Year 12 Chemistry Module 6 — Acid/Base Reactions ⏱ ~45 min Lesson 9 of 19 IQ2

pH of Weak Acids & Bases — Ka, Kb & ICE Tables

Aspirin (acetylsalicylic acid) has Ka = 3.0 × 10⁻⁴ — and the ICE table you will build in this lesson predicts exactly how much H⁺ aspirin releases in your stomach, why it irritates the gastric lining, and why enteric-coated tablets dissolve in the intestine instead.

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Think First — Aspirin vs Ibuprofen

A pharmacology researcher is comparing two pain relief tablets. Tablet A contains 500 mg of aspirin (acetylsalicylic acid, Ka = 3.0 × 10⁻⁴, M = 180 g/mol). Tablet B contains 500 mg of ibuprofen (Ka = 1.3 × 10⁻⁵, M = 206 g/mol). Both dissolve in 200 mL of stomach fluid (approximately 0.1 mol/L HCl, pH ≈ 1).

The researcher wants to predict which tablet releases more H⁺ ions and therefore causes more gastric irritation. Before you read on, write down your prediction: which tablet do you think releases more H⁺? Is it the one with the higher Ka, the higher mass, or the higher molar concentration in stomach fluid? Will either tablet significantly change the pH of stomach acid? You will return to this prediction at the end of the lesson.

📚 Know

  • ICE tables track Initial, Change, and Equilibrium concentrations
  • The simplifying assumption [HA]initial − x ≈ [HA]initial is valid when Ka/c < 0.0025
  • Kb = Kw/Ka for conjugate acid-base pairs

🔗 Understand

  • Why weak acids require ICE tables while strong acids do not
  • When the simplifying assumption fails and how to solve exactly
  • Why mixing weak acid with strong base creates a buffer in the intermediate region

✅ Can Do

  • Set up and solve ICE tables for weak acid and weak base equilibria
  • Calculate pH of weak acids and weak bases
  • Determine Ka from measured pH data
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Key Formulas — Ka, Kb, ICE Tables, Assumption & Henderson-Hasselbalch

Ka = [H⁺][A⁻] / [HA]  |  pKa = −log₁₀(Ka)  |  Ka = 10⁻ᵖᴷᵃ
Weak acid equilibrium: HA(aq) ⇌ H⁺(aq) + A⁻(aq)
ICE table → Ka = x² / (c − x)
Simplifying assumption (x << c): valid when Ka/c < 0.0025 → x = √(Ka × c) = [H⁺]
If invalid (Ka/c ≥ 0.0025): x = (−Ka + √(Ka² + 4·Ka·c)) / 2   (positive root only)
Weak base: Kb = [BH⁺][OH⁻] / [B]  |  [OH⁻] = √(Kb × c) if assumption valid
Then: pOH = −log[OH⁻] → pH = 14 − pOH
Conjugate pair: Ka × Kb = Kw = 1.0 × 10⁻¹⁴  |  Kb = Kw / Ka  |  Ka = Kw / Kb
Ka from measured pH: [H⁺] = 10⁻ᵖᴴ → Ka = [H⁺]² / (c − [H⁺])
Degree of ionisation: α = ([H⁺]/c) × 100%
Henderson-Hasselbalch: pH = pKa + log([A⁻]/[HA])
For partial neutralisation: [A⁻]/[HA] can be replaced by n(A⁻)/n(HA) (same volume, cancels)
At half-equivalence point: [A⁻] = [HA] → log(1) = 0 → pH = pKa

Choose how you work — type your answers below or write in your book.

01

Learning Intentions

  • Construct an ICE table for a weak acid or base and derive Ka = x²/(c − x)
  • Apply the simplifying assumption (Ka/c < 0.0025) and verify it after calculating x
  • Solve the full quadratic when the simplifying assumption is invalid
  • Calculate pH of weak base solutions via [OH⁻] → pOH → pH
  • Use Ka × Kb = Kw to find Kb for a conjugate base given Ka of the parent acid
  • Reverse-calculate Ka from a measured pH using Ka = [H⁺]²/(c − [H⁺])
  • Apply Henderson-Hasselbalch to calculate pH after partial neutralisation of a weak acid
Key Terms — scan these before reading
Dynamic equilibriumA state where forward and reverse reaction rates are equal.
Le Chatelier's PrincipleA system at equilibrium shifts to minimise applied disturbances.
Equilibrium constant (Keq)The ratio of product to reactant concentrations at equilibrium.
Reaction quotient (Q)The ratio of product to reactant concentrations at any instant.
Closed systemA system where neither matter nor energy can escape to surroundings.
Reversible reactionA reaction that can proceed in both forward and reverse directions.
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Card 1 — Why Weak Acids Need a Different Method: The ICE Table Logic

For a strong acid, [H⁺] = concentration because ionisation is complete — no equilibrium to solve. For a weak acid, most molecules remain intact at equilibrium, and the fraction that ionise depends on both Ka and concentration — which is why a systematic method (the ICE table) is required to find the actual [H⁺].

The ICE table is the systematic framework for weak acid calculations. ICE = Initial, Change, Equilibrium — three rows that track concentrations of every species from start through to equilibrium. For a weak acid HA at initial concentration c:

I (Initial)

[HA]: c
[H⁺]: 0
[A⁻]: 0
Notes: Starting concentrations

C (Change)

[HA]: −x
[H⁺]: +x
[A⁻]: +x
Notes: Equilibrium shift (1:1:1 ratio)

E (Equilibrium)

[HA]: c − x
[H⁺]: x
[A⁻]: x
Notes: When forward rate = reverse rate

Substituting E-row into Ka = [H⁺][A⁻]/[HA] gives: Ka = x²/(c − x). Solving for x gives [H⁺] at equilibrium → pH = −log(x).

For 0.1 mol/L CH₃COOH (Ka = 1.8 × 10⁻⁵), using [H⁺] = c (the strong acid shortcut) gives pH = 1.0. The correct ICE method gives pH ≈ 2.87 — a difference of nearly 2 pH units, corresponding to a factor of ~74 in [H⁺].

Must Do
Always write the full ICE table before substituting into Ka. Students who skip to Ka = x²/c frequently make sign errors, stoichiometry errors, or forget the (c − x) denominator. Writing the ICE table takes 30 seconds and eliminates most errors in weak acid calculations.
Common Error
Students write [H⁺] = 10⁻⁷ in the Initial row (from water autoionisation). This is incorrect — the water contribution to [H⁺] is negligible compared to any weak acid at practical concentrations (c >> 10⁻⁷ mol/L). Always set [H⁺] = 0 in the Initial row for weak acid ICE tables.
Exam TipIn acid-base calculations, always write the balanced equation first, identify the conjugate pair, and state any assumptions before substituting into the Ka expression.
03

Card 2 — The Simplifying Assumption: When It Applies and When It Fails

Solving Ka = x²/(c − x) exactly requires the quadratic formula — but for most weak acid problems a simplifying assumption reduces this to a one-step square root calculation, and knowing when the assumption is valid versus when the quadratic is necessary is itself an HSC exam skill.

The simplifying assumption: if x << c, then c − x ≈ c, and Ka ≈ x²/c → x ≈ √(Ka × c).

The assumption is valid when degree of ionisation < 5%. A faster check: if Ka/c < 0.0025, the assumption is valid (since x/c = √(Ka/c)).

When the assumption fails (Ka/c ≥ 0.0025), solve the full quadratic: x² + Ka·x − Ka·c = 0, taking the positive root only:

x = (−Ka + √(Ka² + 4·Ka·c)) / 2

Assumption valid?
✓ Yes
✗ No
✓ Yes (0.01% << 5%)
✗ No (20% >> 5%)
Method
x = √(Ka × c); check x/c < 5% ✓
x = (−Ka + √(Ka² + 4Kac))/2
Square root valid
Quadratic required
Must Do
Always check the simplifying assumption after using it — not before. Calculate x = √(Ka × c), then verify (x/c) × 100% < 5%. If it fails, go back and solve the quadratic. Writing "assumption valid" without checking it is a methodology error that loses marks in HSC extended response.
Common Error
Students who skip the check and use the simplifying assumption when it fails obtain [H⁺] values that are systematically too high (x is overestimated when c − x is not approximated as c). For Ka/c = 0.20, the error in [H⁺] is ~13% — significant for precise pH calculations.
Insight
The 5% rule is a practical compromise — there is nothing magical about 5%. In contexts requiring very precise pH (pharmaceutical quality control, blood buffer calculations), a 1% threshold is used. In HSC, the 5% rule is standard — but knowing where it comes from (acceptable error in [H⁺] propagating to pH) is the Band 6 understanding.
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Card 3 — Weak Base Calculations: Kb and the pOH Route

Weak base pH calculations follow exactly the same ICE table logic as weak acid calculations — the only differences are that the equilibrium produces OH⁻ instead of H⁺, the equilibrium constant is Kb instead of Ka, and the final step requires converting [OH⁻] to pH via the pOH route.

For a weak base B at initial concentration c: B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq). Kb = [BH⁺][OH⁻]/[B].

I

[B]: c
[BH⁺]: 0
[OH⁻]: 0

C

[B]: −x
[BH⁺]: +x
[OH⁻]: +x

E

[B]: c − x
[BH⁺]: x
[OH⁻]: x

If Kb/c < 0.0025: x = √(Kb × c) = [OH⁻]. Then: pOH = −log[OH⁻] → pH = 14 − pOH.

The conjugate pair relationship Ka × Kb = Kw = 1.0 × 10⁻¹⁴ connects acid and base calculations. Given Ka for HA, find Kb for A⁻: Kb = Kw/Ka. For example, CH₃COO⁻ (conjugate base of acetic acid, Ka = 1.8 × 10⁻⁵): Kb = (1.0 × 10⁻¹⁴)/(1.8 × 10⁻⁵) = 5.6 × 10⁻¹⁰.

Weak baseKbc (mol/L)[OH⁻] = √(Kb × c)pOHpH
NH₃1.8 × 10⁻⁵0.101.34 × 10⁻³2.8711.13
CH₃COO⁻5.6 × 10⁻¹⁰0.107.48 × 10⁻⁶5.138.87
CO₃²⁻2.1 × 10⁻⁴0.0503.24 × 10⁻³2.4911.51
Must Do
The mandatory three-step sequence for weak bases: (1) find [OH⁻] from the ICE table; (2) pOH = −log[OH⁻]; (3) pH = 14 − pOH. Never calculate pH = −log[OH⁻] — this gives a number below 7 for a basic solution, which is immediately recognisable as wrong but still loses marks.
Common Error
Students apply Ka × Kb = Kw to non-conjugate pairs. This relationship applies only to a conjugate acid-base pair — the specific acid HA and its conjugate base A⁻. Ka(CH₃COOH) × Kb(NH₃) ≠ Kw because CH₃COOH and NH₃ are not a conjugate pair. Always identify the conjugate pair explicitly before applying this relationship.
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Card 4 — Finding Ka from Measured pH: The Reverse Calculation

Every Ka value in every data table was originally determined from a pH measurement — and being able to reverse the calculation (from measured pH back to Ka) is both a practical laboratory skill and a frequently examined HSC calculation type.

If the pH of a weak acid solution of known concentration is measured, Ka can be calculated by reversing the ICE table:

Calculation
[H⁺] = 10⁻ᵖᴴ
[A⁻] = [H⁺] (stoichiometry)
[HA] = c − [H⁺]
Ka = [H⁺]² / (c − [H⁺])
α = ([H⁺]/c) × 100%
What it finds
Equilibrium [H⁺] = x
Equilibrium [A⁻]
Equilibrium [HA] (amount not ionised)
Acid dissociation constant
Degree of ionisation (check vs 5%)
Must Do
In step 3, [HA] = c − [H⁺], not just c. Students frequently write Ka = [H⁺]²/c instead of Ka = [H⁺]²/(c − [H⁺]) in the reverse calculation. In the reverse direction you already know [H⁺] — use the exact expression Ka = [H⁺]²/(c − [H⁺]) always.
Common Error
Students confuse Ka with pKa — writing Ka = pH or Ka = −log(pH). These are distinct quantities: pH describes the actual [H⁺] in a specific solution; pKa describes the intrinsic acid strength. They are equal only at the half-equivalence point of a titration (developed in L16).
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Card 5 — Mixing Weak Acid with Strong Base: Introduction to the Buffer Region

When a weak acid is partially neutralised by a strong base — before the equivalence point — the solution contains significant amounts of both the weak acid and its conjugate base simultaneously, and the pH calculation must account for this mixture using the Henderson-Hasselbalch equation.

When NaOH is added to HA before the equivalence point: HA + OH⁻ → A⁻ + H₂O (goes to completion — NaOH is strong). After the reaction, some HA remains and A⁻ has been formed. The solution contains both HA and A⁻ — this is a buffer solution (developed fully in L13).

pH is calculated using the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). In the same volume, [A⁻]/[HA] = n(A⁻)/n(HA) (volumes cancel). At the half-equivalence point — exactly half the acid neutralised — n(A⁻) = n(HA), so log(1) = 0 and pH = pKa.

What to calculate
Moles of HA initially
Moles of OH⁻ added
HA remaining after reaction
A⁻ formed
pH of buffer mixture
Formula
n(HA) = c(HA) × V(HA)
n(OH⁻) = c(NaOH) × V(NaOH)
n(HA)rem = n(HA) − n(OH⁻)
n(A⁻) = n(OH⁻)   (1:1 stoich)
pH = pKa + log(n(A⁻)/n(HA))
Must Do
In Henderson-Hasselbalch, [A⁻]/[HA] can be replaced by n(A⁻)/n(HA) when both species are in the same solution — volumes cancel in the ratio. This means you can use moles directly without calculating concentrations. This is the standard shortcut for buffer and partial neutralisation calculations.
Common Error
Students apply the simple ICE table method (x = √(Ka × c)) to a solution containing both HA and A⁻ after partial neutralisation. The ICE table assumes [A⁻] = 0 initially — this is invalid when A⁻ has been produced by neutralisation. A solution containing both HA and A⁻ is a buffer — it requires Henderson-Hasselbalch. The ICE table method ignores the common ion effect of A⁻ and gives a pH that is erroneously too low.

⚠ Common Misconceptions — Weak Acid/Base Calculations

"pH = pKa for any weak acid solution." — Incorrect. pH = pKa only at the half-equivalence point of a titration, when [A⁻] = [HA]. For a pure weak acid solution, pH = −log(√(Ka × c)) which is approximately pKa/2 + log(c)/2 — always lower than pKa.

"I don't need to check the 5% rule if Ka is small." — Incorrect. Ka must be small relative to c. For a very dilute solution (c = 0.001 mol/L) with Ka = 1.0 × 10⁻⁴, Ka/c = 0.10 = 10% — the assumption fails even though Ka appears small in absolute terms.

"Ka × Kb = Kw can be used for any acid and base." — Incorrect. This only applies to a specific conjugate pair (HA and its conjugate base A⁻). Ka(HCl) × Kb(NH₃) ≠ Kw — HCl and NH₃ are not a conjugate pair.

"A salt formed by neutralisation always has pH = 7." — Incorrect. Only salts from strong acid + strong base give pH = 7. Salts from weak acid + strong base (e.g. CH₃COONa) are basic; salts from strong acid + weak base (e.g. NH₄Cl) are acidic.

Worked Example 1 — ICE Table pH Calculation with Assumption Check

Calculate the pH of 0.150 mol/L propanoic acid (CH₃CH₂COOH, Ka = 1.3 × 10⁻⁵) at 25°C. Check whether the simplifying assumption is valid.

1

GIVEN: c = 0.150 mol/L, Ka = 1.3 × 10⁻⁵. FIND: pH.

2

Pre-check assumption: Ka/c = (1.3 × 10⁻⁵)/0.150 = 8.7 × 10⁻⁵ = 0.0087% << 5% → assumption likely valid. Proceed with square root.

3

ICE table:

I

[CH₃CH₂COOH]: 0.150
[H⁺]: 0
[CH₃CH₂COO⁻]: 0

C

[CH₃CH₂COOH]: −x
[H⁺]: +x
[CH₃CH₂COO⁻]: +x

E

[CH₃CH₂COOH]: 0.150 − x
[H⁺]: x
[CH₃CH₂COO⁻]: x
4

Apply simplifying assumption: x = √(Ka × c) = √(1.3 × 10⁻⁵ × 0.150) = √(1.95 × 10⁻⁶) = 1.396 × 10⁻³ mol/L.

Verify: degree of ionisation = (1.396 × 10⁻³/0.150) × 100% = 0.93% < 5% ✓ Assumption valid.

5

Calculate pH: pH = −log(1.396 × 10⁻³) = −log(1.396) + 3 = −0.145 + 3 = 2.85.

Sanity check: pH 2.85 < 7 ✓ (acid). pH 2.85 > 1.0 (not treating it as strong acid) ✓

ANSWER: [H⁺] = 1.40 × 10⁻³ mol/L; pH = 2.85. Degree of ionisation = 0.93% — simplifying assumption valid.

Worked Example 2 — Multi-Part: Ka, Kb, Conjugate Base pH, and Claim Evaluation

Acetic acid has Ka = 1.8 × 10⁻⁵. (a) Calculate the pH of 0.250 mol/L CH₃COOH. (b) Calculate Kb for the acetate ion (CH₃COO⁻). (c) Calculate the pH of 0.250 mol/L sodium acetate (CH₃COONa). (d) Evaluate the claim: "The pH of 0.250 mol/L sodium acetate should be 7 because it is a salt formed by neutralisation."

1

GIVEN: Ka(CH₃COOH) = 1.8 × 10⁻⁵; c = 0.250 mol/L for both solutions.

2

METHOD (a — acetic acid pH): Check: Ka/c = 1.8 × 10⁻⁵/0.250 = 7.2 × 10⁻⁵ << 0.0025 ✓. x = √(1.8 × 10⁻⁵ × 0.250) = √(4.5 × 10⁻⁶) = 2.121 × 10⁻³ mol/L. Verify: 2.121 × 10⁻³/0.250 = 0.85% < 5% ✓. pH = −log(2.121 × 10⁻³) = 2.67.

3

METHOD (b — Kb for CH₃COO⁻): Ka × Kb = Kw → Kb = Kw/Ka = (1.0 × 10⁻¹⁴)/(1.8 × 10⁻⁵) = 5.56 × 10⁻¹⁰.

4

METHOD (c — sodium acetate pH): CH₃COONa → Na⁺ (neutral spectator) + CH₃COO⁻ (weak base). ICE for CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻: Check: Kb/c = 5.56 × 10⁻¹⁰/0.250 = 2.22 × 10⁻⁹ << 0.0025 ✓. x = √(5.56 × 10⁻¹⁰ × 0.250) = √(1.39 × 10⁻¹⁰) = 1.179 × 10⁻⁵ mol/L = [OH⁻]. Verify: 1.179 × 10⁻⁵/0.250 = 0.0047% < 5% ✓. pOH = −log(1.179 × 10⁻⁵) = 4.93. pH = 14.00 − 4.93 = 9.07.

5

METHOD (d — evaluate claim): The student's claim is incorrect. Sodium acetate is the salt of a strong base (NaOH) and a weak acid (CH₃COOH). A neutral solution (pH = 7) results only from a salt of a strong acid + strong base. The acetate ion is the conjugate base of a weak acid — it has a significant tendency to accept H⁺ from water (Kb = 5.56 × 10⁻¹⁰), producing OH⁻ and making the solution basic (pH = 9.07). "Neutralisation" refers to the process, not the product.

ANSWER: (a) pH = 2.67. (b) Kb(CH₃COO⁻) = 5.56 × 10⁻¹⁰. (c) pH = 9.07. (d) Claim incorrect — acetate ion is the conjugate base of a weak acid; it hydrolyses to produce OH⁻, giving a basic solution. pH = 7 requires a salt of a strong acid + strong base (e.g. NaCl).

Worked Example 3 — Band 6: Ka from pH, Quadratic Check, and Partial Neutralisation
Evaluate Band 6 (8 marks)

A 0.0500 mol/L solution of weak monoprotic acid HX is measured at 25°C and found to have pH 2.78. (a) Calculate [H⁺] and the Ka of HX. (b) Check whether the simplifying assumption would have been valid for this calculation. (c) 40.0 mL of 0.0500 mol/L HX is mixed with 10.0 mL of 0.0500 mol/L NaOH. Calculate the pH of the resulting mixture. (d) A student attempts part (c) using x = √(Ka × c(HX)). Identify the conceptual error and explain the correct method.

1

GIVEN: c = 0.0500 mol/L, pH = 2.78; part (c): 40.0 mL HX + 10.0 mL NaOH, both 0.0500 mol/L.

2

METHOD (a — [H⁺] and Ka): [H⁺] = 10⁻²·⁷⁸ = 10⁻³ × 10⁰·²² = 1.0 × 10⁻³ × 1.660 = 1.66 × 10⁻³ mol/L. Ka = [H⁺]²/(c − [H⁺]) = (1.66 × 10⁻³)²/(0.0500 − 1.66 × 10⁻³) = (2.756 × 10⁻⁶)/(0.04834) = 5.70 × 10⁻⁵.

3

METHOD (b — check assumption): α = ([H⁺]/c) × 100% = (1.66 × 10⁻³/0.0500) × 100% = 3.32% < 5% ✓. The simplifying assumption would have been valid — x = √(5.70 × 10⁻⁵ × 0.0500) = √(2.85 × 10⁻⁶) = 1.688 × 10⁻³ → pH = 2.77. Error of only 0.01 pH units vs measured 2.78. ✓

4

METHOD (c — partial neutralisation): n(HX) = 0.0500 × 0.0400 = 2.00 × 10⁻³ mol. n(OH⁻) = 0.0500 × 0.0100 = 5.00 × 10⁻⁴ mol. After HA + OH⁻ → A⁻ + H₂O (complete): n(HX) remaining = 2.00 × 10⁻³ − 5.00 × 10⁻⁴ = 1.50 × 10⁻³ mol. n(X⁻) formed = 5.00 × 10⁻⁴ mol. pKa = −log(5.70 × 10⁻⁵) = 4.244. pH = pKa + log(n(X⁻)/n(HX)) = 4.244 + log(5.00 × 10⁻⁴/1.50 × 10⁻³) = 4.244 + log(0.333) = 4.244 − 0.477 = 3.77.

5

METHOD (d — conceptual error): The student's approach uses x = √(Ka × c(HX)) — the ICE table method for a pure weak acid with [A⁻] = 0 initially. This is wrong because the solution after partial neutralisation contains significant X⁻ (5.00 × 10⁻⁴ mol) simultaneously with HX. The ICE table assumes [A⁻] = 0 at the start — completely invalid here. This is a buffer solution. The X⁻ already present suppresses further ionisation of HX (common ion effect), making [H⁺] lower than the ICE table predicts. The correct method is Henderson-Hasselbalch: pH = pKa + log(n(X⁻)/n(HX)).

ANSWER: (a) [H⁺] = 1.66 × 10⁻³ mol/L; Ka = 5.70 × 10⁻⁵. (b) α = 3.32% < 5% — assumption was valid; pH error only 0.01 units. (c) n(HX)rem = 1.50 × 10⁻³ mol; n(X⁻) = 5.00 × 10⁻⁴ mol; pKa = 4.244; pH = 3.77. (d) Error: ICE table assumes [A⁻] = 0 — invalid when X⁻ is present from neutralisation; the solution is a buffer; Henderson-Hasselbalch is required; ICE method ignores common ion suppression and gives erroneously low pH.

07

📓 Copy Into Your Books

Minimum facts and procedures for Lesson 9.

  • ICE table: I (initial), C (change = −x, +x, +x), E (equilibrium = c−x, x, x) → Ka = x²/(c−x)
  • Simplifying assumption: valid when Ka/c < 0.0025 → x = √(Ka × c); always verify x/c < 5% after
  • If invalid: x = (−Ka + √(Ka² + 4·Ka·c)) / 2 (take positive root)
  • Weak base: same ICE table with Kb → [OH⁻] = x → pOH = −log[OH⁻] → pH = 14 − pOH
  • Conjugate pair: Ka × Kb = 1.0 × 10⁻¹⁴ → Kb = Kw/Ka for conjugate base
  • Ka from pH: [H⁺] = 10⁻ᵖᴴ → Ka = [H⁺]²/(c − [H⁺]); degree of ionisation = ([H⁺]/c) × 100%
  • Henderson-Hasselbalch: pH = pKa + log(n(A⁻)/n(HA)); at half-equivalence point: pH = pKa
  • Buffer (HA + A⁻ both present) → must use H-H equation, NOT the ICE table method
08

Activities

Activity A — Calculate & Interpret: ICE Table Practice

For each weak acid or base, set up a full ICE table, check the simplifying assumption, and calculate pH. Show all working.

SpeciesConcentrationKa or KbKa/c check[H⁺] or [OH⁻]pH
HNO₂ (nitrous acid)0.100 mol/LKa = 4.5 × 10⁻⁴
HCN (hydrocyanic acid)0.0500 mol/LKa = 6.2 × 10⁻¹⁰
NH₃ (ammonia)0.200 mol/LKb = 1.8 × 10⁻⁵
CH₃COOH (acetic acid)0.0100 mol/LKa = 1.8 × 10⁻⁵

Activity B — Analyse & Connect: Ka from pH and Partial Neutralisation

  1. A 0.100 mol/L solution of weak acid HA has pH 3.15 at 25°C. (a) Calculate [H⁺]. (b) Calculate Ka of HA using the exact expression. (c) Calculate the degree of ionisation. Was the simplifying assumption valid?
  2. 25.0 mL of 0.100 mol/L HA (Ka from part 1 above) is mixed with 10.0 mL of 0.100 mol/L NaOH. (a) Calculate n(HA) remaining and n(A⁻) formed. (b) Calculate pH using Henderson-Hasselbalch. (c) What would pH be at the half-equivalence point of this titration?
  3. Explain why the simple ICE table method (x = √(Ka × c)) cannot be used to calculate the pH in question 2(b). What assumption does the ICE table make that is violated?
Interactive — Weak Acid pH Stepper
Revisit Your Initial Thinking

Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?

09

Multiple Choice Questions

Analyse Band 4

1. A student sets up an ICE table for 0.200 mol/L hydrofluoric acid (HF, Ka = 6.8 × 10⁻⁴) and obtains x = 0.0117 mol/L using the simplifying assumption, without checking the validity. What error has the student made?

Apply Band 3

2. The Ka of benzoic acid (C₆H₅COOH) is 6.5 × 10⁻⁵. Calculate the pH of 0.100 mol/L benzoic acid. Which answer and method are correct?

Analyse Band 5

3. 25.0 mL of 0.100 mol/L CH₃COOH (Ka = 1.8 × 10⁻⁵) is mixed with 12.5 mL of 0.100 mol/L NaOH. A student calculates pH using x = √(Ka × 0.100). What is wrong and what is the correct pH?

Apply Band 4

4. Ammonia has Kb = 1.8 × 10⁻⁵. What is the pH of 0.050 mol/L NH₃?

Analyse Band 4

5. A 0.050 mol/L solution of weak acid HA has a measured pH of 3.50 at 25°C. Which of the following correctly calculates Ka?

10

Short Answer Questions

Apply Band 4 (4 marks)

Question 6. Calculate the pH of each of the following at 25°C. Show a full ICE table and assumption check for each.

(a) 0.0800 mol/L chloroacetic acid (ClCH₂COOH, Ka = 1.4 × 10⁻³)   (b) 0.500 mol/L sodium propanoate (CH₃CH₂COONa; Ka(CH₃CH₂COOH) = 1.3 × 10⁻⁵)

Apply Band 4 (4 marks)

Question 7. A 0.200 mol/L solution of weak acid HB has a measured pH of 2.52 at 25°C.

(a) Calculate [H⁺] and Ka of HB. (b) Calculate the degree of ionisation. Would the simplifying assumption have been valid? (c) A student claims "Ka of HB = 10⁻²·⁵² because Ka equals [H⁺] in a weak acid solution." Identify and correct the error in this reasoning.

Evaluate Band 6 (7 marks)

Question 8. Lactic acid (HC₃H₅O₃, Ka = 1.4 × 10⁻⁴) builds up in muscles during intense exercise. Consider a 0.0200 mol/L solution of lactic acid in muscle fluid at 25°C.

(a) Determine whether the simplifying assumption is valid for this system. If not, use the quadratic. Calculate [H⁺] and pH. (3 marks) (b) 30.0 mL of 0.0200 mol/L lactic acid is mixed with 10.0 mL of 0.0200 mol/L NaOH. Calculate the pH of the resulting buffer mixture. (2 marks) (c) Explain why the pH you calculated in (b) is higher than the pH in (a), even though more acid is present than in (b)'s buffer. Use the concept of the common ion effect in your answer. (2 marks)

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Revisit — Think First

Return to your prediction about aspirin vs ibuprofen. You can now calculate this precisely:

  • Aspirin in 200 mL stomach fluid: c = (0.500/180)/0.200 = 0.0139 mol/L. Approximation gives [H⁺] = √(3.0 × 10⁻⁴ × 0.0139) = 2.04 × 10⁻³ mol/L (degree of ionisation = 14.7% > 5%, so assumption fails). Quadratic gives [H⁺] ≈ 1.90 × 10⁻³ mol/L.
  • Ibuprofen in 200 mL stomach fluid: c = (0.500/206)/0.200 = 0.0121 mol/L. [H⁺] = √(1.3 × 10⁻⁵ × 0.0121) = √(1.57 × 10⁻⁷) = 3.97 × 10⁻⁴ mol/L.
  • Aspirin releases ~4.8× more H⁺ than ibuprofen (higher Ka dominates despite similar concentrations). However, stomach acid itself contains [H⁺] = 0.1 mol/L — the H⁺ from both tablets (10⁻³ to 10⁻⁴ mol/L) is negligible compared to existing stomach H⁺. Neither tablet significantly changes stomach pH. The Ka comparison matters more for intestinal absorption (higher pH environment).
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Answers

MC Answers & Explanations

Q1: B
x = √(6.8 × 10⁻⁴ × 0.200) = √(1.36 × 10⁻⁴) = 0.01166 mol/L. Check: 0.01166/0.200 = 5.83% > 5% — assumption marginally invalid. The student must check after calculating x and apply the quadratic for an accurate result. Quadratic gives x = 0.01133 mol/L (~3% smaller). Option A is wrong — the assumption must always be checked. Option C uses an incorrect formula (Ka/c has units mol/L, not mol/L). Option D has wrong ICE table sign — H⁺ is produced (+x), not consumed.

Q2: C
Benzoic acid is weak — ICE method required. Ka/c = 6.5 × 10⁻⁵/0.100 = 6.5 × 10⁻⁴ << 0.0025 ✓. x = √(6.5 × 10⁻⁵ × 0.100) = √(6.5 × 10⁻⁶) = 2.55 × 10⁻³. Verify: 2.55% < 5% ✓. pH = −log(2.55 × 10⁻³) = 2.59. Option A treats it as strong (wrong). Option B confuses pKa with pH — equal only at half-equivalence point. Option D uses Ka × c instead of √(Ka × c) — dimensional error.

Q3: B
n(CH₃COOH) = 0.100 × 0.0250 = 2.50 × 10⁻³ mol. n(OH⁻) = 0.100 × 0.0125 = 1.25 × 10⁻³ mol. After reaction: n(CH₃COOH)rem = 1.25 × 10⁻³ mol; n(CH₃COO⁻) = 1.25 × 10⁻³ mol. Half-equivalence point: [A⁻]/[HA] = 1 → pH = pKa = −log(1.8 × 10⁻⁵) = 4.74. Option A ignores NaOH — serious conceptual error. Option C applies ICE table to total volume — still ignores common ion effect of CH₃COO⁻. Option D incorrectly manipulates pKa.

Q4: C
[OH⁻] = √(1.8 × 10⁻⁵ × 0.050) = √(9.0 × 10⁻⁷) = 9.49 × 10⁻⁴ mol/L. pOH = −log(9.49 × 10⁻⁴) = 3.02. pH = 14.00 − 3.02 = 10.98. Option A took −log[OH⁻] as pH directly. Option B is the same error restated. Option D is wrong — NH₃ is basic, not neutral.

Q5: B
[H⁺] = 10⁻³·⁵⁰ = 3.16 × 10⁻⁴ mol/L. Ka = [H⁺]²/(c − [H⁺]) = (3.16 × 10⁻⁴)²/(0.050 − 3.16 × 10⁻⁴) = (9.99 × 10⁻⁸)/0.04968 = 2.01 × 10⁻⁶. Option A uses Ka = [H⁺]²/c (approximation — omits c − [H⁺] denominator; gives same answer here since α = 0.63% << 5%, but the exact expression should always be used in the reverse calculation). Option C is nonsensical. Option D confuses Ka with [H⁺].

Short Answer — Q6 Sample Answer

(a) 0.0800 mol/L chloroacetic acid (Ka = 1.4 × 10⁻³):
Check: Ka/c = 1.4 × 10⁻³/0.0800 = 0.0175 > 0.0025 ✗. x = √(1.4 × 10⁻³ × 0.0800) = √(1.12 × 10⁻⁴) = 1.058 × 10⁻² mol/L. Verify: (1.058 × 10⁻²/0.0800) × 100% = 13.2% > 5% ✗. Assumption fails — use quadratic.
x² + (1.4 × 10⁻³)x − (1.4 × 10⁻³)(0.0800) = 0 → x² + 1.4 × 10⁻³x − 1.12 × 10⁻⁴ = 0
x = (−1.4 × 10⁻³ + √((1.4 × 10⁻³)² + 4 × 1.12 × 10⁻⁴))/2 = (−1.4 × 10⁻³ + √(4.49 × 10⁻⁴))/2 = (−1.4 × 10⁻³ + 0.02119)/2 = 0.009895/2 = 9.79 × 10⁻³ mol/L
pH = −log(9.79 × 10⁻³) = 2.01

(b) 0.500 mol/L sodium propanoate (Ka(propanoic acid) = 1.3 × 10⁻⁵):
Kb(CH₃CH₂COO⁻) = Kw/Ka = (1.0 × 10⁻¹⁴)/(1.3 × 10⁻⁵) = 7.69 × 10⁻¹⁰
Check: Kb/c = 7.69 × 10⁻¹⁰/0.500 = 1.54 × 10⁻⁹ << 0.0025 ✓
[OH⁻] = √(7.69 × 10⁻¹⁰ × 0.500) = √(3.85 × 10⁻¹⁰) = 1.962 × 10⁻⁵ mol/L
Verify: (1.962 × 10⁻⁵/0.500) × 100% = 0.0039% << 5% ✓
pOH = −log(1.962 × 10⁻⁵) = 4.707; pH = 14.00 − 4.707 = 9.29

Short Answer — Q7 Sample Answer

(a) [H⁺] and Ka:
[H⁺] = 10⁻²·⁵² = 10⁻³ × 10⁰·⁴⁸ = 1.0 × 10⁻³ × 3.020 = 3.02 × 10⁻³ mol/L
Ka = [H⁺]²/(c − [H⁺]) = (3.02 × 10⁻³)²/(0.200 − 3.02 × 10⁻³) = (9.12 × 10⁻⁶)/(0.1970) = 4.63 × 10⁻⁵

(b) Degree of ionisation:
α = (3.02 × 10⁻³/0.200) × 100% = 1.51% < 5% ✓. The simplifying assumption would have been valid — the error from using x = √(Ka × c) would be less than 5% in [H⁺].

(c) Student's error:
The student claims Ka = [H⁺] = 10⁻²·⁵². This is incorrect. Ka is an equilibrium constant with units related to concentration — it equals [H⁺][A⁻]/[HA] = [H⁺]²/(c − [H⁺]), not [H⁺] itself. Ka describes the position of the equilibrium (the ratio of products to reactants); [H⁺] describes the actual concentration of H⁺ in a specific solution. They would only be numerically equal in the highly specific (and physically unrealistic) case where [H⁺][A⁻] = [H⁺][HA] simultaneously — which cannot occur in a simple weak acid equilibrium. Correct Ka = 4.63 × 10⁻⁵ ≠ [H⁺] = 3.02 × 10⁻³.

Short Answer — Q8 Sample Answer (Band 6)

(a) [H⁺] and pH of 0.0200 mol/L lactic acid:
Ka/c = 1.4 × 10⁻⁴/0.0200 = 7.0 × 10⁻³ > 0.0025 ✗. x = √(1.4 × 10⁻⁴ × 0.0200) = √(2.8 × 10⁻⁶) = 1.673 × 10⁻³ mol/L.
Verify: (1.673 × 10⁻³/0.0200) × 100% = 8.37% > 5% ✗. Assumption fails — use quadratic.
x² + (1.4 × 10⁻⁴)x − (1.4 × 10⁻⁴)(0.0200) = 0
x = (−1.4 × 10⁻⁴ + √((1.4 × 10⁻⁴)² + 4 × 1.4 × 10⁻⁴ × 0.0200))/2
= (−1.4 × 10⁻⁴ + √(1.96 × 10⁻⁸ + 1.12 × 10⁻⁵))/2 = (−1.4 × 10⁻⁴ + √(1.122 × 10⁻⁵))/2
= (−1.4 × 10⁻⁴ + 3.350 × 10⁻³)/2 = 3.210 × 10⁻³/2 = 1.605 × 10⁻³ mol/L
pH = −log(1.605 × 10⁻³) = 2.79

(b) pH of buffer (30.0 mL HA + 10.0 mL NaOH, both 0.0200 mol/L):
n(HA) = 0.0200 × 0.0300 = 6.00 × 10⁻⁴ mol; n(OH⁻) = 0.0200 × 0.0100 = 2.00 × 10⁻⁴ mol
After HA + OH⁻ → A⁻ + H₂O: n(HA)rem = 4.00 × 10⁻⁴ mol; n(A⁻) = 2.00 × 10⁻⁴ mol
pKa = −log(1.4 × 10⁻⁴) = 3.854
pH = 3.854 + log(2.00 × 10⁻⁴/4.00 × 10⁻⁴) = 3.854 + log(0.500) = 3.854 − 0.301 = 3.55

(c) Why pH(buffer) > pH(pure acid):
In the buffer (b), the solution contains both lactic acid HA and its conjugate base A⁻ (lactate). The A⁻ ion is already present at significant concentration (2.00 × 10⁻⁴ mol in 40 mL total). By Le Chatelier's principle, this product of the equilibrium HA ⇌ H⁺ + A⁻ suppresses the ionisation of HA — this is the common ion effect. The equilibrium shifts to the left, reducing [H⁺] compared to what pure HA alone would produce. As a result, the buffer has a higher pH (less acidic) than the pure weak acid at the same total concentration of HA, even though the buffer contains undissociated HA. The Henderson-Hasselbalch equation accounts for this suppression mathematically through the log(n(A⁻)/n(HA)) term, which here gives log(0.5) = −0.30 — the pH is 0.30 units lower than pKa = 3.85, not as low as the pure acid's pH of 2.79.

Lesson 9 Complete

You can now construct ICE tables for weak acids and bases, apply the simplifying assumption with a proper validity check, solve the quadratic when required, reverse-calculate Ka from measured pH, and use Henderson-Hasselbalch for partial neutralisation and buffer calculations. These skills are the foundation of Lessons 13–16 (buffers and titrations).