SCIENCE · INVESTIGATE AND EXPLAIN

Cross a titration equivalence point without changing conservation laws

One charge balance can describe initial acid, buffer, equivalence and excess base.

Learning outcome: Compare initial, half-equivalence, equivalence and excess-base points. Retain dilution and charge residuals; contrast the strong-acid curve with identical starting equivalents.

Starting recap

Refresh proton equivalents, conjugate pairs, logarithmic dimensionless activity, analytical amount/volume, mass and charge balances, and bounded observational criteria.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

The packet starts with .00250 mol HA. At 25.0 mL of .100 M base, total volume .0500 L and acid-family concentration .0500 M; conjugate-base hydrolysis makes equivalence basic.

Open the experiment

Predict

Why can equal acid/base equivalents leave pH above 7 in a weak-acid titration?

Your prediction and reason

Experiment

Compare initial, half-equivalence, equivalence and excess-base points. Retain dilution and charge residuals; contrast the strong-acid curve with identical starting equivalents.

Follow a titration through one global charge balance

Worked teaching model · synthetic values · Fictional25.0 mL of .100 M neutral HA receives .100 M fully dissociated monobasic base with inert sodium ion; additive volumes. At each point C=.00250/(.025+Vb), Na=.100Vb/(.025+Vb); h+Na=Kw/h+C Ka/(Ka+h), Kw10⁻¹⁴. Ideal supplied packet, not an experimental procedure.

Added .100 M monobasic strong-base volume: 25 mL Weak-acid pKa: 5 dimensionless

Reset keeps your prediction, captures and practice history.

Weak acid exact pH: solid
Strong acid comparison at same amounts: long dashes

Axes rescale. A concentration scan, imposed-pH distribution and titration curve have different horizontal meanings. Read each axis and preserve the difference between an imposed condition and an inferred equilibrium.

All calculated plot coordinates

Weak acid exact pH
added .100 M base volume (mL)	pH
0	3.002171
0.5	3.393088
1	3.645664
1.5	3.817301
2	3.946461
2.5	4.050463
3	4.138041
3.5	4.214136
4	4.281797
4.5	4.343033
5	4.399238
5.5	4.451419
6	4.50033
6.5	4.546549
7	4.590533
7.5	4.632649
8	4.6732
8.5	4.712438
9	4.750578
9.5	4.787806
10	4.824288
10.5	4.860171
11	4.895587
11.5	4.930663
12	4.965517
12.5	5.00026
13	5.035006
13.5	5.069865
14	5.104951
14.5	5.140383
15	5.176284
15.5	5.212791
16	5.250051
16.5	5.28823
17	5.327517
17.5	5.368127
18	5.410318
18.5	5.454396
19	5.500735
19.5	5.549799
20	5.602182
20.5	5.658659
21	5.720272
21.5	5.788479
22	5.865406
22.5	5.954344
23	6.060795
23.5	6.19507
24	6.380298
24.5	6.690264
25	8.849498
25.5	10.9957
26	11.29244
26.5	11.46429
27	11.58503
27.5	11.67778
28	11.75285
28.5	11.81571
29	11.86967
29.5	11.91682
30	11.95861
30.5	11.99607
31	12.02996
31.5	12.06087
32	12.08922
32.5	12.11539
33	12.13966
33.5	12.16226
34	12.18339
34.5	12.20321
35	12.22185
35.5	12.23943
36	12.25606
36.5	12.27182
37	12.28679
37.5	12.30103
38	12.3146
38.5	12.32756
39	12.33995
39.5	12.35181
40	12.36318
40.5	12.37409
41	12.38458
41.5	12.39466
42	12.40437
42.5	12.41373
43	12.42276
43.5	12.43148
44	12.4399
44.5	12.44805
45	12.45593
45.5	12.46356
46	12.47096
46.5	12.47813
47	12.48509
47.5	12.49184
48	12.4984
48.5	12.50478
49	12.51098
49.5	12.51701
50	12.52288

Strong acid comparison at same amounts
added .100 M base volume (mL)	pH
0	1
0.5	1.017374
1	1.034762
1.5	1.052178
2	1.069636
2.5	1.08715
3	1.104735
3.5	1.122406
4	1.140179
4.5	1.158068
5	1.176091
5.5	1.194265
6	1.212608
6.5	1.231139
7	1.249877
7.5	1.268845
8	1.288065
8.5	1.307561
9	1.327359
9.5	1.347487
10	1.367977
10.5	1.38886
11	1.410174
11.5	1.431959
12	1.454258
12.5	1.477121
13	1.500602
13.5	1.524763
14	1.549672
14.5	1.575408
15	1.60206
15.5	1.629731
16	1.658541
16.5	1.688629
17	1.720159
17.5	1.753328
18	1.78837
18.5	1.825576
19	1.865301
19.5	1.907997
20	1.954243
20.5	2.004799
21	2.060698
21.5	2.123385
22	2.194977
22.5	2.278754
23	2.380211
23.5	2.50965
24	2.690196
24.5	2.995635
25	7
25.5	10.99568
26	11.29243
26.5	11.46428
27	11.58503
27.5	11.67778
28	11.75285
28.5	11.81571
29	11.86967
29.5	11.91682
30	11.95861
30.5	11.99607
31	12.02996
31.5	12.06086
32	12.08922
32.5	12.11539
33	12.13966
33.5	12.16226
34	12.18339
34.5	12.20321
35	12.22185
35.5	12.23943
36	12.25606
36.5	12.27182
37	12.28679
37.5	12.30103
38	12.3146
38.5	12.32756
39	12.33995
39.5	12.35181
40	12.36318
40.5	12.37409
41	12.38458
41.5	12.39466
42	12.40437
42.5	12.41373
43	12.42276
43.5	12.43148
44	12.4399
44.5	12.44805
45	12.45593
45.5	12.46356
46	12.47096
46.5	12.47813
47	12.48509
47.5	12.49184
48	12.4984
48.5	12.50478
49	12.51098
49.5	12.51701
50	12.52288

Calculated under the declared model
Quantity	Value	Unit
Total mixed volume	0.05	L
Analytical acid-family concentration	0.05	mol/L
Inert sodium concentration	0.05	mol/L
Exact equilibrated pH	8.849498	pH units
Equivalence volume	25	mL
Charge-balance residual	-1.387779e-17	mol/L

Stoichiometric equivalence leaves a hydrolyzing conjugate base, not necessarily neutral water.

One charge-balance equation handles initial acid, buffer region, equivalence and excess base with dilution included. Near half-equivalence the HH pH≈pKa shortcut is useful, not mathematically exact once water and residual acid ionization are retained. Strong/strong equivalence is neutral under this ideal 25°C convention; weak-acid/strong-base equivalence is basic.

These calculated packets are not performed chemical measurements. Keep feasible inventories, activity conventions, fitting observations and independent checks distinct.

Stoichiometric equivalence leaves a hydrolyzing conjugate base, not necessarily neutral water.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Keep amounts and volume separate

Initially 25.0 mL of .100 M HA contains .00250 mol acid family. Adding volume Vb in liters of .100 M monobasic strong base contributes .100Vb mol inert sodium ion and increases total volume to .0250+Vb L. The acid-family total concentration and sodium concentration therefore have different numerators but the same changing denominator.

For ideal activities and Kw10⁻¹⁴, solve h+Na=Kw/h+C Ka/(Ka+h). The same equation applies before and after stoichiometric equivalence. Its physical interpretation changes, but charge conservation does not switch off at a convenient region boundary.

Explain equivalence without assuming neutrality

At 25.0 mL base, the sodium and acid-family analytical concentrations are both .0500 M. The weak-acid conjugate base hydrolyzes, so equilibrium is basic. In the comparison strong-acid/strong-base packet with inert ions, equal equivalents give neutrality under the declared25°C convention.

Near half-equivalence, equal nominal HA and A− give the useful pH≈pKa relation. Residual ionization and water mean it is not an exact identity in the full model. After equivalence, excess hydroxide is a good leading approximation but dilution remains essential.

Transfer and check

For the same starting acid and 35.0 mL base, excess base is .00350−.00250=.00100 mol in .0600 L, approximately .0166667 M hydroxide. Thus pOH≈1.77815 and pH≈12.22185 at pKw 14, with a very small conjugate-base correction. Explain why dividing excess moles by the original25 mL would overstate basicity.

Source and evidence boundary

Conceptual reference checked 30 October 2026: OpenStax Chemistry 2e. Prose, numerical packets and diagrams are original. All chemistry is fictional or supplied; no substance handling, mixing, titration apparatus or health interpretation is requested. The ideal concentration approximation, fixed temperature and inert-ion assumptions are explicit, not measured calibration. Retain your charge/mass balance, prediction, changed-case check and limits.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why is pH≈pKa at half-equivalence a useful approximation rather than an identity under the full water/charge model?

Your explanation and limitations

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Previous: Distinguish a pH ratio from a differential amount reserve Next: Map an indicator transition onto an asymmetric volume interval

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