SCIENCE · INVESTIGATE AND EXPLAIN

Reject a basic prediction for an extremely dilute strong acid

Complete dissociation does not eliminate water from the charge balance.

Learning outcome: Vary analytical concentration across the water scale and compare exact versus neglect-water pH. Verify h−OH=C and reject the negative quadratic root.

Starting recap

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

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Try

At C=10⁻⁸ M and Kw=10⁻¹⁴, h=(C+√(C²+4Kw))/2≈1.05125×10⁻⁷ M, pH≈6.9783 rather than 8.

Open the experiment

Predict

Which assumption fails when pH=−log C predicts a basic result after adding acid to pure ideal water?

Your prediction and reason

Experiment

Vary analytical concentration across the water scale and compare exact versus neglect-water pH. Verify h−OH=C and reject the negative quadratic root.

Retain water when strong acid becomes extremely dilute

Worked teaching model · synthetic values · Completely dissociated monoprotonic fictional acid with inert monovalent counteranion, ideal activities and no dissolved carbon dioxide. Charge balance h=C+OH and h*OH=Kw. Concentrations numerically in M; c°=1 M.

Negative log analytical strong-acid concentration: 8 −log10(C/1 M) Supplied pKw: 14 dimensionless

Reset keeps your prediction, captures and practice history.

Exact pH: solid
Neglect-water pH: 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

Exact pH
−log10 analytical acid concentration / 1 M	pH
3	3
3.06	3.06
3.12	3.12
3.18	3.18
3.24	3.24
3.3	3.3
3.36	3.36
3.42	3.42
3.48	3.48
3.54	3.54
3.6	3.6
3.66	3.66
3.72	3.72
3.78	3.78
3.84	3.84
3.9	3.9
3.96	3.96
4.02	4.02
4.08	4.079999
4.14	4.139999
4.2	4.199999
4.26	4.259999
4.32	4.319998
4.38	4.379998
4.44	4.439997
4.5	4.499996
4.56	4.559994
4.62	4.619992
4.68	4.67999
4.74	4.739987
4.8	4.799983
4.86	4.859977
4.92	4.91997
4.98	4.97996
5.04	5.039948
5.1	5.099931
5.16	5.159909
5.22	5.21988
5.28	5.279842
5.34	5.339792
5.4	5.399726
5.46	5.459639
5.52	5.519525
5.58	5.579374
5.64	5.639175
5.7	5.698913
5.76	5.758569
5.82	5.818117
5.88	5.877522
5.94	5.936742
6	5.995721
6.06	6.054385
6.12	6.112642
6.18	6.170376
6.24	6.227442
6.3	6.28366
6.36	6.338818
6.42	6.392666
6.48	6.444921
6.54	6.495279
6.6	6.543426
6.66	6.58906
6.72	6.631913
6.78	6.671776
6.84	6.70851
6.9	6.742062
6.96	6.772457
7.02	6.799793
7.08	6.824223
7.14	6.845942
7.2	6.865166
7.26	6.882121
7.32	6.897034
7.38	6.910121
7.44	6.921585
7.5	6.931615
7.56	6.94038
7.62	6.948034
7.68	6.954714
7.74	6.96054
7.8	6.96562
7.86	6.970049
7.92	6.973909
7.98	6.977272
8.04	6.980203
8.1	6.982756
8.16	6.98498
8.22	6.986918
8.28	6.988605
8.34	6.990075
8.4	6.991356
8.46	6.992471
8.52	6.993443
8.58	6.994289
8.64	6.995026
8.7	6.995667
8.76	6.996226
8.82	6.996713
8.88	6.997137
8.94	6.997507
9	6.997829

Neglect-water pH
−log10 analytical acid concentration / 1 M	pH
3	3
3.06	3.06
3.12	3.12
3.18	3.18
3.24	3.24
3.3	3.3
3.36	3.36
3.42	3.42
3.48	3.48
3.54	3.54
3.6	3.6
3.66	3.66
3.72	3.72
3.78	3.78
3.84	3.84
3.9	3.9
3.96	3.96
4.02	4.02
4.08	4.08
4.14	4.14
4.2	4.2
4.26	4.26
4.32	4.32
4.38	4.38
4.44	4.44
4.5	4.5
4.56	4.56
4.62	4.62
4.68	4.68
4.74	4.74
4.8	4.8
4.86	4.86
4.92	4.92
4.98	4.98
5.04	5.04
5.1	5.1
5.16	5.16
5.22	5.22
5.28	5.28
5.34	5.34
5.4	5.4
5.46	5.46
5.52	5.52
5.58	5.58
5.64	5.64
5.7	5.7
5.76	5.76
5.82	5.82
5.88	5.88
5.94	5.94
6	6
6.06	6.06
6.12	6.12
6.18	6.18
6.24	6.24
6.3	6.3
6.36	6.36
6.42	6.42
6.48	6.48
6.54	6.54
6.6	6.6
6.66	6.66
6.72	6.72
6.78	6.78
6.84	6.84
6.9	6.9
6.96	6.96
7.02	7.02
7.08	7.08
7.14	7.14
7.2	7.2
7.26	7.26
7.32	7.32
7.38	7.38
7.44	7.44
7.5	7.5
7.56	7.56
7.62	7.62
7.68	7.68
7.74	7.74
7.8	7.8
7.86	7.86
7.92	7.92
7.98	7.98
8.04	8.04
8.1	8.1
8.16	8.16
8.22	8.22
8.28	8.28
8.34	8.34
8.4	8.4
8.46	8.46
8.52	8.52
8.58	8.58
8.64	8.64
8.7	8.7
8.76	8.76
8.82	8.82
8.88	8.88
8.94	8.94
9	9

Calculated under the declared model
Quantity	Value	Unit
Analytical acid concentration	1.000000e-8	mol/L
Hydronium including water	1.051249e-7	mol/L
Hydroxide concentration	9.512492e-8	mol/L
Charge-balance residual	2.316106e-23	mol/L
Exact ideal pH	6.978294	pH units
Neglect-water pH	8	pH units
Neutral pH	7	pH units

A dilute strong acid approaches neutrality from the acidic side, not from the basic side.

Solve h²−Ch−Kw=0 using the positive root. Complete solute dissociation does not mean all hydronium comes from the added acid. The negative root is inadmissible; fixed-temperature water autoionization and charge balance prevent the incorrect pH8 prediction for a 10⁻⁸ M acid at pKw 14.

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

A dilute strong acid approaches neutrality from the acidic side, not from the basic side.

Observation to attach to a capture

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

Understand

Write both equations

A fictional monoprotonic strong acid completely dissociates into hydronium and an inert monovalent anion at analytical concentration C. Water still contributes hydronium and hydroxide. Charge balance is h=C+OH, while autoionization gives h OH=Kw.

Substitution yields h²−Ch−Kw=0. Its positive root is (C+√(C²+4Kw))/2. The negative root cannot describe a concentration. For C much larger than √Kw, h≈C is adequate; the condition must be checked rather than applied to every strong acid.

Inspect the dilute boundary

At C=10⁻⁸ M and Kw=10⁻¹⁴, the positive root is about 1.05125×10⁻⁷ M, giving pH6.9783. The tempting −log C=8 result would call an acid addition basic because it silently discarded the water contribution. As C approaches zero, the correct model approaches neutral pH from the acidic side.

This does not describe atmospheric contamination, electrode limitations or real ultradilute sample preparation. Those effects could dominate an actual measurement and require independent evidence; the model isolates one logical bookkeeping issue.

Transfer and check

At C=10⁻⁷ M with the same Kw, h=(1+√5)×.5×10⁻⁷≈1.61803×10⁻⁷ M. Thus pH≈6.7910, OH≈6.18034×10⁻⁸ M, and h−OH returns10⁻⁷ M. Predict whether increasing C to 10⁻⁶ M makes the neglect-water shortcut better or worse, then justify the comparison of scales.

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 does complete dissociation describe the solute without specifying the total source of hydronium?

Your explanation and limitations

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Previous: Use the water constant instead of assuming neutral always means seven Next: Infer a weak-acid state from mass, charge and water together

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