★ Consolidation Lesson — No New Syllabus Dot Points
This lesson deepens and integrates content from L08–L10: strong/weak pH calculations, ICE tables, mixing problems, Henderson-Hasselbalch, and ΔHn comparisons. The goal is to eliminate the five highest-frequency IQ2 calculation errors through explicit diagnosis, decision-tree thinking, and Band 6 extended response practice.
Year 12 Chemistry Module 6 — Acid/Base Reactions ★ Consolidation ⏱ ~45 min Lesson 11 of 19 IQ2 Mastery

★ IQ2 Mastery — pH Calculations, Mixing & Band 6 Explanations

Three students have each been given a different acid solution and asked to calculate the pH. Each has chosen a different method. Only one method is correct for their acid. Before reading on — can you identify which student has chosen the right method, and precisely why each wrong method fails?

🔍
Printable worksheet

Download this lesson's worksheet

Use the PDF for classwork, homework or revision. It includes key ideas, activities, questions, an extend task and success-criteria proof.

Think First — Three Methods, One Correct

Three students are each given a 0.100 mol/L solution of a different acid and asked to calculate the pH.

Student A (given HNO₃): "HNO₃ is a strong acid. I write HNO₃ → H⁺ + NO₃⁻. Since it ionises completely, [H⁺] = 0.100 mol/L. pH = −log(0.100) = 1.00."

Student B (given CH₃COOH, Ka = 1.8 × 10⁻⁵): "CH₃COOH is an acid. I write Ka = [H⁺][CH₃COO⁻]/[CH₃COOH]. I set [H⁺] = 0.100 mol/L because that is the concentration given, so Ka = (0.100)(0.100)/(0.100) = 0.100. pH = −log(0.100) = 1.00."

Student C (given HF, Ka = 6.8 × 10⁻⁴): "HF is a weak acid. I set up an ICE table: x = √(Ka × c) = √(6.8 × 10⁻⁵) = 8.25 × 10⁻³ mol/L. I check: 8.25% > 5% — assumption invalid. I solve the quadratic and get x = 7.91 × 10⁻³ mol/L. pH = −log(7.91 × 10⁻³) = 2.10."

Before reading on — which student used the correct method? Write a precise diagnosis of the specific error each incorrect student made. Then write what the correct pH should be for each acid.

📚 Know

  • The decision tree: strong/weak → acid/base → given concentration or Ka → select method
  • Common error patterns in IQ2 calculations and their diagnoses
  • The six strong acids: HCl, H₂SO₄ (1st), HNO₃, HClO₄, HBr, HI

🔗 Understand

  • Why method selection depends on what information is given and what is asked
  • Why V(total) is always required when mixing two solutions
  • How to diagnose errors by working backwards from incorrect answers

✅ Can Do

  • Select the correct calculation method for any pH scenario
  • Diagnose and fix the five most common IQ2 calculation errors
  • Justify method selection using chemical reasoning in Band 6 responses
🌳

IQ2 Decision Tree — Select Method Before Every Calculation

Step 1: Acid or base? → Step 2: Strong or weak?
Strong acid (HCl, HNO₃, H₂SO₄, HClO₄, HBr, HI): [H⁺] = c × n(H⁺) → pH = −log[H⁺]
Weak acid (everything else): ICE table → Ka = x²/(c−x) → x = √(Ka×c) or quadratic → pH = −log(x)
Strong base (NaOH, KOH, Ca(OH)₂, Ba(OH)₂): [OH⁻] = c × n(OH⁻) → pOH → pH = 14 − pOH
Weak base: ICE table (Kb) → [OH⁻] = x → pOH → pH = 14 − pOH
Mixing strong acid + strong base:
n(H⁺) = c(acid) × V(acid)  |  n(OH⁻) = c(base) × V(base) × n(OH⁻ per unit)
Excess → c(excess) = n(excess) / V(total)  |  V(total) = V(acid) + V(base) always
Partial neutralisation (weak acid + strong base, before EP):
HA + OH⁻ → A⁻ + H₂O (goes to completion)
pH = pKa + log(n(A⁻)/n(HA))  |  At half-EP: n(A⁻) = n(HA) → pH = pKa
Five-error checklist (run after every multi-step pH calculation):
(1) Did I identify acid/base type?   (2) Did I check the 5% assumption?   (3) For base: pH = 14 − pOH?
(4) In mixing: V(total) used?   (5) If A⁻ present from neutralisation: used H-H, not ICE table?

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

01

Learning Intentions

  • Diagnose the exact error in Student B's calculation and explain why [H⁺] = c is only valid for strong acids
  • Apply the pH decision tree to any acid or base scenario without defaulting to the wrong method
  • Calculate pH for all six scenario types: strong acid, weak acid (assumption + quadratic), strong base, weak base, mixing, partial neutralisation
  • Identify and correct each of the five highest-frequency IQ2 errors in student working
  • Explain why pH values of equal-concentration weak acid and weak base sum to 14 when Ka = Kb, and why this does not make them a conjugate pair
  • Construct a Band 6 extended response integrating pH calculations, solution classification, and Ka × Kb relationships
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.
02

Card 1 — Who Is Correct? The Three Students Analysed

The three students represent the three most consequential calculation errors in IQ2 — and diagnosing exactly what went wrong for each incorrect student, rather than simply knowing who is right, is the precision that separates Band 4 from Band 6 responses.

Student A is correct. HNO₃ is a strong acid — it ionises completely. The single arrow (→) is correct. [H⁺] = 0.100 mol/L exactly. pH = 1.00. This is the only case among the three where [H⁺] = c is a legitimate step.

Student B is incorrect — Error: applied the strong acid shortcut to a weak acid.

Diagnosis: Student B writes [H⁺] = 0.100 mol/L for CH₃COOH — treating it as if it were completely ionised. But CH₃COOH is a weak acid with Ka = 1.8 × 10⁻⁵. At equilibrium, only ~1.3% of CH₃COOH molecules have ionised. [H⁺] = 1.34 × 10⁻³ mol/L — not 0.100 mol/L. The stated pH = 1.00 is approximately 1.87 units too low, overestimating [H⁺] by a factor of 74. Student B also reveals a secondary error: calculating Ka = 0.100 from the assumed concentrations treats Ka as a calculated result, when it is a fixed constant (1.8 × 10⁻⁵) — not something derived from assumed [H⁺].
Fix: Identify acid type first: CH₃COOH is NOT on the six strong acid list → weak acid → ICE table required. Check assumption: Ka/c = 1.8 × 10⁻⁵/0.100 = 1.8 × 10⁻⁴ << 0.0025 ✓. x = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol/L. Verify: 1.34% < 5% ✓. Correct pH = 2.87.

Student C is correct. Student C correctly identifies HF as weak, sets up the ICE table, uses x = √(Ka × c) as first estimate, checks assumption (8.25% > 5% — invalid), solves the quadratic (x = 7.91 × 10⁻³ mol/L), and obtains pH = 2.10. This is a methodologically complete solution.

StudentAcidSpecific errorCorrect pH
AHNO₃ (strong)None — correct ✓pH = 1.00 ✓
BCH₃COOH (Ka = 1.8 × 10⁻⁵)Applied [H⁺] = c (strong acid shortcut) to a weak acid; [H⁺] is ~74× too highpH = 2.87 (ICE table)
CHF (Ka = 6.8 × 10⁻⁴)None — correct ✓ (assumption correctly identified as invalid, quadratic applied)pH = 2.10 ✓
Must Do
Before writing a single equation or number in any pH calculation, identify the acid or base type. Write this explicitly at the start of your working: "HNO₃ is a strong acid — complete ionisation" or "CH₃COOH is a weak acid — ICE table required." This five-second identification step prevents the most common category of error in the entire module and is required for full method marks.
Common Error
Student B's error — using [H⁺] = c for a weak acid — is the most frequently penalised calculation error in Module 6 HSC marking. It typically costs 3–4 marks across a multi-part question because every subsequent calculation (Ka, ΔHn comparison, buffer pH) built on this wrong [H⁺] is also wrong.
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 Decision Tree: Selecting the Right Method Every Time

The reason students apply the wrong calculation method is not a lack of mathematical ability — it is the absence of a systematic identification step before the calculation begins. A decision tree makes the identification automatic and the method selection unambiguous.

Every pH calculation in Module 6 begins with the same two questions: Is this an acid or a base? Is it strong or weak? The answers completely determine the calculation method.

ScenarioIdentification testMethodKey formula
Strong acid aloneOn the 6 strong acid listDirect[H⁺] = c → pH = −log[H⁺]
Weak acid aloneNOT on strong acid listICE table + assumption checkx = √(Ka×c) or quadratic → pH = −log(x)
Strong base aloneNaOH, KOH, Ca(OH)₂, Ba(OH)₂Direct[OH⁻] = c×n(OH⁻) → pOH → pH = 14−pOH
Weak base aloneNOT on strong base listICE table (Kb)[OH⁻] = √(Kb×c) → pOH → pH = 14−pOH
Strong acid + strong base mixedBoth strongMoles → excess → c/V(total)c(excess) = n(excess)/V(total)
Weak acid + strong base (before EP)HA and A⁻ both presentHenderson-HasselbalchpH = pKa + log(n(A⁻)/n(HA))

The most critical branch is the strong/weak identification — which uses the six strong acid list from L05: HCl, H₂SO₄ (1st), HNO₃, HClO₄, HBr, HI. Everything else is weak.

Must Do
Laminate this decision tree in your working memory before the HSC. In every exam question involving pH, write the identification step first, then select the method. The decision tree does not slow you down — it prevents the 3–4 mark error of using the wrong method, which always costs more time to recover from than the 5 seconds the identification step takes.
Common Error
Students treat H₂SO₄ as monoprotic and calculate [H⁺] = c(H₂SO₄). H₂SO₄ is diprotic — in dilute solution both protons are donated → [H⁺] = 2 × c(H₂SO₄). A 0.050 mol/L H₂SO₄ solution gives [H⁺] = 0.100 mol/L → pH = 1.00, not pH = 1.30. This is an error on the strong acid branch — equally common and equally costly as the strong/weak confusion.
04

Card 3 — Analogy 1: The Medical Triage System

The decision tree in Card 2 is the chemistry equivalent of a hospital triage system — and just as a doctor who gives every patient the same treatment regardless of diagnosis will harm some of them, a student who uses the same pH calculation method for every acid will get most problems wrong.

In a hospital emergency department, a triage nurse assesses every patient before any treatment begins. Two questions: How severe? What category? The answers direct the patient to the right team. The treatment only begins after the triage is complete.

A nurse who sends every patient to the cardiac team — regardless of actual condition — would be catastrophically wrong for most patients even if they applied the cardiac treatment perfectly. The pH equivalent: a student who applies [H⁺] = c for every acid is making the same categorical error. They are applying the right treatment (strong acid method) to the wrong patient (weak acid), and no matter how accurately they execute the arithmetic, the answer is fundamentally wrong because the method was selected before the diagnosis was made.

The triage step (strong or weak?) must always come first. The treatment step (which formula?) always comes second.

Insight
Where this analogy breaks down: A patient's condition can be ambiguous and require further testing. In chemistry, the acid type identification is unambiguous once the six strong acid list is memorised — HCl, H₂SO₄ (1st), HNO₃, HClO₄, HBr, HI are always strong, everything else is always weak, with no grey area. The analogy correctly captures the sequential diagnosis-then-treatment logic but overstates the ambiguity in the chemistry diagnosis step.
Must Do
Use the triage analogy in study practice. Before each pH calculation, physically write or say aloud: "Triage: this acid is [strong/weak] — method is [direct/ICE table]." This verbal triage step takes five seconds and hard-wires the identification habit before the habit of jumping straight to calculation can override it.
05

Card 4 — Analogy 2: The Currency Exchange (Why V(total) Is Required in Mixing)

The most common arithmetic error in mixing calculations — using only one volume instead of the total combined volume — has an exact economic analogy that makes the error immediately obvious once the parallel is seen.

Imagine you have $50 Australian dollars and exchange $30 worth into Euros, leaving $20 AUD. You want to find the density of AUD in your wallet — AUD per unit of wallet space. Your wallet now holds both AUD and Euros: its total capacity is larger than when it only held AUD. To find the AUD density (concentration), divide $20 by the total wallet capacity — not by the original AUD-only capacity. Using the original (smaller) capacity gives a concentration that is too high.

The mixing equivalent: when excess H⁺ or OH⁻ remains after neutralisation, its concentration must be calculated using the total combined volume. The "wallet" is V(total) = V(acid) + V(base). The "AUD remaining" is n(excess species). The "AUD density" is c(excess) = n(excess)/V(total).

Common Error
Using V(acid) alone as the total volume after mixing always overestimates c(excess) by a factor of V(total)/V(acid). For a 50 mL + 50 mL mix, this factor is 2 — the error doubles [H⁺] or [OH⁻], reducing pH by log(2) = 0.30 units for excess acid. This 0.30 pH unit error is large enough to move a correct answer into the wrong mark band. Write "V(total) = V₁ + V₂ = ___" explicitly before calculating c(excess).
Insight
Where this analogy breaks down: Currency exchange involves a physical exchange — AUD is gone, replaced by Euros. In neutralisation, H⁺ and OH⁻ do not exchange — they react and are destroyed, forming H₂O. The remaining species simply occupies a larger volume. The analogy correctly captures the volume-expansion aspect but misrepresents the chemistry of what happens to the reacting species.
06

Card 5 — The Five Most Common IQ2 Calculation Errors: Diagnosed with Fixes

The five errors below are not random — they are the specific, predictable mistakes that appear most frequently in HSC Module 6 marking, and diagnosing each with a precise fix converts them from recurring traps into solved problems.

Error 1 — Using [H⁺] = c for a weak acid

Diagnosis: applied strong acid shortcut without identifying acid type
Fix: identify acid type first (six strong acid list); if weak, set up ICE table

Error 2 — Forgetting to check the simplifying assumption

Diagnosis: used x = √(Ka × c) without verifying x/c < 5%
Fix: after calculating x, always compute (x/c) × 100% before accepting the result. If ≥ 5%, apply quadratic

Error 3 — Writing pOH as pH for a base

Diagnosis: calculated pOH correctly but wrote it as the final answer without subtracting from 14
Fix: for any base, the final step is always pH = 14 − pOH. Sanity check: pH must be > 7 for a base

Error 4 — Using only V(acid) or V(base) in c(excess) calculation

Diagnosis: used the original component volume instead of the combined total volume
Fix: V(total) = V(acid) + V(base) always. Write this line explicitly before calculating c(excess)

Error 5 — Applying ICE table to a buffer mixture after partial neutralisation

Diagnosis: used x = √(Ka × c) for a solution containing both HA and A⁻ produced by neutralisation
Fix: if A⁻ is present in significant amounts, the solution is a buffer — use Henderson-Hasselbalch: pH = pKa + log(n(A⁻)/n(HA))
Must Do
Run the five-error checklist at the end of every multi-step pH calculation: (1) Did I identify acid/base type before calculating? (2) Did I check the assumption if I used the square root shortcut? (3) For a base, did I subtract pOH from 14? (4) In a mixing problem, did I use V(total)? (5) If A⁻ was formed by neutralisation, did I use Henderson-Hasselbalch? Five checks, 30 seconds — eliminates the five highest-frequency errors in one pass.
Common Error
Errors 1 and 5 frequently co-occur in a single extended response. A student applies [H⁺] = c for a weak acid in part (a), then applies the ICE table (incorrectly, ignoring A⁻) after partial neutralisation in part (b). Both errors cascade — every wrong intermediate result makes every subsequent calculation wrong. The fix for both is the same starting point: identify acid type and solution type before selecting the method.

⚠ Persistent IQ2 Misconceptions

"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 0.100 mol/L weak acid, pH < pKa always.

"If Ka(acid) = Kb(base), they must be a conjugate pair." — Incorrect. Conjugate pairs are defined by a one-proton difference in formula, not by equal equilibrium constants. Ka(CH₃COOH) = Kb(NH₃) = 1.8 × 10⁻⁵ is a numerical coincidence — CH₃COOH and NH₃ are not conjugate.

"After partial neutralisation, I use the ICE table on the remaining HA." — Incorrect. The solution contains both HA and A⁻ — it is a buffer. ICE tables assume [A⁻] = 0 initially, which is violated. Henderson-Hasselbalch must be used.

"H₂SO₄ is monoprotic — [H⁺] = c(H₂SO₄)." — Incorrect. H₂SO₄ is diprotic (both ionisations are essentially complete in dilute solution) → [H⁺] = 2 × c(H₂SO₄).

Worked Example 1 — Decision Tree Applied to Three Contrasting Scenarios

Calculate the pH of each at 25°C. Show the identification step explicitly. (a) 0.0400 mol/L KOH; (b) 0.0400 mol/L HBr; (c) 0.0400 mol/L HCN (Ka = 6.2 × 10⁻¹⁰).

1

(a) KOH — Identification: KOH is a strong base (on the strong base list). Method: direct. [OH⁻] = c(KOH) = 0.0400 mol/L (1 OH⁻ per formula unit). pOH = −log(0.0400) = 1.40. pH = 14.00 − 1.40 = 12.60. Sanity check: pH 12.60 > 7 ✓ (base).

2

(b) HBr — Identification: HBr is a strong acid (on the six strong acid list). Method: direct. [H⁺] = 0.0400 mol/L. pH = −log(0.0400) = 1.40. Sanity check: pH 1.40 < 7 ✓ (acid).

3

(c) HCN — Identification: HCN is NOT on the six strong acid list → weak acid. Ka = 6.2 × 10⁻¹⁰. Method: ICE table. Check assumption: Ka/c = 6.2 × 10⁻¹⁰/0.0400 = 1.55 × 10⁻⁸ << 0.0025 ✓. x = √(6.2 × 10⁻¹⁰ × 0.0400) = √(2.48 × 10⁻¹¹) = 4.98 × 10⁻⁶ mol/L. Verify: 4.98 × 10⁻⁶/0.0400 = 0.012% << 5% ✓. pH = −log(4.98 × 10⁻⁶) = 5.30. Sanity check: pH 5.30 < 7 ✓ (weak acid).

ANSWER: (a) pH = 12.60. (b) pH = 1.40. (c) pH = 5.30.

Worked Example 2 — Mixing: Two Strong Acid + Strong Base Scenarios

(a) 35.0 mL of 0.200 mol/L Ba(OH)₂ is mixed with 65.0 mL of 0.150 mol/L HNO₃. Calculate the pH. (b) Repeat with 65.0 mL of 0.0800 mol/L HNO₃ instead.

1

Both scenarios — common setup: n(OH⁻) from Ba(OH)₂ = 0.200 × 0.0350 × 2 = 1.40 × 10⁻² mol (Ba(OH)₂ is diprotic base → ×2). V(total) = 35.0 + 65.0 = 100.0 mL = 0.1000 L for both.

2

(a) HNO₃ at 0.150 mol/L: n(H⁺) = 0.150 × 0.0650 = 9.75 × 10⁻³ mol. Compare: n(OH⁻) = 0.01400 > n(H⁺) = 0.009750 → excess OH⁻. n(excess OH⁻) = 0.01400 − 0.009750 = 4.25 × 10⁻³ mol. c(OH⁻) = 4.25 × 10⁻³/0.1000 = 0.0425 mol/L. pOH = −log(0.0425) = 1.37. pH = 14.00 − 1.37 = 12.63. Sanity check: excess OH⁻ → pH > 7 ✓.

3

(b) HNO₃ at 0.0800 mol/L: n(H⁺) = 0.0800 × 0.0650 = 5.20 × 10⁻³ mol. n(OH⁻) = 0.01400 > n(H⁺) = 0.005200 → still excess OH⁻. n(excess) = 0.01400 − 0.005200 = 8.80 × 10⁻³ mol. c(OH⁻) = 8.80 × 10⁻³/0.1000 = 0.0880 mol/L. pOH = −log(0.0880) = 1.056. pH = 14.00 − 1.056 = 12.94.

ANSWER: (a) Excess OH⁻ = 4.25 × 10⁻³ mol; c(OH⁻) = 0.0425 mol/L; pH = 12.63. (b) Excess OH⁻ = 8.80 × 10⁻³ mol; c(OH⁻) = 0.0880 mol/L; pH = 12.94.

Worked Example 3 — Band 6: Three Solutions, Mixing, Partial Neutralisation, Ka × Kb
Evaluate Band 6 (8 marks)

A student has three 0.100 mol/L solutions: Solution 1 is HCl; Solution 2 is CH₃COOH (Ka = 1.8 × 10⁻⁵); Solution 3 is NH₃ (Kb = 1.8 × 10⁻⁵). (a) Calculate pH of each. (b) Mix 40.0 mL of Solution 1 with 60.0 mL of 0.100 mol/L NaOH — calculate pH. (c) Add 25.0 mL of 0.100 mol/L NaOH to 25.0 mL of Solution 2 — calculate pH and classify the solution formed. (d) Explain why Solution 2 and Solution 3 have the same Ka × Kb product but different pH values, and what this tells us about the relative strengths of CH₃COOH as an acid and NH₃ as a base.

1

(a) pH of three solutions:

Solution 1 (HCl, strong acid): [H⁺] = 0.100 mol/L → pH = 1.00.

Solution 2 (CH₃COOH, weak acid): x = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol/L. Verify: 1.34% < 5% ✓. pH = 2.87.

Solution 3 (NH₃, weak base): [OH⁻] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³ mol/L. pOH = 2.87. pH = 14.00 − 2.87 = 11.13.

2

(b) Mixing HCl with NaOH: n(H⁺) = 0.100 × 0.0400 = 4.00 × 10⁻³ mol. n(OH⁻) = 0.100 × 0.0600 = 6.00 × 10⁻³ mol. Excess OH⁻ = 2.00 × 10⁻³ mol. V(total) = 100.0 mL = 0.1000 L. c(OH⁻) = 0.0200 mol/L. pOH = 1.70. pH = 12.30.

3

(c) Partial neutralisation of CH₃COOH: n(CH₃COOH) = 0.100 × 0.0250 = 2.50 × 10⁻³ mol. n(OH⁻) = 0.100 × 0.0250 = 2.50 × 10⁻³ mol. Moles are equal → equivalence point — all CH₃COOH converted to CH₃COO⁻. n(CH₃COO⁻) = 2.50 × 10⁻³ mol; n(CH₃COOH) = 0.

Solution type: salt solution of a weak acid's conjugate base (NOT a buffer — no HA remaining). CH₃COO⁻ hydrolyses: CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻. Kb(CH₃COO⁻) = Kw/Ka = 1.0 × 10⁻¹⁴/1.8 × 10⁻⁵ = 5.56 × 10⁻¹⁰. c(CH₃COO⁻) = 2.50 × 10⁻³/0.0500 = 0.0500 mol/L. [OH⁻] = √(5.56 × 10⁻¹⁰ × 0.0500) = 5.27 × 10⁻⁶ mol/L. pOH = 5.28. pH = 14.00 − 5.28 = 8.72 (basic salt solution).

4

(d) Ka × Kb and relative strengths: Ka(CH₃COOH) × Kb(NH₃) = 1.8 × 10⁻⁵ × 1.8 × 10⁻⁵ = 3.24 × 10⁻¹⁰ ≠ Kw (1.0 × 10⁻¹⁴). Therefore CH₃COOH and NH₃ are NOT a conjugate pair. The Ka × Kb = Kw relationship applies only within conjugate pairs. The equal Ka and Kb values are a numerical coincidence — CH₃COOH and NH₃ are equally strong in their respective roles (acid and base), which is confirmed by their pH values (2.87 and 11.13) being symmetric around 7. But this symmetry arises because Ka(CH₃COOH) = Kb(NH₃), not because they are conjugate.

ANSWER: (a) HCl: pH 1.00; CH₃COOH: pH 2.87; NH₃: pH 11.13. (b) Excess OH⁻ = 2.00 × 10⁻³ mol; pH = 12.30. (c) Equivalence point — basic salt solution; Kb(CH₃COO⁻) = 5.56 × 10⁻¹⁰; [OH⁻] = 5.27 × 10⁻⁶ mol/L; pH = 8.72. (d) Ka × Kb ≠ Kw → not conjugate; equal Ka and Kb is numerical coincidence; both equally strong in their respective roles; Ka × Kb = Kw applies only within conjugate pairs.

07

📓 Copy Into Your Books

Minimum rules for Lesson 11 — consolidation checklist.

  • Always identify acid/base type before selecting calculation method — write it explicitly
  • Strong acids: HCl, H₂SO₄ (1st), HNO₃, HClO₄, HBr, HI — everything else is weak
  • H₂SO₄ is diprotic: [H⁺] = 2 × c(H₂SO₄) in dilute solution
  • Always check x/c × 100% < 5% after using the simplifying assumption — if ≥ 5%, apply quadratic
  • For bases: pH = 14 − pOH always; sanity check pH > 7
  • Mixing: V(total) = V₁ + V₂ — write this before calculating c(excess)
  • Buffer (HA + A⁻ both present): use Henderson-Hasselbalch, NOT ICE table
  • Ka × Kb = Kw applies only within conjugate pairs — not for any random acid and base
08

Activities

Activity A — Spot & Fix: Five Student Working Samples

Each student response contains exactly one of the five IQ2 errors. Identify which error it is, state what is wrong, and write the corrected calculation.

  1. Student P (0.050 mol/L HCOOH, Ka = 1.8 × 10⁻⁴): "[H⁺] = 0.050 mol/L; pH = −log(0.050) = 1.30." Error type: ___ Correct pH: ___
  2. Student Q (0.100 mol/L NH₃, Kb = 1.8 × 10⁻⁵): "[OH⁻] = √(1.8 × 10⁻⁵ × 0.100) = 1.34 × 10⁻³; pH = −log(1.34 × 10⁻³) = 2.87." Error type: ___ Correct pH: ___
  3. Student R (mixing: 30.0 mL of 0.200 mol/L HCl + 20.0 mL of 0.100 mol/L NaOH): "n(H⁺) = 6.0 × 10⁻³; n(OH⁻) = 2.0 × 10⁻³; excess H⁺ = 4.0 × 10⁻³ mol; c(H⁺) = 4.0 × 10⁻³/0.030 = 0.133 mol/L; pH = 0.875." Error type: ___ Correct pH: ___
  4. Student S (HF, Ka = 6.8 × 10⁻⁴, c = 0.100 mol/L): "x = √(6.8 × 10⁻⁴ × 0.100) = 8.25 × 10⁻³ mol/L. pH = −log(8.25 × 10⁻³) = 2.08." Error type: ___ Correct pH: ___
  5. Student T (25.0 mL 0.100 mol/L CH₃COOH + 12.5 mL 0.100 mol/L NaOH added; Ka = 1.8 × 10⁻⁵): "I use the ICE table: x = √(Ka × 0.100) = 1.34 × 10⁻³; pH = 2.87." Error type: ___ Correct pH: ___

Activity B — Analyse & Connect: Decision Tree Practice

For each of the following, state the identification (acid/base type), the method, and calculate pH. Show all working.

  1. 0.200 mol/L H₂SO₄ (treat both ionisations as complete in dilute solution)
  2. 0.0500 mol/L Ca(OH)₂
  3. 0.150 mol/L CH₃NH₂ (methylamine, Kb = 4.4 × 10⁻⁴)
  4. 40.0 mL of 0.100 mol/L HCl mixed with 10.0 mL of 0.100 mol/L NaOH
  5. 30.0 mL of 0.200 mol/L CH₃COOH (Ka = 1.8 × 10⁻⁵) mixed with 10.0 mL of 0.200 mol/L NaOH
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 is asked to find the pH of 0.050 mol/L formic acid (HCOOH, Ka = 1.8 × 10⁻⁴) and writes: "[H⁺] = 0.050 mol/L. pH = −log(0.050) = 1.30." Which response correctly identifies all errors?

Apply Band 4

2. 20.0 mL of 0.300 mol/L HCl is mixed with 30.0 mL of 0.150 mol/L NaOH. Which correctly calculates the pH?

Analyse Band 5

3. The pH of 0.100 mol/L solutions are: P = 1.00; Q = 11.13; R = 2.87; S = 12.70. A student claims Q and R must be a conjugate pair because their pH values sum to 14 (11.13 + 2.87 = 14.00). Evaluate this claim.

Apply Band 4

4. A student adds 25.0 mL of 0.100 mol/L NaOH to 25.0 mL of 0.100 mol/L CH₃COOH (Ka = 1.8 × 10⁻⁵). Which correctly calculates the pH?

Analyse Band 4

5. Which of the following correctly distinguishes between using Henderson-Hasselbalch and using the ICE table method for calculating pH of a weak acid solution?

10

Short Answer Questions

Apply Band 4 (4 marks)

Question 6. Calculate the pH of each at 25°C. Show the identification step and full working for each. (a) 0.0250 mol/L HClO₄. (b) 0.0500 mol/L Ba(OH)₂. (c) 0.100 mol/L lactic acid (HC₃H₅O₃, Ka = 1.4 × 10⁻⁴). State whether the simplifying assumption is valid for each.

Apply Band 4 (4 marks)

Question 7. 50.0 mL of 0.200 mol/L CH₃COOH (Ka = 1.8 × 10⁻⁵) is mixed with 20.0 mL of 0.200 mol/L NaOH. (a) Calculate the moles of CH₃COOH remaining and CH₃COO⁻ formed after the reaction. (b) Calculate the pH of the resulting mixture. (c) Explain why this pH is higher than the pH of the original pure 0.200 mol/L CH₃COOH solution (pH ≈ 2.57).

Evaluate Band 6 (7 marks)

Question 8. A student has unlabelled solutions of 0.100 mol/L HNO₃ and 0.100 mol/L HNO₂ (Ka = 4.5 × 10⁻⁴). (a) Calculate the expected pH of each. (2 marks) (b) The student mixes 40.0 mL of each solution with 60.0 mL of 0.100 mol/L NaOH. Calculate the pH of each resulting mixture — show identification of what type of solution each forms. (3 marks) (c) Explain why the two mixing calculations require different methods (one requires simple excess calculation; one requires Henderson-Hasselbalch), despite both using "the same volume of the same NaOH." (2 marks)

11

Revisit — Think First

Return to your diagnosis of the three students. The full analysis:

  • Student A (HNO₃): Correct. HNO₃ is a strong acid → → [H⁺] = c = 0.100 mol/L → pH = 1.00. No errors.
  • Student B (CH₃COOH): Incorrect. Applied [H⁺] = c to a weak acid — Error 1. CH₃COOH is ~1.3% ionised at 0.100 mol/L; [H⁺] = 1.34 × 10⁻³ mol/L, not 0.100 mol/L. Correct pH = 2.87 using ICE table. Student B also misused Ka — treating it as a calculated result (0.100) rather than a fixed constant (1.8 × 10⁻⁵).
  • Student C (HF): Correct. Correctly identified as weak, used ICE table, caught the failed assumption (8.25% > 5%), applied quadratic, obtained pH = 2.10. Complete and methodologically correct.

Two students were correct (A and C) — one for a strong acid, one for a weak acid requiring the quadratic. The only incorrect student (B) made the single most common Module 6 error: applying the strong acid shortcut to a weak acid.

12

Answers

MC Answers & Explanations

Q1: C
HCOOH is a weak acid (not on the six strong acid list). [H⁺] = c is Error 1. ICE table required: x = √(1.8 × 10⁻⁴ × 0.050) = √(9.0 × 10⁻⁶) = 3.0 × 10⁻³. Check: 3.0 × 10⁻³/0.050 = 6.0% > 5% — assumption fails. Quadratic: x² + 1.8 × 10⁻⁴x − 9.0 × 10⁻⁶ = 0 → x ≈ 2.93 × 10⁻³ mol/L → pH ≈ 2.53. Option B confuses pKa with pH. Option D invents a non-existent formula.

Q2: B
n(H⁺) = 0.300 × 0.0200 = 6.00 × 10⁻³ mol. n(OH⁻) = 0.150 × 0.0300 = 4.50 × 10⁻³ mol. Excess H⁺ = 1.50 × 10⁻³ mol. V(total) = 20.0 + 30.0 = 50.0 mL = 0.0500 L. c(H⁺) = 1.50 × 10⁻³/0.0500 = 0.0300 mol/L. pH = 1.52. Option A uses V = 0.020 L (acid only — Error 4). Option C uses V = 0.030 L (base only — also Error 4). Option D incorrectly claims equal moles.

Q3: B
pH(R) + pH(Q) = 2.87 + 11.13 = 14.00 because Ka(R) = Kb(Q) = 1.8 × 10⁻⁵ — a numerical coincidence resulting in equal [H⁺] from R and [OH⁻] from Q. Conjugate pairs are defined by differing by exactly one H⁺: CH₃COOH/CH₃COO⁻ or NH₄⁺/NH₃ are conjugate pairs; CH₃COOH/NH₃ are not. Option A and C incorrectly redefine conjugate pairs using pH sums. Option D is wrong — pH values can sum to 14.

Q4: C
Equal moles of CH₃COOH and NaOH (0.100 × 0.0250 = 2.50 × 10⁻³ mol each) → equivalence point — all HA converted to A⁻. Solution contains CH₃COO⁻ (conjugate base of weak acid) → basic salt solution. Kb(CH₃COO⁻) = Kw/Ka = 5.56 × 10⁻¹⁰. c(CH₃COO⁻) = 2.50 × 10⁻³/0.0500 = 0.0500 mol/L. [OH⁻] = √(5.56 × 10⁻¹⁰ × 0.0500) = 5.27 × 10⁻⁶ mol/L. pOH = 5.28. pH = 8.72. Option A incorrectly identifies this as a buffer. Option B applies ICE table to post-equivalence solution — Error 5. Option D incorrectly assumes neutral salt.

Q5: B
The ICE table assumes [A⁻] = 0 initially — valid for a pure weak acid before any A⁻ has been produced. Henderson-Hasselbalch is required when significant A⁻ is present (from partial neutralisation), because the common ion effect of A⁻ suppresses ionisation of HA, making the simple ICE table method invalid. Option A gives wrong criteria. Option C is incorrect — H-H applies only to buffer solutions, not to pure weak acid. Option D is wrong — they give different answers when [A⁻] ≠ 0.

Short Answer — Q6 Sample Answer

(a) HClO₄: Strong acid (on strong acid list) → [H⁺] = 0.0250 mol/L. pH = −log(0.0250) = 1.60.

(b) Ba(OH)₂: Strong base (on strong base list), diprotic → [OH⁻] = 2 × 0.0500 = 0.100 mol/L. pOH = −log(0.100) = 1.00. pH = 14.00 − 1.00 = 13.00. Sanity check: pH 13.00 > 7 ✓.

(c) Lactic acid: NOT on strong acid list → weak acid. Ka/c = 1.4 × 10⁻⁴/0.100 = 1.4 × 10⁻³ < 0.0025 ✓. x = √(1.4 × 10⁻⁴ × 0.100) = √(1.4 × 10⁻⁵) = 3.742 × 10⁻³ mol/L. Verify: 3.742 × 10⁻³/0.100 = 3.74% < 5% ✓ — assumption valid. pH = −log(3.742 × 10⁻³) = 2.43. Sanity check: pH 2.43 < 7 ✓.

Short Answer — Q7 Sample Answer

(a) Moles after reaction: n(CH₃COOH) = 0.200 × 0.0500 = 0.01000 mol. n(OH⁻) = 0.200 × 0.0200 = 4.00 × 10⁻³ mol. CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O (goes to completion). n(CH₃COOH) remaining = 0.01000 − 4.00 × 10⁻³ = 6.00 × 10⁻³ mol. n(CH₃COO⁻) formed = 4.00 × 10⁻³ mol.

(b) pH of buffer: pKa = −log(1.8 × 10⁻⁵) = 4.744. pH = pKa + log(n(A⁻)/n(HA)) = 4.744 + log(4.00 × 10⁻³/6.00 × 10⁻³) = 4.744 + log(0.667) = 4.744 − 0.176 = 4.57.

(c) Why pH is higher than pure 0.200 mol/L CH₃COOH: In the original pure acid solution, no CH₃COO⁻ was present initially — the equilibrium CH₃COOH ⇌ H⁺ + CH₃COO⁻ produced [H⁺] = 1.90 × 10⁻³ mol/L (pH = 2.72). After adding NaOH, the solution is a buffer containing both CH₃COOH (6.00 × 10⁻³ mol) and CH₃COO⁻ (4.00 × 10⁻³ mol). The CH₃COO⁻ already present suppresses further ionisation of CH₃COOH (common ion effect — the product of the equilibrium is already present, shifting equilibrium left by Le Chatelier). This reduces [H⁺] well below what the pure acid would produce, raising pH from ≈2.72 to 4.57. Henderson-Hasselbalch accounts for this suppression mathematically through the log(n(A⁻)/n(HA)) term.

Short Answer — Q8 Sample Answer (Band 6)

(a) Expected pH: HNO₃ (strong acid): [H⁺] = 0.100 mol/L → pH = 1.00. HNO₂ (weak acid, Ka = 4.5 × 10⁻⁴): Check: Ka/c = 4.5 × 10⁻⁴/0.100 = 4.5 × 10⁻³ > 0.0025 ✗. x = √(4.5 × 10⁻⁴ × 0.100) = √(4.5 × 10⁻⁵) = 6.71 × 10⁻³ mol/L. Verify: 6.71% > 5% ✗ — assumption fails. Quadratic: x² + 4.5 × 10⁻⁴x − 4.5 × 10⁻⁵ = 0 → x = (−4.5 × 10⁻⁴ + √(2.025 × 10⁻⁷ + 1.8 × 10⁻⁴))/2 = (−4.5 × 10⁻⁴ + 0.01345)/2 = 6.50 × 10⁻³ mol/L → pH = −log(6.50 × 10⁻³) = 2.19.

(b) Mixing with NaOH: n(NaOH) = 0.100 × 0.0600 = 6.00 × 10⁻³ mol for both. n(HNO₃) = n(HNO₂) = 0.100 × 0.0400 = 4.00 × 10⁻³ mol for both. V(total) = 100.0 mL = 0.1000 L for both.

HNO₃ + NaOH: n(OH⁻) > n(H⁺) → excess OH⁻ = 6.00 × 10⁻³ − 4.00 × 10⁻³ = 2.00 × 10⁻³ mol. c(OH⁻) = 2.00 × 10⁻³/0.1000 = 0.0200 mol/L. pOH = 1.70. pH = 12.30 (excess strong base solution).

HNO₂ + NaOH: n(OH⁻) = 6.00 × 10⁻³ mol > n(HNO₂) = 4.00 × 10⁻³ mol. All HNO₂ is neutralised and there is excess NaOH: excess OH⁻ = 6.00 × 10⁻³ − 4.00 × 10⁻³ = 2.00 × 10⁻³ mol. c(OH⁻) = 0.0200 mol/L. pOH = 1.70. pH = 12.30 (same excess NaOH calculation — beyond equivalence point).

(c) Why different methods: For HNO₃ + NaOH: HNO₃ is strong — it is fully ionised before mixing, with H⁺ freely available. When NaOH is added in excess beyond equivalence, there is simply more OH⁻ than H⁺ — a straightforward excess calculation using c(excess OH⁻)/V(total). No equilibrium is involved after the reaction. For HNO₂ + NaOH with NaOH in excess: same logic applies — both are treated as "simple excess" calculations beyond the equivalence point. However, if NaOH were insufficient (e.g. only 20.0 mL NaOH), the HNO₂ calculation would differ: HNO₂ is weak — partial neutralisation would leave both HNO₂ and NO₂⁻ in solution simultaneously (a buffer). The common ion effect of NO₂⁻ suppresses further ionisation of HNO₂, making the simple ICE table method invalid and requiring Henderson-Hasselbalch. This is the fundamental distinction: strong acid partial neutralisation still gives a simple excess calculation (all H⁺ from the strong acid already "counts"); weak acid partial neutralisation creates a buffer that requires H-H because both HA and A⁻ are significant species at equilibrium.

Science Jump

Jump Through pH Mastery!

Climb platforms, hit checkpoints, and answer questions on pH calculations, mixing acids and bases, and Band 6 explanations. Quick recall from lessons 1–11.

Lesson 11 Complete — IQ2 Mastered

You can now apply the pH decision tree without defaulting to the wrong method, diagnose each of the five highest-frequency IQ2 errors in student working, and construct Band 6 responses integrating strong/weak calculations, mixing, partial neutralisation, and Ka × Kb relationships. Next: L12 — IQ3 begins with Ka, pKa, and polyprotic acids.