# Potentiometric Determination lab

Figure out how to get the graphs and the inflection point of each trial.

Quantitative Analysis Lab 2260
POTENTIOMETRIC DETERMINATION OF FORMULA WEIGHT AND
DISSOCIATION CONSTANTS OF AN ACID
Background
An acid can be identified by determining its molecular weight and its acid dissociation
constant(s). This is readily done by measuring the pH of a solution of the acid during its titration
with a strong base. A pH meter fitted with a glass/reference electrode system and a magnetic
stirrer is used. The pH is measured at enough points to show all of the inflection points clearly and
also give several points within each buffer region. This method is referred to as a potentiometric
titration, in which the potential is measured across the analyte and no indicator is needed.
It is important that pH be measured at one drop (or less) increments at and near the
equivalence point of the titration. The volume of titrant required to reach each inflection point,
Ve, may be calculated as the volume of the titrant corresponding to the point of maximum slope
for a plot of pH vs. volume of the titrant. This value can be determined graphically from the plot
or by plotting the first or second derivative of the titration curve.
To plot the first derivative, calculate the slope of the titration curve (pH/V) at small
intervals over the titration curve and plot this against volume. This gives the first derivative and
indicates the inflection point (equivalence point) in the form of a maximum.
The second derivative can be obtained by taking the derivative of the first derivative data
to obtain the rate of change of the slope. In other words, calculate the slope of the 1 st derivative
curve ((pH/V)/V) and plot that against volume (V). In this instance the plot is characterized
by a maximum which sharply passes through zero and then goes to a minimum. The point indicates
the equivalence point where it crosses through zero.
1. Once the inflection point (Ve) is known, the molarity of the titrant, and the mass of acid
titrated, one may calculate the molecular weight of the unknown acid.
2. Determination of Ka is based on the treatment of the equilibrium
HA
H+ + A-
for which the following expression can be written:
[𝐻 + ]
5-1
𝐶𝐻𝐴 − [𝐻 + ]
𝐶𝐻𝐴
(1 − 𝑥)
= 𝐾𝑎 ∗

𝐾

=
𝐾

𝑎
𝑎
𝐶𝑁𝑎𝐴 − [𝐻 + ]
𝐶𝑁𝑎𝐴
𝑥
Quantitative Analysis Lab 2260
Where x is the fraction of HA neutralized at volume V, i.e., x = V/V e. Alternatively, one can
convert the above relationship to a logarithmic form, e.g.
𝑃𝐾𝑎 = 𝑝𝐻 + 𝑙𝑜𝑔
(1 − 𝑥)
𝑥
If the titration curve shows two (or more) distinct inflection points, then the sample is a
diprotic or polyprotic acid and multiple pKa values may be obtained, e.g. pKa1 and pKa2…etc. These
can be determined as described above using x = V/Ve1 and the points from the first buffer region
for pK1 and x = [ (V – Ve1) / (Ve2 – Ve1)] and the points from the second buffer region for pK2.
Sometimes only one inflection point is observed, even so, the acid may still be diprotic. If
the inflection of the second equivalence point corresponding to NaHA has disappeared because
the ratio of (K1 / K2) is too small, the simple practice of reading the pH at the apparent half
equivalence will yield a value of “𝐾𝑎 ” = √𝐾1 𝐾2. If the inflection point corresponding to Na2A is
indistinct because K2 is too small, one calculates pK1 as before, taking the observed inflection point
volume as Ve1 and twice that volume as Ve2.
Procedure
1.
Prepare and standardize a 0.1 M NaOH solution following the procedure described in
the soda ash determination. If you have sufficient NaOH left over from the soda ash
determination and you are confident of its molarity, you may use it here. Calculate how
much you will need from the procedure below.
2.
Obtain an unknown acid, but do not dry it unless specifically instructed to do so. Weigh
out one sample (as instructed in lab) and dissolve it in 100 mL of distilled water in a 250
mL beaker. If necessary, add more water or you may speed dissolution by heating a
little. However, cool the solution back to room temperature before beginning the
titration. Be sure that the entire sample has dissolved.
3.
Have your laboratory instructor familiarize you with the operation of the pH meter.
The following precautions should be observed.
a.
b.
c.
d.
5-2
Let the meter warm up for at least 15 minutes before using it.
Handle the electrodes carefully, especially protecting the tip since they are
fragile and expensive.
Always return the meter to STANDBY when removing the electrodes from a
solution.
When you are through, leave the electrodes soaking in distilled water and the
meter set on standby.
Quantitative Analysis Lab 2260
4.
Calibrate the meter before each use with the reference buffer solutions provided. To
avoid contamination of the standard buffer, rinse the electrodes with distilled water
and dry them with a soft tissue before immersing them in the buffer. Also rinse and dry
the electrodes before immersing them in your sample solution.
5.
Titrate the sample potentiometrically with standard NaOH. Set the stirrer for efficient
stirring. Do a careful titration to locate the equivalence points, adding ~0.5-1 mL
increments until a little beyond the inflection point as indicated by a clear maximum
change in pH for each volume increment. Keep adding the titrant at ~0.5-1 mL
increments through a possible second inflection point and clearly beyond it. NOTE: At
this point the pH should be somewhat above 10 or 11. If not, consult your laboratory
instructor.
6.
Weigh out two more samples and do two more titrations. Now that you know
approximately where the inflection point(s) are, be sure to take readings at 4 to 5
points within the first buffer region and then take readings carefully drop-by-drop
around -2 mL to +2 mL of the inflection point. Repeat this process for the second
equivalence point.
7.
For each trial create three graphs: One graph for the titration, one for the first
derivative, and one for the second derivative. (Use Excel or an equivalent spreadsheet
program).
Questions
1. Calculate and report the molecular weight of the unknown acid.
2. Calculate the pKa value(s) for your unknown acid from each of the graphs and determine
the average and standard deviation.
3. Use the molecular weight and average pka value(s) to identify the unknown acid from a
provided table of possibilities.
Safety note: Please observe the utmost care in doing this lab. It calls for careful work and
concentration on the tasks involved. Keeping your bench top organized is a good way to make the
results more reliable.
5-3
NaOH and KHP Titration
Trial 1
Volume (mL)
1
2
3
5
7
9
11
13
15
17
19
20
21
22
23
24
25
26
26.5
27
27.5
28
28.5
29
29.5
30
30.5
31
31.5
32
32.5
32.7
33
33.2
33.4
33.5
pHi = 3.91
pH
4
4.08
4.2
4.34
4.48
4.6
4.71
4.82
4.92
5.03
5.13
5.18
5.23
5.29
5.35
5.41
5.48
5.55
5.59
5.63
5.68
5.72
5.77
5.82
5.88
5.94
6.01
6.1
6.19
6.3
6.47
6.62
6.72
6.87
7.1
7.48
(0 mL vol. and ∆ for all inititially)
∆Volume (mL)
1
1
1
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.3
0.2
0.2
0.1
.7822 g KHP
∆pH
0.09
0.08
0.12
0.14
0.14
0.12
0.11
0.11
0.1
0.11
0.1
0.05
0.05
0.06
0.06
0.06
0.07
0.07
0.04
0.04
0.05
0.04
0.05
0.05
0.06
0.06
0.07
0.09
0.09
0.11
0.17
0.15
0.1
0.15
0.23
0.38
Trial 2
Volume (mL)
5
10
15
17
19
pHi = 3.92
pH
4.33
4.64
4.9
5
5.1
(0 mL vol. and ∆ for all inititially)
∆Volume (mL)
5
5
5
2
2
.8106 g KHP
∆pH
0.41
0.31
0.26
0.1
0.1
21
22
23
24
25
25.5
26
26.5
27
27.5
28
28.5
29
29.5
30
30.5
31
31.2
31.5
31.7
32
32.2
32.5
32.7
32.9
33.1
33.3
33.5
33.7
33.9
34.1
34.2
34.3
34.4
34.45
34.5
34.6
35
35.5
36
37
38
39
40
5.2
5.25
5.3
5.37
5.43
5.46
5.49
5.52
5.56
5.6
5.63
5.68
5.72
5.77
5.82
5.88
5.94
5.96
6.01
6.04
6.09
6.12
6.17
6.22
6.27
6.33
6.38
6.45
6.52
6.61
6.7
6.76
6.8
6.94
7
7.06
7.14
9.97
10.81
11.09
11.39
11.58
11.68
11.77
2
1
1
1
1
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.05
0.05
0.1
0.4
0.5
0.5
1
1
1
1
0.1
0.05
0.05
0.07
0.06
0.03
0.03
0.03
0.04
0.04
0.03
0.05
0.04
0.05
0.05
0.06
0.06
0.02
0.05
0.03
0.05
0.03
0.05
0.05
0.05
0.06
0.05
0.07
0.07
0.09
0.09
0.06
0.04
0.14
0.06
0.06
0.08
2.83
0.84
0.28
0.3
0.19
0.1
0.09
Trial 3
Volume (mL)
pHi = 3.91
pH
(0 mL vol. and ∆ for all inititially)
∆Volume (mL)
.8819 g KHP
∆pH
5
10
15
17.1
19
21
23
25
27
29
31
32
33
33.5
34
34.5
34.7
35
35.2
35.5
35.7
36
36.2
36.4
36.6
36.8
37
37.1
37.25
37.3
37.4
37.5
37.6
37.7
37.8
38
40.1
41
4.3
4.59
4.83
4.94
5.02
5.11
5.2
5.3
5.42
5.53
5.67
5.76
5.86
5.92
5.98
6.05
6.08
6.14
6.18
6.22
6.29
6.34
6.41
6.47
6.54
6.63
6.72
6.8
6.93
6.97
7.02
7.08
7.4
7.73
9.33
9.95
11.43
11.56
5
5
5
2.1
1.9
2
2
2
2
2
2
1
1
0.5
0.5
0.5
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.2
0.2
0.2
0.2
0.1
0.15
0.05
0.1
0.1
0.1
0.1
0.1
0.2
2.1
0.9
0.39
0.29
0.24
0.11
0.08
0.09
0.09
0.1
0.12
0.11
0.14
0.09
0.1
0.06
0.06
0.07
0.03
0.06
0.04
0.04
0.07
0.05
0.07
0.06
0.07
0.09
0.09
0.08
0.13
0.04
0.05
0.06
0.32
0.33
1.6
0.62
1.48
0.13
Potentiometric Titration of an Acid
Trial 1
Volume (mL)
0.5
1
1.5
2
2.5
pHi = 2.08
pH
2.1
2.11
2.13
2.15
2.18
(0 mL vol. and ∆ for all inititially)
∆Volume (mL)
0.5
0.5
0.5
0.5
0.5
.2608 g unknown
∆pH
0.02
0.01
0.02
0.02
0.03
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.6
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
17.5
18
18.5
19
19.5
20
20.5
21
21.6
22
22.5
23
23.5
24
24.5
25
25.5
26
2.2
2.24
2.27
2.3
2.32
2.35
2.38
2.41
2.44
2.47
2.5
2.53
2.56
2.6
2.62
2.65
2.68
2.71
2.75
2.78
2.82
2.85
2.89
2.93
2.98
3.02
3.06
3.11
3.16
3.21
3.26
3.32
3.4
3.47
3.54
3.64
3.73
3.86
3.96
4.08
4.19
4.29
4.4
4.48
4.56
4.63
4.7
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.4
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.4
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.02
0.04
0.03
0.03
0.02
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.03
0.04
0.02
0.03
0.03
0.03
0.04
0.03
0.04
0.03
0.04
0.04
0.05
0.04
0.04
0.05
0.05
0.05
0.05
0.06
0.08
0.07
0.07
0.1
0.09
0.13
0.1
0.12
0.11
0.1
0.11
0.08
0.08
0.07
0.07
26.5
27
27.5
28
28.5
29
29.5
30
30.5
31
31.5
32
32.5
33
33.5
34
34.5
35
35.5
36
36.5
37
37.5
38
38.5
39
39.5
40
40.5
40.7
41
41.2
41.5
41.7
42
42.2
42.5
42.7
43
43.2
43.5
43.7
43.8
43.9
44
44.2
44.5
4.75
4.81
4.86
4.91
4.96
5
5.05
5.09
5.12
5.17
5.2
5.24
5.29
5.31
5.35
5.39
5.43
5.48
5.52
5.56
5.6
5.64
5.68
5.73
5.79
5.83
5.9
5.95
6.03
6.05
6.09
6.13
6.18
6.21
6.28
6.33
6.39
6.45
6.53
6.63
6.8
6.95
7
7.12
7.31
7.64
9.85
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.3
0.2
0.1
0.1
0.1
0.2
0.3
0.05
0.06
0.05
0.05
0.05
0.04
0.05
0.04
0.03
0.05
0.03
0.04
0.05
0.02
0.04
0.04
0.04
0.05
0.04
0.04
0.04
0.04
0.04
0.05
0.06
0.04
0.07
0.05
0.08
0.02
0.04
0.04
0.05
0.03
0.07
0.05
0.06
0.06
0.08
0.1
0.17
0.15
0.05
0.12
0.19
0.33
2.21
44.7
45
45.5
46
10.38
10.58
10.84
10.98
Trial 2
Volume (mL)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
16.5
17
17.2
17.4
17.6
17.8
18
18.2
0.2
0.3
0.5
0.5
0.53
0.2
0.26
0.14
(0 mL vol. and ∆ for all inititially) .2142 g unknown
pHi = 2.16
pH
∆Volume (mL)
∆pH
2.24
0.5
0.08
2.26
0.5
0.02
2.28
0.5
0.02
2.31
0.5
0.03
2.33
0.5
0.02
2.35
0.5
0.02
2.37
0.5
0.02
2.4
0.5
0.03
2.43
0.5
0.03
2.46
0.5
0.03
2.48
0.5
0.02
2.5
0.5
0.02
2.53
0.5
0.03
2.56
0.5
0.03
2.59
0.5
0.03
2.62
0.5
0.03
2.66
0.5
0.04
2.69
0.5
0.03
2.73
0.5
0.04
2.77
0.5
0.04
2.81
0.5
0.04
2.86
0.5
0.05
2.9
0.5
0.04
2.95
0.5
0.05
3
0.5
0.05
3.05
0.5
0.05
3.1
0.5
0.05
3.16
0.5
0.06
3.23
0.5
0.07
3.3
0.5
0.07
3.37
0.5
0.07
3.46
0.5
0.09
3.57
0.5
0.11
3.68
0.5
0.11
3.74
0.2
0.06
3.81
0.2
0.07
3.86
0.2
0.05
3.92
0.2
0.06
3.98
0.2
0.06
4.04
0.2
0.06
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
20.5
21
21.5
22
22.5
23
23.5
24
24.5
25
25.5
26
26.5
27
27.5
28
28.5
29
29.5
30
30.5
31
31.5
32
32.5
33
33.2
33.4
33.6
33.8
34
34.2
34.4
34.6
34.8
35
35.2
35.4
4.1
4.16
4.21
4.26
4.32
4.37
4.42
4.47
4.5
4.6
4.69
4.77
4.84
4.91
4.96
5.03
5.08
5.13
5.19
5.24
5.28
5.33
5.38
5.44
5.49
5.53
5.59
5.63
5.68
5.74
5.8
5.85
5.91
5.98
6.06
6.1
6.12
6.15
6.19
6.23
6.27
6.32
6.36
6.42
6.48
6.54
6.64
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.06
0.06
0.05
0.05
0.06
0.05
0.05
0.05
0.03
0.1
0.09
0.08
0.07
0.07
0.05
0.07
0.05
0.05
0.06
0.05
0.04
0.05
0.05
0.06
0.05
0.04
0.06
0.04
0.05
0.06
0.06
0.05
0.06
0.07
0.08
0.04
0.02
0.03
0.04
0.04
0.04
0.05
0.04
0.06
0.06
0.06
0.1
35.6
35.7
35.8
35.9
36
36.05
36.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
37
37.2
37.4
37.6
37.8
38
Trial 3
6.74
6.77
6.83
6.9
6.98
7.04
7.1
7.23
7.32
7.56
8.01
8.94
9.81
10.14
10.26
10.49
10.65
10.81
10.92
11
11.09
pHi = 2.20
pH
Volume (mL)
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.6
9
9.5
10
10.5
11
11.5
0.2
0.1
0.1
0.1
0.1
0.05
0.05
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.2
0.1
0.03
0.06
0.07
0.08
0.06
0.06
0.13
0.09
0.24
0.45
0.93
0.87
0.33
0.12
0.23
0.16
0.16
0.11
0.08
0.09
(0 mL vol. and ∆ for all inititially) .2040 g unknown
∆Volume (mL)
∆pH
2.2
0.5
0
2.26
0.5
0.06
2.29
0.5
0.03
2.32
0.5
0.03
2.34
0.5
0.02
2.39
0.5
0.05
2.41
0.5
0.02
2.44
0.5
0.03
2.47
0.5
0.03
2.5
0.5
0.03
2.54
0.5
0.04
2.58
0.5
0.04
2.61
0.5
0.03
2.64
0.5
0.03
2.68
0.5
0.04
2.71
0.5
0.03
2.77
0.6
0.06
2.8
0.4
0.03
2.84
0.5
0.04
2.88
0.5
0.04
2.93
0.5
0.05
2.98
0.5
0.05
3.02
0.5
0.04
12
12.5
13
13.5
14
14.5
15
15.2
15.4
15.6
15.8
16
16.2
16.4
16.6
16.8
17
17.1
17.2
17.3
17.4
17.5
17.7
18
18.2
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
20.2
20.4
20.6
20.8
21
21.5
22
22.5
23
23.5
24
24.5
25
3.08
3.13
3.19
3.24
3.32
3.39
3.48
3.51
3.54
3.58
3.63
3.68
3.72
3.77
3.83
3.87
3.94
3.98
4.01
4.04
4.07
4.09
4.15
4.24
4.3
4.34
4.39
4.44
4.48
4.54
4.58
4.62
4.65
4.69
4.73
4.76
4.8
4.82
4.84
4.92
4.97
5.03
5.1
5.15
5.19
5.25
5.3
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.2
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.06
0.05
0.06
0.05
0.08
0.07
0.09
0.03
0.03
0.04
0.05
0.05
0.04
0.05
0.06
0.04
0.07
0.04
0.03
0.03
0.03
0.02
0.06
0.09
0.06
0.04
0.05
0.05
0.04
0.06
0.04
0.04
0.03
0.04
0.04
0.03
0.04
0.02
0.02
0.08
0.05
0.06
0.07
0.05
0.04
0.06
0.05
25.5
26
26.5
27
27.5
28
28.5
29
29.5
30
30.5
31
31.5
32
32.2
32.4
32.6
32.8
33
33.2
33.4
33.5
33.6
33.7
33.8
33.9
34
34.1
34.2
34.3
34.4
34.5
34.6
34.7
34.8
34.9
35
35.1
35.2
35.3
35.4
35.5
35.6
35.7
35.8
35.9
36
5.35
5.4
5.45
5.5
5.55
5.6
5.65
5.7
5.76
5.82
5.88
5.94
6.03
6.12
6.14
6.18
6.21
6.26
6.3
6.36
6.42
6.44
6.49
6.53
6.56
6.6
6.65
6.68
6.73
6.81
6.89
6.97
7.05
7.15
7.32
7.59
8.18
9.42
9.93
10.11
10.29
10.45
10.55
10.64
10.68
10.79
10.83
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0.06
0.06
0.06
0.06
0.09
0.09
0.02
0.04
0.03
0.05
0.04
0.06
0.06
0.02
0.05
0.04
0.03
0.04
0.05
0.03
0.05
0.08
0.08
0.08
0.08
0.1
0.17
0.27
0.59
1.24
0.51
0.18
0.18
0.16
0.1
0.09
0.04
0.11
0.04
36.1
36.2
36.3
36.5
37
10.89
10.94
10.98
11.04
11.17
0.1
0.1
0.1
0.2
0.5
0.06
0.05
0.04
0.06
0.13
Standardization of NaOH with KHP: Trial
8
7
6
5
pH
Avg. Vol. (mL)
0.5
1.5
2.5
4
6
8
10
12
14
16
18
19.5
20.5
21.5
22.5
23.5
24.5
25.5
26.25
26.75
27.25
27.75
28.25
28.75
29.25
29.75
30.25
30.75
31.25
31.75
32.25
32.6
32.85
33.1
33.3
33.45
4
3
2
1
0
0
5
10
15
20
Vol. NaOH (mL)
1st Derivative for Equivalence Volume NaOH:
4
3.5
3
∆pH/∆Vol
∆Vol/∆pH
11.11111111
12.5
8.333333333
14.28571429
14.28571429
16.66666667
18.18181818
18.18181818
20
18.18181818
20
20
20
16.66666667
16.66666667
16.66666667
14.28571429
14.28571429
12.5
12.5
10
12.5
10
10
8.333333333
8.333333333
7.142857143
5.555555556
5.555555556
4.545454545
2.941176471
1.333333333
3
1.333333333
0.869565217
0.263157895
2.5
2
1.5
1
0.5
0
0
5
10
15
20
Avg. Vol. NaOH (mL)
1st Derivative for pKa NaOH: Trial 1
25
20
∆Vol/∆pH
∆pH/∆Vol
0.09
0.08
0.12
0.07
0.07
0.06
0.055
0.055
0.05
0.055
0.05
0.05
0.05
0.06
0.06
0.06
0.07
0.07
0.08
0.08
0.1
0.08
0.1
0.1
0.12
0.12
0.14
0.18
0.18
0.22
0.34
0.75
0.333333333
0.75
1.15
3.8
15
10
5
0
∆pH/∆Vol
0.082
0.062
0.052
0.05
0.05
∆Vol/∆pH
12.19512195
16.12903226
19.23076923
20
20
Avg. Vol. (mL)
2.5
7.5
12.5
16
18
0
1
2
3
4
pH
Standardization of NaOH with KHP: Trial
14
12
∆pH/∆Vol
∆Vol/∆pH
Avg. Vol. (mL)
12
10
pH
20
21.5
22.5
23.5
24.5
25.25
25.75
26.25
26.75
27.25
27.75
28.25
28.75
29.25
29.75
30.25
30.75
31.1
31.35
31.6
31.85
32.1
32.35
32.6
32.8
33
33.2
33.4
33.6
33.8
34
34.15
34.25
34.35
34.425
34.475
34.55
34.8
35.25
35.75
36.5
37.5
38.5
39.5
8
6
4
2
0
0
5
10
15
20
Vol. NaOH (mL)
1st Derivative for Equivalence Volume NaOH:
8
7
6
∆pH/∆Vol
20
20
20
14.28571429
16.66666667
16.66666667
16.66666667
16.66666667
12.5
12.5
16.66666667
10
12.5
10
10
8.333333333
8.333333333
10
6
6.666666667
6
6.666666667
6
4
4
3.333333333
4
2.857142857
2.857142857
2.222222222
2.222222222
1.666666667
2.5
0.714285714
0.833333333
0.833333333
1.25
0.141342756
0.595238095
1.785714286
3.333333333
5.263157895
10
11.11111111
5
4
3
2
1
0
0
5
10
15
20
Avg. Vol. NaOH (mL)
1st Derivative for pKa NaOH: Trial 2
25
20
∆Vol/∆pH
0.05
0.05
0.05
0.07
0.06
0.06
0.06
0.06
0.08
0.08
0.06
0.1
0.08
0.1
0.1
0.12
0.12
0.1
0.166666667
0.15
0.166666667
0.15
0.166666667
0.25
0.25
0.3
0.25
0.35
0.35
0.45
0.45
0.6
0.4
1.4
1.2
1.2
0.8
7.075
1.68
0.56
0.3
0.19
0.1
0.09
15
10
5
0
0
2
4
6
pH
Standardization of NaOH with KHP: Trial
2.5
7.5
12.5
16.05
18.05
20
22
24
26
28
30
31.5
32.5
33.25
33.75
34.25
34.6
34.85
35.1
35.35
35.6
35.85
36.1
36.3
36.5
36.7
36.9
37.05
37.175
37.275
37.35
37.45
37.55
37.65
37.75
37.9
39.05
40.55
Standardization of NaOH with KHP: Trial
14
12
10
pH
12.82051282
17.24137931
20.83333333
19.09090909
23.75
22.22222222
22.22222222
20
16.66666667
18.18181818
14.28571429
11.11111111
10
8.333333333
8.333333333
7.142857143
6.666666667
5
5
7.5
2.857142857
6
2.857142857
3.333333333
2.857142857
2.222222222
2.222222222
1.25
1.153846154
1.25
2
1.666666667
0.3125
0.303030303
0.0625
0.322580645
1.418918919
6.923076923
8
6
4
2
0
0
5
10
15
20
Vol. NaOH (mL)
1st Derivative for Equivalence Value NaOH: T
18
16
14
∆pH/∆Vol
0.078
0.058
0.048
0.052380952
0.042105263
0.045
0.045
0.05
0.06
0.055
0.07
0.09
0.1
0.12
0.12
0.14
0.15
0.2
0.2
0.133333333
0.35
0.166666667
0.35
0.3
0.35
0.45
0.45
0.8
0.866666667
0.8
0.5
0.6
3.2
3.3
16
3.1
0.704761905
0.144444444
12
10
8
6
4
2
0
0
5
10
15
20
Avg. Vol. NaOH (mL)
1st Derivative for pKa NaOH: Trial 3
25
20
15
10
5
∆pH/∆Vol
0.04
0.02
0.04
0.04
0.06
∆Vol/∆pH
25
50
25
25
16.66666667
Avg. Vol. (mL)
0.25
0.75
1.25
1.75
2.25
0
0
2
4
6
Unknown Acid Potentiometric Titation: Tri
12
10
10
8
pH
2.75
3.25
3.75
4.25
4.75
5.25
5.75
6.25
6.75
7.25
7.75
8.25
8.75
9.3
9.8
10.25
10.75
11.25
11.75
12.25
12.75
13.25
13.75
14.25
14.75
15.25
15.75
16.25
16.75
17.25
17.75
18.25
18.75
19.25
19.75
20.25
20.75
21.3
21.8
22.25
22.75
23.25
23.75
24.25
24.75
25.25
25.75
6
4
2
0
0
5
10
15
20
25
Vol. NaOH (mL)
1st Derivative for Equivalence Volume Unknown: T
8
7
6
5
∆pH/∆Vol
25
12.5
16.66666667
16.66666667
25
16.66666667
16.66666667
16.66666667
16.66666667
16.66666667
16.66666667
16.66666667
16.66666667
15
20
16.66666667
16.66666667
16.66666667
12.5
16.66666667
12.5
16.66666667
12.5
12.5
10
12.5
12.5
10
10
10
10
8.333333333
6.25
7.142857143
7.142857143
5
5.555555556
4.615384615
4
4.166666667
4.545454545
5
4.545454545
6.25
6.25
7.142857143
7.142857143
4
3
2
1
0
0
10
20
30
Avg. Vol. NaOH (mL)
1st Derivative for pKa: Trial 1
60
50
40
∆Vol/pH
0.04
0.08
0.06
0.06
0.04
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.066666667
0.05
0.06
0.06
0.06
0.08
0.06
0.08
0.06
0.08
0.08
0.1
0.08
0.08
0.1
0.1
0.1
0.1
0.12
0.16
0.14
0.14
0.2
0.18
0.216666667
0.25
0.24
0.22
0.2
0.22
0.16
0.16
0.14
0.14
30
20
10
0
0
2
4
6
pH
0.1
0.12
0.1
0.1
0.1
0.08
0.1
0.08
0.06
0.1
0.06
0.08
0.1
0.04
0.08
0.08
0.08
0.1
0.08
0.08
0.08
0.08
0.08
0.1
0.12
0.08
0.14
0.1
0.16
0.1
0.133333333
0.2
0.166666667
0.15
0.233333333
0.25
0.2
0.3
0.266666667
0.5
0.566666667
0.75
0.5
1.2
1.9
1.65
7.366666667
10
8.333333333
10
10
10
12.5
10
12.5
16.66666667
10
16.66666667
12.5
10
25
12.5
12.5
12.5
10
12.5
12.5
12.5
12.5
12.5
10
8.333333333
12.5
7.142857143
10
6.25
10
7.5
5
6
6.666666667
4.285714286
4
5
3.333333333
3.75
2
1.764705882
1.333333333
2
0.833333333
0.526315789
0.606060606
0.135746606
26.25
26.75
27.25
27.75
28.25
28.75
29.25
29.75
30.25
30.75
31.25
31.75
32.25
32.75
33.25
33.75
34.25
34.75
35.25
35.75
36.25
36.75
37.25
37.75
38.25
38.75
39.25
39.75
40.25
40.6
40.85
41.1
41.35
41.6
41.85
42.1
42.35
42.6
42.85
43.1
43.35
43.6
43.75
43.85
43.95
44.1
44.35
∆pH/∆Vol
∆Vol/∆pH
6.25
25
25
16.66666667
25
25
25
16.66666667
16.66666667
16.66666667
25
25
16.66666667
16.66666667
16.66666667
16.66666667
12.5
16.66666667
12.5
12.5
12.5
10
12.5
10
10
10
10
8.333333333
7.142857143
7.142857143
7.142857143
5.555555556
4.545454545
4.545454545
3.333333333
2.857142857
4
3.333333333
3.333333333
3.333333333
Avg. Vol. (mL)
0.25
0.75
1.25
1.75
2.25
2.75
3.25
3.75
4.25
4.75
5.25
5.75
6.25
6.75
7.25
7.75
8.25
8.75
9.25
9.75
10.25
10.75
11.25
11.75
12.25
12.75
13.25
13.75
14.25
14.75
15.25
15.75
16.25
16.75
17.1
17.3
17.5
17.7
17.9
18.1
0.16
0.04
0.04
0.06
0.04
0.04
0.04
0.06
0.06
0.06
0.04
0.04
0.06
0.06
0.06
0.06
0.08
0.06
0.08
0.08
0.08
0.1
0.08
0.1
0.1
0.1
0.1
0.12
0.14
0.14
0.14
0.18
0.22
0.22
0.3
0.35
0.25
0.3
0.3
0.3
Unknown Acid Potentiometric Titration: Tri
12
10
8
pH
44.6
44.85
45.25
45.75
6
4
2
0
0
5
10
15
20
Vol. NaOH (mL)
1st Derivative for Equivalence Volume Unkn
Trial 2
12
10
∆pH/∆Vol
0.377358491
1.5
1.923076923
3.571428571
8
6
4
2
0
0
5
10
15
20
Avg. Vol. NaOH (mL)
1st Derivative for pKa Unknown: Trial 2
30
25
∆Vol/∆pH
2.65
0.666666667
0.52
0.28
20
15
10
5
0
0
2
4
6
pH
0
0.3
0.3
0.25
0.25
0.3
0.25
0.25
0.25
0.15
0.2
0.18
0.16
0.14
0.14
0.1
0.14
0.1
0.1
0.12
0.1
0.08
0.1
0.1
0.12
0.1
0.08
0.12
0.08
0.1
0.12
0.12
0.1
0.12
0.14
0.16
0.2
0.1
0.15
0.2
0.2
0.2
0.25
0.2
0.3
0.3
0.3
0.5
3.333333333
3.333333333
4
4
3.333333333
4
4
4
6.666666667
5
5.555555556
6.25
7.142857143
7.142857143
10
7.142857143
10
10
8.333333333
10
12.5
10
10
8.333333333
10
12.5
8.333333333
12.5
10
8.333333333
8.333333333
10
8.333333333
7.142857143
6.25
5
10
6.666666667
5
5
5
4
5
3.333333333
3.333333333
3.333333333
2
18.3
18.5
18.7
18.9
19.1
19.3
19.5
19.7
19.9
20.25
20.75
21.25
21.75
22.25
22.75
23.25
23.75
24.25
24.75
25.25
25.75
26.25
26.75
27.25
27.75
28.25
28.75
29.25
29.75
30.25
30.75
31.25
31.75
32.25
32.75
33.1
33.3
33.5
33.7
33.9
34.1
34.3
34.5
34.7
34.9
35.1
35.3
2
4
6
pH
0
0.12
0.06
0.06
0.04
0.1
0.04
0.06
0.06
0.06
0.08
0.08
0.06
0.06
0.08
0.06
0.1
0.075
0.08
0.08
0.1
0.1
0.08
∆Vol/∆pH
0
8.333333333
16.66666667
16.66666667
25
10
25
16.66666667
16.66666667
16.66666667
12.5
12.5
16.66666667
16.66666667
12.5
16.66666667
10
13.33333333
12.5
12.5
10
10
12.5
35.5
35.65
35.75
35.85
35.95
36.025
36.075
36.15
36.25
36.35
36.45
36.55
36.65
36.75
36.85
36.95
37.1
37.3
37.5
37.7
37.9
Avg. Vol. (mL)
0.25

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