UMGC Neutralization of HCl with NaOH Titration Problem

The following data came from the titration of H3PO4 with NaOHNaOH
(mL)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
2
2.05
2.1
2.15
2.2
pH
1.82174
1.81706
1.82174
1.82174
1.82174
1.82174
1.82642
1.82642
1.82642
1.82642
1.8311
1.8311
1.8311
1.83579
1.83579
1.83579
1.83579
1.84047
1.84515
1.84515
1.84515
1.84515
1.84515
1.84515
1.84983
1.85452
1.85924
1.85924
1.85924
1.86392
1.86392
1.85924
1.8686
1.8686
1.8686
1.8686
1.8686
1.8686
1.87328
1.87328
1.87328
1.87328
1.88265
1.88265
2.25
2.3
2.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
2.8
2.85
2.9
2.95
3
3.05
3.1
3.15
3.2
3.25
3.3
3.35
3.4
3.45
3.5
3.55
3.6
3.65
3.7
3.75
3.8
3.85
3.9
3.95
4
4.05
4.1
4.15
4.2
4.25
4.3
4.35
4.4
4.45
4.5
4.55
4.6
4.65
4.7
4.75
4.8
1.88265
1.88733
1.88733
1.88733
1.89201
1.89201
1.89201
1.8967
1.8967
1.8967
1.91078
1.91078
1.91078
1.91078
1.91078
1.91078
1.91546
1.91546
1.91546
1.92483
1.92483
1.92483
1.92483
1.92483
1.93419
1.93419
1.93419
1.94356
1.94356
1.94356
1.94356
1.94356
1.94356
1.95296
1.95296
1.95296
1.95764
1.95764
1.95764
1.96233
1.96233
1.96233
1.96233
1.96701
1.96701
1.96701
1.96701
1.97637
1.97637
1.97637
1.98105
1.98105
4.85
4.9
4.95
5
5.05
5.1
5.15
5.2
5.25
5.3
5.35
5.4
5.45
5.5
5.55
5.6
5.65
5.7
5.75
5.8
5.85
5.9
5.95
6
6.05
6.1
6.15
6.2
6.25
6.3
6.35
6.4
6.45
6.5
6.55
6.6
6.65
6.7
6.75
6.8
6.85
6.9
6.95
7
7.05
7.1
7.15
7.2
7.25
7.3
7.35
7.4
1.98105
1.98105
1.98574
1.98574
1.98574
1.98574
1.98574
1.99042
1.9951
1.9951
1.9951
1.9951
2.00451
1.99982
1.99982
2.00451
2.00451
2.00451
2.01387
2.01387
2.01387
2.01387
2.01387
2.01387
2.02323
2.02323
2.02323
2.02323
2.02792
2.02792
2.02792
2.02792
2.02792
2.02792
2.03728
2.03728
2.03728
2.03728
2.03728
2.03728
2.05137
2.05137
2.05137
2.05137
2.06073
2.05605
2.05605
2.05605
2.05605
2.05605
2.0701
2.0701
7.45
7.5
7.55
7.6
7.65
7.7
7.75
7.8
7.85
7.9
7.95
8
8.05
8.1
8.15
8.2
8.25
8.3
8.35
8.4
8.45
8.5
8.55
8.6
8.65
8.7
8.75
8.8
8.85
8.9
8.95
9
9.05
9.1
9.15
9.2
9.25
9.3
9.35
9.4
9.45
9.5
9.55
9.6
9.65
9.7
9.75
9.8
9.85
9.9
9.95
10
2.0701
2.07478
2.07946
2.07946
2.08883
2.08883
2.08883
2.08883
2.08883
2.08883
2.09355
2.09823
2.09823
2.09823
2.10291
2.11228
2.11228
2.11228
2.11228
2.11228
2.12632
2.12632
2.12632
2.12632
2.13101
2.13101
2.13101
2.14041
2.14509
2.14509
2.14977
2.14977
2.14977
2.15914
2.15914
2.15914
2.15914
2.16382
2.16382
2.16382
2.16382
2.16382
2.17787
2.17787
2.17787
2.17787
2.18255
2.18255
2.18255
2.18255
2.19664
2.19664
10.05
10.1
10.15
10.2
10.25
10.3
10.35
10.4
10.45
10.5
10.55
10.6
10.65
10.7
10.75
10.8
10.85
10.9
10.95
11
11.05
11.1
11.15
11.2
11.25
11.3
11.35
11.4
11.45
11.5
11.55
11.6
11.65
11.7
11.75
11.8
11.85
11.9
11.95
12
12.05
12.1
12.15
12.2
12.25
12.3
12.35
12.4
12.45
12.5
12.55
12.6
2.19664
2.19664
2.206
2.206
2.206
2.206
2.21068
2.21068
2.21068
2.22005
2.22005
2.22473
2.22941
2.22941
2.22941
2.23413
2.2435
2.2435
2.2435
2.2435
2.25286
2.25286
2.25286
2.24818
2.26223
2.26223
2.26223
2.26223
2.27159
2.27159
2.27159
2.27627
2.27627
2.27627
2.28568
2.28568
2.28568
2.28568
2.29504
2.29504
2.29504
2.30441
2.31377
2.31377
2.31377
2.31377
2.31377
2.31377
2.32786
2.32786
2.32786
2.32786
12.65
12.7
12.75
12.8
12.85
12.9
12.95
13
13.05
13.1
13.15
13.2
13.25
13.3
13.35
13.4
13.45
13.5
13.55
13.6
13.65
13.7
13.75
13.8
13.85
13.9
13.95
14
14.05
14.1
14.15
14.2
14.25
14.3
14.35
14.4
14.45
14.5
14.55
14.6
14.65
14.7
14.75
14.8
14.85
14.9
14.95
15
15.05
15.1
15.15
15.2
2.32786
2.33722
2.3419
2.3419
2.3419
2.35127
2.36532
2.36532
2.36532
2.36532
2.36532
2.37
2.38408
2.38408
2.38408
2.38408
2.38408
2.38408
2.38408
2.38408
2.40281
2.41686
2.41686
2.41686
2.42158
2.42158
2.42158
2.44031
2.44031
2.44031
2.44031
2.44031
2.44499
2.46372
2.46372
2.46372
2.47312
2.47312
2.47781
2.48717
2.48717
2.48717
2.49185
2.49185
2.50122
2.5153
2.5153
2.5153
2.5153
2.5153
2.52467
2.53403
15.25
15.3
15.35
15.4
15.45
15.5
15.55
15.6
15.65
15.7
15.75
15.8
15.85
15.9
15.95
16
16.05
16.1
16.15
16.2
16.25
16.3
16.35
16.4
16.45
16.5
16.55
16.6
16.65
16.7
16.75
16.8
16.85
16.9
16.95
17
17.05
17.1
17.15
17.2
17.25
17.3
17.35
17.4
17.45
17.5
17.55
17.6
17.65
17.7
17.75
17.8
2.53403
2.53403
2.53403
2.55745
2.55745
2.55745
2.56217
2.56217
2.56217
2.57621
2.57621
2.57621
2.58558
2.58558
2.58558
2.60435
2.60435
2.60435
2.60903
2.62308
2.62308
2.62308
2.62776
2.62776
2.62776
2.65117
2.65117
2.65117
2.66057
2.66057
2.66057
2.67462
2.67462
2.67462
2.6793
2.6793
2.68867
2.70743
2.70743
2.70743
2.70743
2.70743
2.7168
2.72616
2.72616
2.74021
2.7543
2.7543
2.7543
2.75898
2.75898
2.76366
17.85
17.9
17.95
18
18.05
18.1
18.15
18.2
18.25
18.3
18.35
18.4
18.45
18.5
18.55
18.6
18.65
18.7
18.75
18.8
18.85
18.9
18.95
19
19.05
19.1
19.15
19.2
19.25
19.3
19.35
19.4
19.45
19.5
19.55
19.6
19.65
19.7
19.75
19.8
19.85
19.9
19.95
20
20.05
20.1
20.15
20.2
20.25
20.3
20.35
20.4
2.78239
2.78239
2.78239
2.78707
2.78707
2.80116
2.80116
2.81052
2.81052
2.82925
2.82925
2.82925
2.84802
2.85739
2.85739
2.85739
2.86675
2.86675
2.87611
2.87611
2.8902
2.8902
2.89957
2.89957
2.92766
2.92766
2.92766
2.92766
2.92766
2.94643
2.94643
2.95579
2.95579
2.98392
2.98392
2.98861
2.98861
2.98861
3.00734
3.00734
3.0167
3.0167
3.03547
3.03547
3.04483
3.04483
3.06356
3.06356
3.06356
3.07765
3.07765
3.11042
20.45
20.5
20.55
20.6
20.65
20.7
20.75
20.8
20.85
20.9
20.95
21
21.05
21.1
21.15
21.2
21.25
21.3
21.35
21.4
21.45
21.5
21.55
21.6
21.65
21.7
21.75
21.8
21.85
21.9
21.95
22
22.05
22.1
22.15
22.2
22.25
22.3
22.35
22.4
22.45
22.5
22.55
22.6
22.65
22.7
22.75
22.8
22.85
22.9
22.95
23
3.11042
3.11511
3.11511
3.12919
3.12919
3.13856
3.13856
3.13856
3.17605
3.17605
3.1901
3.1901
3.22292
3.22292
3.23696
3.23696
3.2651
3.2651
3.2651
3.2651
3.2651
3.32601
3.32601
3.34942
3.34942
3.34942
3.37755
3.37755
3.41505
3.41505
3.41505
3.41505
3.41505
3.48064
3.48064
3.54159
3.54159
3.54159
3.54159
3.54159
3.62122
3.62122
3.7009
3.7009
3.74776
3.74776
3.82744
3.82744
3.82744
3.93053
3.93053
3.98207
23.05
23.1
23.15
23.2
23.25
23.3
23.35
23.4
23.45
23.5
23.55
23.6
23.65
23.7
23.75
23.8
23.85
23.9
23.95
24
24.05
24.1
24.15
24.2
24.25
24.3
24.35
24.4
24.45
24.5
24.55
24.6
24.65
24.7
24.75
24.8
24.85
24.9
24.95
25
25.05
25.1
25.15
25.2
25.25
25.3
25.35
25.4
25.45
25.5
25.55
25.6
3.98207
4.10393
4.10393
4.10393
4.22107
4.22107
4.27261
4.27261
4.40383
4.40383
4.40383
4.47883
4.47883
4.61001
4.61001
4.74123
4.74123
4.74123
4.88182
4.88182
4.95213
4.95213
5.07395
5.07395
5.18644
5.18644
5.18644
5.25203
5.25203
5.35512
5.35512
5.45821
5.45821
5.45821
5.45821
5.45821
5.58475
5.58475
5.65974
5.65974
5.65974
5.73001
5.73001
5.76283
5.76283
5.81905
5.81905
5.81905
5.86592
5.86592
5.86592
5.86592
25.65
25.7
25.75
25.8
25.85
25.9
25.95
26
26.05
26.1
26.15
26.2
26.25
26.3
26.35
26.4
26.45
26.5
26.55
26.6
26.65
26.7
26.75
26.8
26.85
26.9
26.95
27
27.05
27.1
27.15
27.2
27.25
27.3
27.35
27.4
27.45
27.5
27.55
27.6
27.65
27.7
27.75
27.8
27.85
27.9
27.95
28
28.05
28.1
28.15
28.2
5.94091
5.94091
5.96901
5.96901
5.96901
6.0065
6.0065
6.044
6.044
6.044
6.05805
6.05805
6.08618
6.08618
6.10959
6.10959
6.10959
6.13304
6.13304
6.16114
6.16114
6.17054
6.17054
6.19395
6.19395
6.20332
6.20332
6.22208
6.22208
6.23613
6.23613
6.25486
6.25486
6.25958
6.25958
6.27831
6.27831
6.28767
6.28767
6.30644
6.30644
6.31581
6.31581
6.33454
6.33922
6.33922
6.3533
6.3533
6.36267
6.36267
6.3814
6.3814
28.25
28.3
28.35
28.4
28.45
28.5
28.55
28.6
28.65
28.7
28.75
28.8
28.85
28.9
28.95
29
29.05
29.1
29.15
29.2
29.25
29.3
29.35
29.4
29.45
29.5
29.55
29.6
29.65
29.7
29.75
29.8
29.85
29.9
29.95
30
30.05
30.1
30.15
30.2
30.25
30.3
30.35
30.4
30.45
30.5
30.55
30.6
30.65
30.7
30.75
30.8
6.39548
6.39548
6.40953
6.40953
6.41421
6.41421
6.43294
6.43294
6.44235
6.44235
6.44235
6.44235
6.46576
6.46576
6.48449
6.48449
6.49389
6.49389
6.50326
6.50326
6.51262
6.51262
6.52667
6.52667
6.54075
6.55012
6.55012
6.55012
6.55012
6.57353
6.57353
6.58293
6.58293
6.5923
6.5923
6.60166
6.60166
6.61571
6.62979
6.62979
6.62979
6.62979
6.63916
6.63916
6.65321
6.66257
6.66257
6.66257
6.66257
6.67194
6.67194
6.68134
30.85
30.9
30.95
31
31.05
31.1
31.15
31.2
31.25
31.3
31.35
31.4
31.45
31.5
31.55
31.6
31.65
31.7
31.75
31.8
31.85
31.9
31.95
32
32.05
32.1
32.15
32.2
32.25
32.3
32.35
32.4
32.45
32.5
32.55
32.6
32.65
32.7
32.75
32.8
32.85
32.9
32.95
33
33.05
33.1
33.15
33.2
33.25
33.3
33.35
33.4
6.68134
6.6907
6.6907
6.69539
6.71411
6.71411
6.71411
6.71411
6.7282
6.7282
6.7282
6.7282
6.73757
6.75629
6.75629
6.75629
6.75629
6.76098
6.76098
6.77038
6.77038
6.77974
6.78911
6.78911
6.78911
6.78911
6.79379
6.79379
6.80316
6.81252
6.81252
6.81252
6.81252
6.82192
6.82192
6.82192
6.84534
6.84534
6.84534
6.84534
6.8547
6.86879
6.86879
6.86879
6.86879
6.87347
6.88752
6.88752
6.88752
6.88752
6.8922
6.8922
33.45
33.5
33.55
33.6
33.65
33.7
33.75
33.8
33.85
33.9
33.95
34
34.05
34.1
34.15
34.2
34.25
34.3
34.35
34.4
34.45
34.5
34.55
34.6
34.65
34.7
34.75
34.8
34.85
34.9
34.95
35
35.05
35.1
35.15
35.2
35.25
35.3
35.35
35.4
35.45
35.5
35.55
35.6
35.65
35.7
35.75
35.8
35.85
35.9
35.95
36
6.90156
6.91565
6.91565
6.91565
6.91565
6.92033
6.93906
6.93906
6.93906
6.93906
6.93906
6.94374
6.94374
6.94842
6.96719
6.96719
6.96719
6.96719
6.97188
6.97656
6.97656
6.97656
6.97656
6.98592
6.99997
6.99997
6.99997
6.99529
7.00469
7.00469
7.00469
7.00469
7.00469
7.00937
7.01874
7.01874
7.01874
7.01874
7.0281
7.0281
7.0281
7.0281
7.03747
7.03747
7.04215
7.04215
7.04215
7.06092
7.06092
7.06092
7.06092
7.0656
36.05
36.1
36.15
36.2
36.25
36.3
36.35
36.4
36.45
36.5
36.55
36.6
36.65
36.7
36.75
36.8
36.85
36.9
36.95
37
37.05
37.1
37.15
37.2
37.25
37.3
37.35
37.4
37.45
37.5
37.55
37.6
37.65
37.7
37.75
37.8
37.85
37.9
37.95
38
38.05
38.1
38.15
38.2
38.25
38.3
38.35
38.4
38.45
38.5
38.55
38.6
7.0656
7.07028
7.07028
7.07496
7.08433
7.08433
7.09369
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.11246
7.13119
7.13119
7.13119
7.13119
7.15464
7.15464
7.15464
7.15464
7.16869
7.16869
7.16869
7.16869
7.18273
7.18273
7.18273
7.18273
7.19214
7.19214
7.19214
7.19214
7.20618
7.20618
7.20618
7.20618
7.22491
7.22491
7.22491
7.22491
7.239
7.239
7.239
7.239
7.25305
38.65
38.7
38.75
38.8
38.85
38.9
38.95
39
39.05
39.1
39.15
39.2
39.25
39.3
39.35
39.4
39.45
39.5
39.55
39.6
39.65
39.7
39.75
39.8
39.85
39.9
39.95
40
40.05
40.1
40.15
40.2
40.25
40.3
40.35
40.4
40.45
40.5
40.55
40.6
40.65
40.7
40.75
40.8
40.85
40.9
40.95
41
41.05
41.1
41.15
41.2
7.25305
7.25305
7.25305
7.26241
7.26241
7.26241
7.27646
7.27646
7.27646
7.27646
7.29054
7.29054
7.29054
7.29054
7.31864
7.31864
7.31864
7.31864
7.328
7.328
7.328
7.34209
7.34209
7.34209
7.34209
7.34209
7.3655
7.3655
7.3655
7.3655
7.37959
7.37959
7.37959
7.39363
7.39363
7.39363
7.39363
7.40768
7.40768
7.40768
7.40768
7.43113
7.43113
7.43113
7.45454
7.45454
7.45454
7.45454
7.47331
7.47331
7.47331
7.47799
41.25
41.3
41.35
41.4
41.45
41.5
41.55
41.6
41.65
41.7
41.75
41.8
41.85
41.9
41.95
42
42.05
42.1
42.15
42.2
42.25
42.3
42.35
42.4
42.45
42.5
42.55
42.6
42.65
42.7
42.75
42.8
42.85
42.9
42.95
43
43.05
43.1
43.15
43.2
43.25
43.3
43.35
43.4
43.45
43.5
43.55
43.6
43.65
43.7
43.75
43.8
7.47799
7.47799
7.47799
7.51077
7.51077
7.51077
7.51077
7.52485
7.52485
7.52485
7.54358
7.54358
7.54358
7.54358
7.55763
7.55763
7.55763
7.55763
7.58108
7.58108
7.58108
7.59513
7.59513
7.59513
7.59513
7.61858
7.61858
7.61858
7.61858
7.63263
7.63263
7.63263
7.64667
7.64667
7.64667
7.64667
7.67012
7.67012
7.67012
7.70762
7.70762
7.70762
7.70762
7.72635
7.72635
7.72635
7.73571
7.73571
7.73571
7.73571
7.76385
7.76385
43.85
43.9
43.95
44
44.05
44.1
44.15
44.2
44.25
44.3
44.35
44.4
44.45
44.5
44.55
44.6
44.65
44.7
44.75
44.8
44.85
44.9
44.95
45
45.05
45.1
45.15
45.2
45.25
45.3
45.35
45.4
45.45
45.5
45.55
45.6
45.65
45.7
45.75
45.8
45.85
45.9
45.95
46
46.05
46.1
46.15
46.2
46.25
46.3
46.35
46.4
7.76385
7.78726
7.78726
7.78726
7.78726
7.82007
7.82007
7.82007
7.8388
7.8388
7.8388
7.8388
7.88098
7.88098
7.88098
7.89975
7.89975
7.89975
7.89975
7.91848
7.91848
7.91848
7.96066
7.96066
7.96066
7.96066
7.97939
7.97939
7.97939
8.03093
8.03093
8.03093
8.06375
8.06375
8.06375
8.06375
8.09656
8.09656
8.09656
8.13874
8.13874
8.13874
8.13874
8.17624
8.17624
8.17624
8.24183
8.24183
8.24183
8.24183
8.27933
8.27933
46.45
46.5
46.55
46.6
46.65
46.7
46.75
46.8
46.85
46.9
46.95
47
47.05
47.1
47.15
47.2
47.25
47.3
47.35
47.4
47.45
47.5
47.55
47.6
47.65
47.7
47.75
47.8
47.85
47.9
47.95
48
48.05
48.1
48.15
48.2
48.25
48.3
48.35
48.4
48.45
48.5
48.55
48.6
48.65
48.7
48.75
48.8
48.85
48.9
48.95
49
8.27933
8.34024
8.34024
8.34024
8.34024
8.3871
8.3871
8.3871
8.49955
8.49955
8.49955
8.49955
8.58391
8.58391
8.58391
8.65891
8.65891
8.65891
8.72918
8.72918
8.72918
8.72918
8.90726
8.90726
8.90726
9.0619
9.0619
9.0619
9.0619
9.17439
9.17439
9.17439
9.28216
9.28216
9.28216
9.28216
9.51179
9.51179
9.51179
9.6711
9.6711
9.6711
9.83982
9.83982
9.83982
9.83982
9.94292
9.94292
9.94292
10.0413
10.0413
10.0413
49.05
49.1
49.15
49.2
49.25
49.3
49.35
49.4
49.45
49.5
49.55
49.6
49.65
49.7
49.75
49.8
49.85
49.9
49.95
50
50.05
50.1
50.15
50.2
50.25
50.3
50.35
50.4
50.45
50.5
50.55
50.6
50.65
50.7
50.75
50.8
50.85
50.9
50.95
51
51.05
51.1
51.15
51.2
51.25
51.3
51.35
51.4
51.45
51.5
51.55
51.6
10.0413
10.2241
10.2241
10.2241
10.3459
10.3459
10.3459
10.4397
10.4397
10.4397
10.4397
10.5006
10.5006
10.5006
10.5615
10.5615
10.5615
10.6552
10.6552
10.6552
10.6974
10.6974
10.6974
10.6974
10.7583
10.7583
10.7583
10.7864
10.7864
10.7864
10.838
10.838
10.838
10.8567
10.8567
10.8567
10.8567
10.9083
10.9083
10.9083
10.9364
10.9364
10.9364
10.9551
10.9551
10.9551
10.9879
10.9879
10.9879
11.002
11.002
11.002
51.65
51.7
51.75
51.8
51.85
51.9
51.95
52
52.05
52.1
52.15
52.2
52.25
52.3
52.35
52.4
52.45
52.5
52.55
52.6
52.65
52.7
52.75
52.8
52.85
52.9
52.95
53
53.05
53.1
53.15
53.2
53.25
53.3
53.35
53.4
53.45
53.5
53.55
53.6
53.65
53.7
53.75
53.8
53.85
53.9
53.95
54
54.05
54.1
54.15
54.2
11.002
11.0348
11.0348
11.0348
11.0489
11.0489
11.0489
11.077
11.077
11.077
11.0957
11.0957
11.0957
11.1192
11.1192
11.1192
11.1192
11.1332
11.1332
11.1332
11.1613
11.1613
11.1613
11.166
11.166
11.166
11.1894
11.1894
11.1894
11.1988
11.1988
11.1988
11.2176
11.2176
11.2176
11.2363
11.2363
11.2363
11.2504
11.2504
11.2504
11.2644
11.2644
11.2644
11.2785
11.2785
11.2785
11.2925
11.2925
11.2925
11.3066
11.3066
54.25
54.3
54.35
54.4
54.45
54.5
54.55
54.6
54.65
54.7
54.75
54.8
54.85
54.9
54.95
55
55.05
55.1
55.15
55.2
55.25
55.3
55.35
55.4
55.45
55.5
55.55
55.6
55.65
55.7
55.75
55.8
55.85
55.9
55.95
56
56.05
56.1
56.15
56.2
56.25
56.3
56.35
56.4
56.45
56.5
11.3066
11.316
11.316
11.316
11.33
11.33
11.33
11.3347
11.3347
11.3347
11.3488
11.3488
11.3488
11.3628
11.3628
11.3628
11.3628
11.3628
11.3628
11.3816
11.3816
11.3816
11.3863
11.3863
11.3863
11.3956
11.3956
11.4003
11.4003
11.4003
11.4144
11.4144
11.4144
11.4238
11.4238
11.4238
11.4284
11.4284
11.4284
11.4378
11.4378
11.4378
11.4519
11.4519
11.4612
11.4612
11.4612
The following data refers to the data taken from the titration of HCl with NaOH.
Logger Pro Data:
NaOH
Volume
(mL)
pH
0.00E+00
1.00E+00
1.00E+00
1.00E+00
2.00E+00
2.00E+00
3.00E+00
3.00E+00
4.00E+00
4.00E+00
4.00E+00
5.00E+00
5.00E+00
6.00E+00
6.00E+00
6.00E+00
7.00E+00
7.00E+00
8.00E+00
8.00E+00
9.00E+00
9.00E+00
9.00E+00
1.00E+01
1.00E+01
1.10E+01
1.10E+01
1.20E+01
1.20E+01
1.20E+01
1.30E+01
1.30E+01
1.40E+01
1.40E+01
1.40E+01
1.50E+01
1.50E+01
1.60E+01
1.20E+00
1.21E+00
1.21E+00
1.22E+00
1.22E+00
1.22E+00
1.22E+00
1.22E+00
1.22E+00
1.22E+00
1.22E+00
1.23E+00
1.24E+00
1.24E+00
1.24E+00
1.24E+00
1.24E+00
1.24E+00
1.24E+00
1.25E+00
1.25E+00
1.25E+00
1.25E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.27E+00
1.28E+00
1.29E+00
1.29E+00
1.30E+00
1.30E+00
1.30E+00
1.32E+00
1.32E+00
1.34E+00
1.34E+00
1.60E+01
1.60E+01
1.70E+01
1.70E+01
1.80E+01
1.80E+01
1.90E+01
1.90E+01
1.90E+01
2.00E+01
2.00E+01
2.10E+01
2.10E+01
2.10E+01
2.20E+01
2.20E+01
2.30E+01
2.30E+01
2.30E+01
2.40E+01
2.40E+01
2.50E+01
2.50E+01
2.60E+01
2.60E+01
2.60E+01
2.70E+01
2.70E+01
2.80E+01
2.80E+01
2.80E+01
2.90E+01
2.90E+01
3.00E+01
3.00E+01
3.00E+01
3.10E+01
3.10E+01
3.20E+01
3.20E+01
3.20E+01
3.30E+01
3.30E+01
3.40E+01
3.40E+01
3.50E+01
3.50E+01
1.34E+00
1.34E+00
1.35E+00
1.35E+00
1.37E+00
1.37E+00
1.37E+00
1.39E+00
1.39E+00
1.41E+00
1.41E+00
1.42E+00
1.44E+00
1.44E+00
1.44E+00
1.45E+00
1.46E+00
1.46E+00
1.47E+00
1.47E+00
1.47E+00
1.50E+00
1.51E+00
1.52E+00
1.53E+00
1.54E+00
1.56E+00
1.59E+00
1.62E+00
1.64E+00
1.68E+00
1.68E+00
1.69E+00
1.73E+00
1.78E+00
1.83E+00
1.91E+00
1.94E+00
2.08E+00
2.12E+00
2.20E+00
2.89E+00
3.63E+00
4.74E+00
5.85E+00
7.40E+00
8.76E+00
3.50E+01
3.60E+01
3.60E+01
3.70E+01
3.70E+01
3.70E+01
3.80E+01
3.80E+01
3.90E+01
3.90E+01
3.90E+01
4.00E+01
4.00E+01
4.10E+01
4.10E+01
4.10E+01
4.20E+01
4.20E+01
4.30E+01
4.30E+01
4.30E+01
4.40E+01
4.40E+01
4.50E+01
4.50E+01
4.50E+01
4.60E+01
4.60E+01
4.70E+01
4.70E+01
4.70E+01
4.80E+01
4.80E+01
4.90E+01
4.90E+01
4.90E+01
5.00E+01
5.00E+01
5.10E+01
5.10E+01
5.10E+01
5.20E+01
5.20E+01
5.30E+01
5.30E+01
5.30E+01
5.40E+01
9.80E+00
1.04E+01
1.08E+01
1.09E+01
1.10E+01
1.12E+01
1.13E+01
1.14E+01
1.14E+01
1.15E+01
1.16E+01
1.16E+01
1.17E+01
1.17E+01
1.17E+01
1.18E+01
1.18E+01
1.18E+01
1.18E+01
1.18E+01
1.19E+01
1.19E+01
1.19E+01
1.19E+01
1.19E+01
1.20E+01
1.20E+01
1.20E+01
1.20E+01
1.20E+01
1.20E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.21E+01
1.22E+01
1.22E+01
1.22E+01
1.22E+01
1.22E+01
1.22E+01
1.22E+01
5.40E+01
5.50E+01
5.50E+01
5.50E+01
5.60E+01
5.60E+01
5.70E+01
5.70E+01
5.70E+01
5.80E+01
5.80E+01
5.90E+01
5.90E+01
5.90E+01
6.00E+01
6.00E+01
6.10E+01
6.10E+01
6.10E+01
6.20E+01
6.20E+01
6.30E+01
6.30E+01
6.30E+01
6.40E+01
6.40E+01
6.40E+01
6.50E+01
6.50E+01
6.60E+01
6.60E+01
6.60E+01
6.70E+01
6.70E+01
6.80E+01
6.80E+01
6.80E+01
6.90E+01
6.90E+01
7.00E+01
7.00E+01
7.00E+01
7.10E+01
7.10E+01
7.20E+01
7.20E+01
7.20E+01
1.22E+01
1.22E+01
1.22E+01
1.22E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.23E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.24E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
7.30E+01
7.30E+01
7.30E+01
7.40E+01
7.40E+01
7.50E+01
7.50E+01
7.50E+01
7.60E+01
7.60E+01
7.70E+01
7.70E+01
7.70E+01
7.80E+01
7.80E+01
7.80E+01
7.90E+01
7.90E+01
8.00E+01
8.00E+01
8.00E+01
8.10E+01
8.10E+01
8.20E+01
8.20E+01
8.20E+01
8.30E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.25E+01
1.26E+01
1.26E+01
1.26E+01
1.26E+01
1.26E+01
1.26E+01
1.26E+01
1.26E+01
Acid Base Titration Curves
OBJECTIVE
The focus for this experiment is to understand how chemist generate titration curves, perform calculations based on
these curves, and identify important regions within the curves.
Titration curves of strong acid with strong base will be compared to weak acid titrated with a strong base.
Students will be able to identify buffer regions, half titration points and their equivalent Ka values, equivalence points
as well as concentration of important species at various points along the titration curve.
BACKGROUND
The best way to understand the principles governing acid-base titration is to generate and study a pH vs. V(titrant)
titration curve. These can be generated using computer interfacing with probes, e.g. a pH probe to monitor changes
in pH and a drop counter to measure the volume of titrant. Vernier equipment and software can collect data accurately
and rapidly. The data is subsequently transferred to a spreadsheet for analysis.
TITRATION OF STRONG ACID WITH STRONG BASE
Search for and view a few you-tube videos that reflect the experimental set up of a strong base (NaOH) with a strong
acid (HCl) titration.
NaOH(aq) + HCl(aq)  NaCl(aq) + H2O(l)
Watch a few you-tube videos
The graph generated from the Vernier would have the following shape:
The equivalence point (also referred to as the midpoint in the inflection region) is the point in a titration where the
strong acid is fully neutralized by the strong base. The solution contains salt and water which in this case is NaCl(aq).
Notice that at equivalence point, the pH=7.0. This is because the NaCl(aq) is a neutral salt. Na+ does not change the
pH of the water. Cl- is the conjugate base of a strong acid and therefore does not react with water to change the pH.
TITRATION OF WEAK ACID WITH STRONG BASE
The second video topic shows the titration of strong base with weak acid.
The titration curve for a weak acid with a strong base is slightly more complex. This is because other factors must be
taken into account:
a) The acid is not completely dissociated before the equivalence point.
Titration
Page 109
b) After some base is added, a soluble salt is formed. The anion of this salt suppresses the dissociation of
c)
the acid (the common ion effect). This helps to flatten the curve in what is referred to as the “buffer
region” where there is weak acid and conjugate base present.
The pH at equivalence point is not neutral. The anion in the salt formed is the conjugate base of a weak
acid and thus is basic.
There is a lot of information that can be obtained from the titration curve. In fact, you should find and study some
you-tube videos by searching for weak (polyprotic) acid titrated with a strong base. Studying these will help you
prepare your report.
(A) Concentration:
The concentration of the acid can be determined from the equivalence points.
For example, if there is only one equivalence point, we can use
𝑀𝑎𝑐𝑖𝑑 =
(𝑀
𝑚𝑚𝑜𝑙
1𝑚𝑚𝑜𝑙𝑎𝑐𝑖𝑑
)
(𝑉𝑚𝐿)𝑏𝑎𝑠𝑒 (
)
𝑚𝐿 𝑏𝑎𝑠𝑒
1𝑚𝑚𝑜𝑙𝑏𝑎𝑠𝑒
(𝑉𝑚𝐿)𝑎𝑐𝑖𝑑
where Cbase is known from standardization, Vbase is obtained from burette, and Vacid measured from pipet.
If there is a second equivalence point, then
𝑚𝑚𝑜𝑙
1𝑚𝑚𝑜𝑙𝑎𝑐𝑖𝑑
)
(𝑉𝑚𝐿)𝑏𝑎𝑠𝑒 (
)
𝑚𝐿 𝑏𝑎𝑠𝑒
2𝑚𝑚𝑜𝑙𝑏𝑎𝑠𝑒
𝑀𝑎𝑐𝑖𝑑 =
(𝑉𝑚𝐿)𝑎𝑐𝑖𝑑
Note: mmol are used to avoid converting mL to L.
(𝑀
(B) Dissociations Constants:
Monoprotic Weak Acid. For monoprotic weak acid, one can determine the dissociation constant, K a, from
the titration curve. When the volume of the base added is half the volume required to reach the equivalence point,
[acid] = [conjugate base], and thus the pH of the solution is equal to the pK a of the acid. For example, in Figure 1, the
equivalence point is reached when 25.0-mL of NaOH is introduced. Thus, the sample is half-titrated (or halfneutralized) when 12.5-mL of NaOH is added. At this volume the pH is 4.8, therefore for acetic acid pK a = 4.8.
Diprotic Weak Acid. For diprotic weak acid or a mixture of two weak acids, one can determine K 1 and K2.
Suppose you have a mixture of two acids, HX and HY, and HX is much stronger than HY. When a strong base is
added, the HX will react first, leaving HY virtually untouched. This, however, will not be the case when the strengths
of HX and HY are relatively close. The rule of thumb is when K 1/K2 104, two distinct inflection points will be
observed. When K1/K2 is considerably less than 104, distortion of the titration curve will occur. In cases when K 1 
K2 , only one inflection point may appear giving the impression that it is a monoprotic weak acid.
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Polyprotic acids behave similar to the mixture of acids as mentioned above. Consider a diprotic acid, H 2A. This acid
dissociates in two steps:
𝐻2 𝐴 + 𝐻2 𝑂 ⇔ 𝐻3 𝑂+ + 𝐻𝐴−
𝐾𝑎1 =
𝐻𝐴− + 𝐻2 𝑂 ⇔ 𝐻3 𝑂 + + 𝐴2−
𝐾𝑎2 =
[𝐻3 𝑂+][𝐻𝐴−]
[𝐻2 𝐴]
[𝐻3 𝑂+][𝐴2− ]
[𝐻𝐴− ]
If 𝐾𝑎1 /𝐾𝑎2 ≥ 104 , the titration curve will show two distinct steep portions, the first one corresponding to the formation
of HA-, and the second, A2-. 𝐾𝑎1 and 𝐾𝑎2 may be determined from the titration curve. Assuming Figure 2 is the
titration curve of H2A. The first equivalence point occurs at ~50.0-mL of NaOH. At half of this volume the pH is 2.2
(indicated by the lower set of the dotted line), 𝑝𝐾𝑎1 is therefore 2.2. The second equivalence point occurs at ~100.0mL. Half the distance between the first and second equivalence points is ~((100.0+50.0)/2=) 75.0-mL. The pH at
~75.0 ml is 7.2 (indicated by the upper set of the dotted line), thus 𝑝𝐾𝑎2 = 7.2. Notice that the distance a1 and a2 are
nearly equal.
There is another useful although approximate relationship for the pH at the first equivalence point,
𝑝𝐻 =
𝑝𝐾𝑎1 + 𝑝𝐾𝑎2
2
Use the titration curve in figure 2 to check the validity of this relationship.
(C) Determination of Buffer region:
Recall the Henderson-Hasselbalch equation,
𝒑𝑯 = 𝒑𝑲𝒂 + 𝒍𝒐𝒈
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[𝑩𝒂𝒔𝒆]
[𝑨𝒄𝒊𝒅]
When [Base] = [Acid], pH = pKa. This should remind you of the half neutralized point. To be more quantitative, the
buffer region can be defined by [Base]=10[Acid] or [Base]=(1/10)[Acid], and that means,
𝑝𝐻 = 𝑝𝐾𝑎 ± 1
This is also known as the buffer capacity or region. When the pH is beyond pKa >  1, the buffer capacity is said to
be destroyed.
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Report preparation
The titration data is provided for you in two separate excel files, HCl.xls and H3PO4.xls. Please follow
the instructions below and submit the results in the form of three graphs. When complete, submit your
file(s) (as a pdf, or picture or ?) using the upload file option in the Acid-Base Titration Assignment
section in Canvas.
Strong Acid titration with a Strong Base
Graph 1 – Using the provided HCl data, make a plot of pH versus the volume of NaOH titrated pertaining
to the HCl neutralization with NaOH titration. Then, print out the appropriately titled (including axes and
units if needed) plot filling the page as best as possible. You may want to watch a you tube video or two
about strong acids titrated with strong bases.
On Graph 1
1. Use the midpoint of the inflection region (the vertical part of your plot) to mark on the x axis the
volume of NaOH required to reach the equivalence point and write the numerical value of this
volume on the x-axis.
2. Mark the spot and write out the pH value at the equivalence point on the y-axis.
3. Note, phenolphthalein changes from colorless to pink in a pH range from about 8.0 to 9.8. On the
plot, note the pH where it is active (changes color) using a bracket to mark on the titration curve
the region where the change of color occurs.
4. Give the balanced chemical reaction of HCl with NaOH. Use this along with the volume of NaOH
required to reach the equivalence point to calculate the concentration of the original 15 ml sample
of HCl.
Graph 2 and 3 – Using the provided H3PO4 data, make a plot of pH versus the volume of NaOH titrated
pertaining to the H3PO4 neutralization with NaOH titration. Then, print two copies of the appropriately titled
(including axes and units if needed) plot filling the page as best as possible. You may want to watch a you
tube video or two about weak polyprotic acids titrated with a strong base. These plots are called “Graph
2” and “Graph 3”. You may want to watch a you tube video or two about Weak acids titrated with Strong
bases.
On Graph 2
1. Use the midpoint of the inflection regions (the two vertical parts of the plot) to mark and write out
the values for both of the volumes (on the x-axis) of NaOH needed to reach the first and second
equivalence points.
2. Give the values for the pH’s at the equivalence points on the y-axis.
3. Give the two balanced chemical equations for H3PO4 with NaOH that correspond to the reactions
that took place before the first equivalence point as well as the reaction that takes place between
the first and the second equivalence point. Use the first balanced equation (H3PO4 + NaOH =>)
along with the first equivalence point volume of NaOH to calculate the concentration of the
original 15 ml sample of H3PO4. Then use the second balanced equation (H3PO4 + 2NaOH =>)
along with the second equivalence point volume of NaOH to calculate the concentration of the
original 15 ml sample of H3PO4. Find the percent difference in the two calculated concentrations
of H3PO4.
On Graph 3 (see above “Background” for definitions)
1. Indicate on the y axis the locations and numerical values of the pKa’s .
2. Roughly bracket the NaOH volumes corresponding to both of the buffer regions. Write the
equilibrium equations that correspond to both buffer regions, e.g. show the acid in equilibrium
with its’ conjugate base for each case.
3. Use phenolphthalein as the indicator for the detection of the second equivalence point. Mark on
the titration curve where the change of color is occurring.
4. Compare the pH values calculated from (1/2)(pKa1 + pKa2) and that measured from the titration
curve at the first equivalence point with a % difference calculation.
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