Determining the Equivalent Mass and Dissociation Constant of an
Unknown Weak Acid by Titrimetry
Adam Capriola
CHM 1122 Section 155
February 28, 2007
Unknown Label: T
Introduction
Acids are substances that donate hydrogen ions and bases are substances that accept
hydrogen ions. Acids and bases react with each other by transferring hydrogen ions. One way to
distinguish an acid is by its equivalent mass, which is the number of grams of the acid needed to
transfer one mole of hydrogen ion to a base. For a monoprotic acid, which only transfers one
hydrogen ion, its equivalent mass equals its molar mass. For a diprotic acid, which transfers two
hydrogen ions, its equivalent mass equals half its molar mass. The equivalent mass of a base is
simply the number of grams required to accept one mole of hydrogen ion. The equivalent mass
of an acid or base is also equal to the mass of the acid or base titrated divided by the number of
equivalents of the acid or base.
Acid strength is measured by how much it dissociates. This is determined by the amount
of hydronium ion formed in water. Most often, it is expressed by pH, which equals the
–log[H3O+]. The equilibrium constant for an acid is represented by Ka = [H3O+] [A-] / [HA],
where HA is the acid and A- is the dissociated acid. When comparing Ka’s, most commonly pKa
is used, which is equal to –log Ka.
In this experiment, the pKa of an unknown acid is determined by titrating it with NaOH
and graphing its pH levels versus volume of NaOH titrated. The inflection point found by
graphing is the equivalence point, and at half that volume is the half-equivalence point. At half
equivalence, the [A-] = [HA], so they cancel out in the equation Ka = [H3O+] [A-] / [HA], leaving
Ka = [H3O+]. With pH being known, Ka is found by [H3O+] equaling 10-pH, and pKa = pH.
Experimental
First, about 2 g of an unknown weak acid was obtained. Then about 0.10 to 0.12 g of the
acid was weighed out on an analytical scale. This mass was recorded to 4 decimal places. The
acid was then transferred to a clean 125 mL Erlenmeyer flask. Distilled water was added to
dissolve the acid, and then 3 drops of phenolphthalein indicator was added to the solution. Next,
a buret was filled with NaOH solution and its initial reading was recorded to 2 decimal places.
The acid solution was titrated with the NaOH solution until the acid solution turned and stayed
pink. This final reading was recorded to 2 decimal places and the volume of NaOH used was
calculated.
Another sample of unknown acid was weighed out using an analytical scale requiring
about 25 mL of standardized NaOH solution. This mass was recorded to 4 decimal places. The
acid was transferred into a clean 150 mL beaker, and was again dissolved using distilled water.
A pH meter and electrode was then obtained. The electrode was rinsed with distilled water and
put into the acid solution. Standardized NaOH solution was again used to titrate the acid. The
initial buret reading was recorded to 2 decimal places and NaOH was added 0.5 mL at a time.
After every portion added, the buret reading and pH meter reading were recorded to 2 decimal
places. This was done until the pH spiked and stopped increasing significantly.
Results
Identification code of weak unknown acid
Mass of unknown acid, g
Final buret reading, mL
Initial buret reading, mL
Volume of NaOH solution required, mL
Concentration of NaOH solution used, M
T
0.1167
14.37
0.75
13.62
1.00 x 10-1
Mass of unknown acid requiring 25 mL of
NaOH solution for titration, g
Mass of unknown acid used, g
Buret Reading, mL
0.50
0.99
1.50
2.00
2.49
3.00
3.49
4.00
4.50
4.99
5.49
6.01
6.50
6.99
7.50
7.99
8.50
8.98
9.50
10.00
10.48
11.00
11.48
12.00
12.50
13.00
13.49
13.98
14.49
15.00
15.50
15.99
16.50
17.00
17.49
17.99
18.50
19.00
19.50
pH
2.95
3.07
3.22
3.38
3.50
3.60
3.70
3.78
3.86
3.92
3.99
4.04
4.09
4.14
4.19
4.23
4.28
4.32
4.36
4.40
4.43
4.47
4.51
4.55
4.59
4.62
4.66
4.69
4.73
4.77
4.80
4.84
4.88
4.92
4.96
5.00
5.05
5.09
5.14
0.2142
0.2152
19.99
20.48
20.99
21.50
22.00
22.50
23.00
23.50
24.00
24.50
25.00
25.50
25.99
26.50
27.00
27.48
27.99
28.50
28.99
29.50
30.00
30.50
31.00
32.02
33.01
5.19
5.23
5.30
5.36
5.43
5.50
5.59
5.70
5.83
6.02
6.30
6.88
10.18
10.73
10.98
11.13
11.23
11.32
11.38
11.44
11.49
11.53
11.57
11.63
11.68
pH vs. Volume of NaOH
14
12
pH
10
8
6
4
2
0
0
5
10
15
20
Volume of NaOH (mL)
Equivalence Point, mL
25.75
25
30
35
Half-Equivalence Point, mL
Half-Equivalence pH
Ka
pKa
pKa of trans-crotonic
Percent Error
12.88
4.62
2.40 x 10-5
4.62
4.69
1.49%
Number of equivalents of NaOH, equiv.
Number of equivalents of acid titrated, equiv.
Equivalent mass of acid, g/equiv.
Equivalent mass of trans-crotonic, g/equiv.
Percent Error
2.58 x 10-3
2.58 x 10-3
83.41
86.09
3.11%
Calculations
In order to find the volume of NaOH used, I subtracted the initial buret reading from the
final reading (14.37 mL - 0.75 mL = 13.62 mL). To find the mass of unknown acid needed using
25 mL of NaOH solution, I used a proportion. The proportion was 0.1167 g / 13.62 mL = x /
25.00 mL, with x equaling the mass of unknown acid needed. To find the half-equivalence
point, I divided the equivalence point volume by 2. I then just looked at the graph to find the pH
at the half-equivalence point. The pKa is equal to the pH, which was 4.62. The Ka is equal to the
concentration of [H3O+]. [H3O+] is equal to 10-pH, so using my numbers, 10-4.62 = 2.40 x 10-5. To
find percent error, I took the theoretical pKa – my found pKa, divided by the theoretical pKa, and
multiplied by 100%. Using my numbers, (4.69 – 4.62) / 4.69 x 100% = 1.49%. In order to find
the number of equivalents of NaOH, I took the volume at the equivalence point (25.75 x 10-3 L)
and multiplied by the molarity (1.00 x 10-1 M). The number of equivalents of acid titrated was
equal to the equivalents of NaOH. Finally, to find the equivalent mass of the acid, I divided the
mass of the acid used by the number of equivalents of acid. Using my numbers, 0.2152 g / 2.58
x 10-3 equiv. = 83.41 g/equiv.
Discussion/Conclusions
Looking at the table in the lab book, the acid with the closest pKa to my calculated pKa is
trans-crotonic. It has a pKa of 4.69 while my calculated pKa was 4.62. I feel that these numbers
are very close, as the percent error is only 1.49%. The percent error for my calculated equivalent
mass of the acid is also small at 3.11%. Error could have come from reading the graph, as I had
to estimate the equivalence point. I should have taken measurements at smaller intervals when
approaching the inflection point. This would have allowed me to read the graph more
accurately. Error could have also come from the pH meter, which may not have been calibrated
precisely. Lastly, error could have resulted if I inaccurately read the buret while recording the
readings.