from a buret and record the volume of titrant and pH. Repeat with successive additions of 1 mL of base until you approach the end point; then add 0.1-mL increments of base and record the pH and milliliters of NaOH added. For the first run plot your titration in your lab book as it progresses. When the pH has gone through a major jump in value you may discontinue data collection. From these data plot a titration curve of pH versus mL titrant added. Repeat the titration with two more 25-mL aliquots of your unknown acid and plot the titration curves. From these curves calculate the ionization constant.
Time may be saved if the first titration is run with larger-volume increments of the titrant to locate an approximate equivalence point; then the second and third titrations may be run with the small increments indicated above. Once you know your approximate endpoint you might wish to collect higher density of points in the V e
/2 region.
B. Concentration of Unknown Acid
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Using the volume at the equivalence point, calculate the concentration of the unknown acid, and record this in your notebook.
Prelab Questions
Before beginning this experiment in the laboratory, you should be able to answer the following questions:
1. Define Brønsted-Lowry acids and bases.
2. Why isn’t the pH at the equivalence point always equal to 7 in a neutralization titration? When would it be 7?
3. What is the p K a
of an acid whose K a
is 2.4 x 10
-5
?
4. What is a buffer solution?
5. The pH at one-half the equivalence point in an acid-base titration was found to be 5.8. What is the value of K a for this unknown acid?
6. If 30.15 mL of 0.0995 M NaOH is required to neutralize 0.180 g of an unknown acid, HA, what is the
molecular weight of the unknown acid?
Report
1.
Prepare and abstract for this lab to include with your report.
2.
Provide properly labeled Data Tables for the data you have collected for the experiment.
3.
Provide Excel plots of the titrations, properly labeled as Figures.
4.
Provide first and second derivative plots of the three titrations. See Table 11-3 (page 210) in your text for how to construct these plots. These will be additional figures for your report.
5.
Provide a Results Table with the endpoints and pKa values determined.
6.
Give a brief Results and Discussion section. Propose an acid that might be your unknown and explain the difference from the book pKa value.
7.
The answers to the above questions should be in your report. They may be on your lab notebook pages but they must be readable.
8.
A copy of the notebook pages should be included. They should contain one plot. (as above)
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