Year 12 Chemistry Module 6 — Acid/Base Reactions ⏱ ~45 min Lesson 7 of 19 IQ2

Conjugate Pairs, Amphiprotic Substances & Water's Role

Pure water is neither just an acid nor just a base — it is both simultaneously, and the tiny fraction of water molecules that react with each other at any given instant is the foundation of every pH calculation in this module.

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Think First — One Compound, Two Behaviours

A chemist prepares three solutions: one containing sodium hydrogen carbonate (NaHCO₃, baking soda), one containing hydrochloric acid, and one containing sodium hydroxide. She adds NaHCO₃ to the HCl solution — bubbles form vigorously and the solution becomes less acidic. She then adds NaHCO₃ to the NaOH solution — the solution becomes less basic, and no bubbles form.

The same compound, in the same amount, made one solution less acidic and another solution less basic. Before you read on, write down your explanation: how can one substance act as a base in one reaction and an acid in another? Is this a contradiction, or does it reveal something fundamental about how acid-base reactions work? Write your reasoning before the lesson gives you the framework to test it.

📚 Know

  • A conjugate acid-base pair differs by one H⁺
  • Amphiprotic substances can act as both acids and bases (e.g. HSO₄⁻, HCO₃⁻, H₂O)
  • Water self-ionises with Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴ at 25°C

🔗 Understand

  • The inverse strength relationship: stronger acid → weaker conjugate base
  • Why intermediate ions of polyprotic acids are amphiprotic
  • How Kw allows calculation of [H₃O⁺] or [OH⁻] in any aqueous solution

✅ Can Do

  • Identify conjugate acids and bases for any given species
  • Write balanced equations showing amphiprotic substances acting as acids and bases
  • Calculate [H₃O⁺] and [OH⁻] using Kw in pure water and mixed solutions
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Key Relationships — Conjugate Pairs, Amphiprotic Species & Kw

Conjugate base: HA → A⁻ + H⁺   (A⁻ is the conjugate base of HA)
A⁻ has one fewer H and one more negative charge than HA
Conjugate acid: B + H⁺ → BH⁺   (BH⁺ is the conjugate acid of B)
BH⁺ has one more H and one less negative charge than B
Amphiprotic (as acid): HX ⇌ H⁺ + X⁻  |  Amphiprotic (as base): HX + H⁺ ⇌ H₂X⁺
Can both donate AND accept H⁺ depending on reaction partner
Water self-ionisation: 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)
Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C  |  At 25°C: [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷ mol/L → pH = 7.00 (neutral)
pH + pOH = pKw = 14 at 25°C  |  [OH⁻] = Kw / [H₃O⁺]
pKw = −log(Kw)  |  Kw increases with temperature (endothermic self-ionisation)

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

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Learning Intentions

  • Identify conjugate acid-base pairs in any Brønsted-Lowry equation and verify using the one-proton rule
  • Define amphiprotic substances and explain the inverse strength relationship between conjugate pairs
  • Write equations showing H₂O, HCO₃⁻, H₂PO₄⁻ and HPO₄²⁻ acting as both acids and bases
  • Identify the amphiprotic ions in the NESA-named salts Na₂HPO₄ and KH₂PO₄ and write all four required equations
  • Explain water's self-ionisation and derive Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴
  • Use Kw to calculate [H₃O⁺] or [OH⁻] and classify solutions at both standard and non-standard temperatures
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 — Conjugate Acid-Base Pairs: Deepening the Relationship

Every Brønsted-Lowry acid-base reaction produces a new acid and a new base on the product side — and the relationship between each parent species and its conjugate is always and only the transfer of a single proton, nothing more and nothing less.

The conjugate acid-base pair relationship was introduced in L01, but Module 6 requires deeper fluency: the ability to identify conjugate pairs in multi-step and polyprotic acid equilibria, to write both equations showing a species acting as acid and as base, and to use the inverse strength relationship to predict equilibrium direction.

Recall the rules: a conjugate base is formed by removing exactly one H⁺ from the acid — the conjugate base has one fewer H and one more negative charge. A conjugate acid is formed by adding exactly one H⁺ to the base — the conjugate acid has one more H and one less negative charge.

The inverse strength relationship is critical: a strong acid has an extremely weak conjugate base (essentially no tendency to accept H⁺ back). A weak acid has a relatively stronger conjugate base (meaningful tendency to accept H⁺ back — which is why the weak acid equilibrium does not go to completion). This inverse relationship is captured quantitatively as Ka × Kb = Kw for a conjugate pair.

The extended conjugate pair chain for phosphoric acid illustrates successive proton loss:

H₃PO₄ ⇌ H⁺ + H₂PO₄⁻ (Ka1 = 7.5 × 10⁻³)

H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻ (Ka2 = 6.2 × 10⁻⁸)

HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ (Ka3 = 4.8 × 10⁻¹³)

Each successive conjugate base is a weaker acid than its predecessor — removing a proton from an already-negative ion is increasingly difficult.

As acid → conjugate base
Donates H⁺ → H₂PO₄⁻
Donates H⁺ → HPO₄²⁻
Donates H⁺ → PO₄³⁻
Donates H⁺ → CO₃²⁻
As base → conjugate acid
Cannot meaningfully accept H⁺ (H₄PO₄⁺ negligible)
Accepts H⁺ → H₃PO₄
Accepts H⁺ → H₂PO₄⁻
Accepts H⁺ → H₂CO₃
Must Do
When asked to identify conjugate pairs, always verify three things: (1) the two species are on opposite sides of the equation; (2) they differ by exactly one H⁺; (3) the charge difference is exactly 1. Failing any one check means you have not identified a genuine conjugate pair.
Common Error
Students identify SO₄²⁻ as the conjugate base of H₂SO₄, removing two protons at once. The conjugate base of H₂SO₄ is HSO₄⁻ (one proton removed). The conjugate base of HSO₄⁻ is SO₄²⁻. These are two separate conjugate pair relationships — H₂SO₄/HSO₄⁻ and HSO₄⁻/SO₄²⁻ — and they must not be conflated.
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.
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Card 2 — Amphiprotic Substances: Definition and Key Examples

An amphiprotic substance is one that can either donate or accept a proton depending entirely on its reaction partner — and this dual capability is a direct consequence of the substance being an intermediate in a polyprotic acid-base system.

A substance is amphiprotic if it contains at least one ionisable H⁺ (so it can act as an acid — proton donor) AND at least one lone pair or basic site capable of accepting a proton (so it can act as a base — proton acceptor).

In practice, the most important amphiprotic substances in HSC chemistry are the intermediate ions of polyprotic acids — species that have already lost one proton from a polyprotic acid but still retain at least one more ionisable proton.

Water is the archetypal amphiprotic substance: it can donate H⁺ (acting as an acid, producing OH⁻) or accept H⁺ (acting as a base, producing H₃O⁺). The hydrogen carbonate ion (HCO₃⁻) is amphiprotic: it can donate its remaining H⁺ to a stronger base (weak acid: HCO₃⁻ ⇌ H⁺ + CO₃²⁻, Ka = 4.7 × 10⁻¹¹) or accept H⁺ from a stronger acid (as a base: HCO₃⁻ + H⁺ ⇌ H₂CO₃).

Acting as acid (proton donor)
H₂O ⇌ H⁺ + OH⁻
HCO₃⁻ ⇌ H⁺ + CO₃²⁻
H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻
HPO₄²⁻ ⇌ H⁺ + PO₄³⁻
Acting as base (proton acceptor)
H₂O + H⁺ → H₃O⁺
HCO₃⁻ + H⁺ ⇌ H₂CO₃
H₂PO₄⁻ + H⁺ ⇌ H₃PO₄
HPO₄²⁻ + H⁺ ⇌ H₂PO₄⁻
Must Do
For any HSC question involving Na₂HPO₄ or KH₂PO₄, you must: (1) identify the amphiprotic ion; (2) write the equation showing it acting as an acid; (3) write the equation showing it acting as a base. Both equations are required — writing only one mode earns partial marks. These are explicitly NESA-named examples.
Common Error
Students confuse "amphiprotic" with "amphoteric." Amphoteric is broader — it includes Lewis acid-base behaviour. Amphiprotic specifically means a substance can both donate AND accept a proton (Brønsted-Lowry). In HSC Module 6, use "amphiprotic" for syllabus dot points. All amphiprotic substances are amphoteric, but not all amphoteric substances are amphiprotic.
Insight
Whether an amphiprotic substance acts as acid or base depends on its reaction partner. HCO₃⁻ acts as a base with HCl (HCl forces HCO₃⁻ to accept H⁺): HCO₃⁻ + HCl → H₂CO₃ + Cl⁻. HCO₃⁻ acts as an acid with NaOH (OH⁻ pulls H⁺ from HCO₃⁻): HCO₃⁻ + OH⁻ → CO₃²⁻ + H₂O. This is exactly the chemist's observation in the Think First.
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Card 3 — NESA-Named Examples: Na₂HPO₄ and KH₂PO₄ in Full Detail

These two salts are named explicitly in the NSW Chemistry Stage 6 syllabus — which means they will appear in HSC exams, and the ability to write both their acid and base equations from memory is a non-negotiable competency for this lesson.

Na₂HPO₄ — Sodium Hydrogen Phosphate

Dissolves completely to give Na⁺ and HPO₄²⁻ ions. Na⁺ is the conjugate of NaOH (strong base) — it is a neutral spectator. HPO₄²⁻ is the amphiprotic ion. It sits in the middle of the phosphate system — it has already lost two protons from H₃PO₄ and retains one more ionisable proton.

  • HPO₄²⁻ acting as an acid (proton donor): HPO₄²⁻(aq) ⇌ H⁺(aq) + PO₄³⁻(aq)   Ka3 = 4.8 × 10⁻¹³ — very weak acid
  • HPO₄²⁻ acting as a base (proton acceptor): HPO₄²⁻(aq) + H⁺(aq) ⇌ H₂PO₄⁻(aq)   (reverse of Ka2)

KH₂PO₄ — Potassium Dihydrogen Phosphate

Dissolves completely to give K⁺ and H₂PO₄⁻ ions. K⁺ is the conjugate of KOH (strong base) — neutral spectator. H₂PO₄⁻ is the amphiprotic ion. It has lost one proton (Ka1 step) and retains two more ionisable protons.

  • H₂PO₄⁻ acting as an acid: H₂PO₄⁻(aq) ⇌ H⁺(aq) + HPO₄²⁻(aq)   Ka2 = 6.2 × 10⁻⁸
  • H₂PO₄⁻ acting as a base: H₂PO₄⁻(aq) + H⁺(aq) ⇌ H₃PO₄(aq)   (reverse of Ka1)

Na₂HPO₄

Amphiprotic ion: HPO₄²⁻
Acting as acid: HPO₄²⁻ ⇌ H⁺ + PO₄³⁻
Acting as base: HPO₄²⁻ + H⁺ ⇌ H₂PO₄⁻

KH₂PO₄

Amphiprotic ion: H₂PO₄⁻
Acting as acid: H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻
Acting as base: H₂PO₄⁻ + H⁺ ⇌ H₃PO₄
Must Do
Chain-navigation method: For each ion, identify its position in the phosphate chain (H₃PO₄ → H₂PO₄⁻ → HPO₄²⁻ → PO₄³⁻). Acting as acid = move one step right (lose one H⁺). Acting as base = move one step left (gain one H⁺). This produces the correct equation every time without memorising four separate equations.
Common Error
Students write HPO₄²⁻ losing two protons to form PO₄³⁻ in one step, or H₂PO₄⁻ losing two protons to form PO₄³⁻ in one step. Amphiprotic behaviour always involves the transfer of exactly one proton per equation — one step in the chain. Two-proton transfers in a single equation are incorrect.
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The Phosphate Proton Chain — Visual Summary

H₃PO₄ triprotic acid H₂PO₄⁻ amphiprotic (KH₂PO₄) HPO₄²⁻ amphiprotic (Na₂HPO₄) PO₄³⁻ conjugate base −H⁺ −H⁺ −H⁺ +H⁺ +H⁺ +H⁺ Ka1=7.5×10⁻³ Ka2=6.2×10⁻⁸ Ka3=4.8×10⁻¹³

Red arrows = acting as acid (−H⁺, move right). Green arrows = acting as base (+H⁺, move left). H₂PO₄⁻ and HPO₄²⁻ are amphiprotic — they can move either direction.

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Card 4 — Water's Self-Ionisation and Kw

The fraction of water molecules that react with each other at any instant is extraordinarily small — but it is precisely this self-ionisation that establishes the H₃O⁺ and OH⁻ present in every aqueous solution, making Kw the foundation of every pH calculation in the module.

Pure water undergoes self-ionisation (autoprotolysis) — a small but thermodynamically significant fraction of water molecules transfer a proton from one molecule to another:

2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)

In this reaction, one water molecule acts as the Brønsted-Lowry acid (proton donor → OH⁻) and the other acts as the Brønsted-Lowry base (proton acceptor → H₃O⁺). This confirms water as amphiprotic — in the same reaction it simultaneously acts as both acid and base.

The equilibrium constant for this reaction is the water dissociation constant: Kw = [H₃O⁺][OH⁻]. At 25°C, Kw = 1.0 × 10⁻¹⁴. The concentration of pure water is omitted from the expression (pure liquid has activity = 1).

Because self-ionisation produces equal amounts: [H₃O⁺] = [OH⁻] = √(1.0 × 10⁻¹⁴) = 1.0 × 10⁻⁷ mol/L at 25°C → pH = 7.00. Kw is temperature-dependent — it increases with temperature because the self-ionisation is endothermic (Le Chatelier: increasing T shifts right, increasing both [H₃O⁺] and [OH⁻]).

10°C

Kw: 2.9 × 10⁻¹⁵
Neutral pH: 7.27
Interpretation: Pure water is neutral but pH > 7

25°C

Kw: 1.0 × 10⁻¹⁴
Neutral pH: 7.00
Interpretation: Standard reference temperature

37°C

Kw: 2.4 × 10⁻¹⁴
Neutral pH: 6.81
Interpretation: Blood temperature — neutral pH slightly below 7

60°C

Kw: 9.6 × 10⁻¹⁴
Neutral pH: 6.51
Interpretation: Hot water — neutral pH well below 7
Must Do
Neutral pH = 7 ONLY at 25°C. At any other temperature, neutral pH = −log(√Kw at that temperature). HSC questions may specify a non-standard temperature and ask whether a solution with pH 7 is acidic, basic, or neutral. At 37°C, pH 7 is slightly basic (neutral pH ≈ 6.81 and pH 7 > 6.81 → [H₃O⁺] < [OH⁻]).
Common Error
"Pure water has pH 7 because it is neutral." The causal relationship is backwards. Pure water is neutral because [H₃O⁺] = [OH⁻] — that is the definition. At 25°C, this happens to give pH 7. At 60°C, pure water is still neutral but pH ≈ 6.51 — not 7. Neutrality is defined by the equality of [H₃O⁺] and [OH⁻], not by the number 7.
Insight
Self-ionisation occurs even in strongly acidic or basic solutions — Kw always applies. In 1.0 mol/L HCl: [H₃O⁺] = 1.0 mol/L and [OH⁻] = Kw/[H₃O⁺] = 1.0 × 10⁻¹⁴ mol/L. OH⁻ ions are still present — just at extraordinarily low concentration. This is important for calculating pH of mixtures and understanding why Kw applies in all aqueous solutions, not just pure water.
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Card 5 — Using Kw: [H₃O⁺] and [OH⁻] in Any Aqueous Solution

Kw is not just a curiosity about pure water — it is a universal constraint on every aqueous solution that links [H₃O⁺] and [OH⁻] at all times, allowing you to calculate one from the other regardless of what else is dissolved.

In any aqueous solution at 25°C, [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴. This is a fixed constraint — if [H₃O⁺] increases (acid added), [OH⁻] must decrease proportionally; if [OH⁻] increases (base added), [H₃O⁺] must decrease.

Three important consequences for HSC calculations:

  1. Given [H₃O⁺], you can always find [OH⁻] = Kw/[H₃O⁺], and vice versa.
  2. Taking −log of both sides: −log[H₃O⁺] + (−log[OH⁻]) = −log(Kw) → pH + pOH = pKw = 14 at 25°C. Essential for base pH calculations in L08.
  3. Classification at 25°C: acidic if [H₃O⁺] > [OH⁻] → pH < 7; basic if [OH⁻] > [H₃O⁺] → pH > 7; neutral if [H₃O⁺] = [OH⁻] → pH = 7. These use 7 as reference only at 25°C.

Acidic

[H₃O⁺] vs [OH⁻]: [H₃O⁺] > [OH⁻]
pH at 25°C: < 7
[OH⁻] from Kw: [OH⁻] = 1.0 × 10⁻¹⁴ / [H₃O⁺]

Neutral

[H₃O⁺] vs [OH⁻]: [H₃O⁺] = [OH⁻] = 1.0 × 10⁻⁷
pH at 25°C: = 7
[OH⁻] from Kw: [OH⁻] = 1.0 × 10⁻⁷

Basic

[H₃O⁺] vs [OH⁻]: [OH⁻] > [H₃O⁺]
pH at 25°C: > 7
[OH⁻] from Kw: [OH⁻] = 1.0 × 10⁻¹⁴ / [H₃O⁺]
Must Do
Memorise and be able to derive: pH + pOH = 14 at 25°C. This is used in every base pH calculation in L08. Standard method for strong base: calculate [OH⁻] → pOH = −log[OH⁻] → pH = 14 − pOH. Derive it once from Kw = [H₃O⁺][OH⁻] so you understand where it comes from.
Common Error
Students apply pH + pOH = 14 at temperatures other than 25°C. At 37°C, Kw = 2.4 × 10⁻¹⁴ → pKw = −log(2.4 × 10⁻¹⁴) = 13.62. At 37°C, pH + pOH = 13.62, not 14. Using 14 at non-standard temperatures gives wrong pH values. Unless a question specifies otherwise, assume 25°C and pH + pOH = 14.

⚠ Common Misconceptions — Conjugate Pairs & Amphiprotic Substances

"SO₄²⁻ is the conjugate base of H₂SO₄." — Incorrect. A conjugate base is formed by removing exactly ONE proton. The conjugate base of H₂SO₄ is HSO₄⁻. Only HSO₄⁻ losing a second proton gives SO₄²⁻, making HSO₄⁻/SO₄²⁻ a separate conjugate pair.

"Amphiprotic and amphoteric mean the same thing." — Incorrect. Amphoteric is broader (includes Lewis acid-base). Amphiprotic specifically means proton donor AND acceptor (Brønsted-Lowry). In Module 6, always use "amphiprotic."

"Neutral pH is always 7." — Incorrect. Neutral pH = −log(√Kw) and depends on temperature. At 37°C, neutral pH ≈ 6.81. pH 7 at 37°C is slightly basic. Only at 25°C does neutral pH equal 7.00.

"HPO₄²⁻ can't donate a proton — it's already negatively charged." — Incorrect. Negative charge does not prevent proton donation. HPO₄²⁻ retains one O–H bond (Ka3 = 4.8 × 10⁻¹³). It can donate this H⁺ to a sufficiently strong base, forming PO₄³⁻.

Worked Example 1 — Conjugate Pairs and Amphiprotic Equations

For the reaction H₂PO₄⁻ + OH⁻ → HPO₄²⁻ + H₂O: (a) identify the Brønsted-Lowry acid and base and write both conjugate pairs. (b) Write equations showing H₂PO₄⁻ acting as (i) an acid and (ii) a base, and state which NESA-named salt provides H₂PO₄⁻ ions.

1

GIVEN: Reaction H₂PO₄⁻ + OH⁻ → HPO₄²⁻ + H₂O. Need to track H⁺ transfer.

FIND: BL acid, BL base, both conjugate pairs; both equations for amphiprotic behaviour; NESA salt.

2

METHOD (a — identify acid/base): H₂PO₄⁻ → HPO₄²⁻: H₂PO₄⁻ has lost one H⁺ → H₂PO₄⁻ is the BL acid; HPO₄²⁻ is its conjugate base. OH⁻ → H₂O: OH⁻ has gained one H⁺ → OH⁻ is the BL base; H₂O is its conjugate acid.

3

Conjugate pairs: Pair 1: H₂PO₄⁻ (acid) / HPO₄²⁻ (conjugate base) — differ by one H⁺, opposite sides ✓. Pair 2: OH⁻ (base) / H₂O (conjugate acid) — differ by one H⁺, opposite sides ✓.

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METHOD (b — H₂PO₄⁻ as acid): H₂PO₄⁻ donates H⁺ → moves one step right in phosphate chain (H₃PO₄ → H₂PO₄⁻ → HPO₄²⁻ → PO₄³⁻). Equation: H₂PO₄⁻(aq) ⇌ H⁺(aq) + HPO₄²⁻(aq). Use ⇌ — this is weak acid ionisation (Ka2 = 6.2 × 10⁻⁸).

H₂PO₄⁻ as base: Accepts H⁺ → moves one step left in chain. Equation: H₂PO₄⁻(aq) + H⁺(aq) ⇌ H₃PO₄(aq). Use ⇌ — this is the reverse of Ka1.

ANSWER: (a) Acid = H₂PO₄⁻; conjugate base = HPO₄²⁻. Base = OH⁻; conjugate acid = H₂O. Conjugate pairs: H₂PO₄⁻/HPO₄²⁻ and OH⁻/H₂O. (b)(i) H₂PO₄⁻(aq) ⇌ H⁺(aq) + HPO₄²⁻(aq). (ii) H₂PO₄⁻(aq) + H⁺(aq) ⇌ H₃PO₄(aq). NESA salt: KH₂PO₄ (potassium dihydrogen phosphate).

Worked Example 2 — Kw Calculations at Non-Standard Temperature

At 50°C, Kw = 5.5 × 10⁻¹⁴. (a) Calculate the pH of pure water at 50°C. (b) A solution at 50°C has pH 6.8. Is it acidic, basic, or neutral? Justify. (c) Calculate [OH⁻] in a solution at 50°C with [H₃O⁺] = 2.5 × 10⁻³ mol/L. Is this solution acidic or basic?

1

GIVEN: Kw = 5.5 × 10⁻¹⁴ at 50°C.

FIND: (a) pH of pure water at 50°C; (b) classification of pH 6.8; (c) [OH⁻] and classification for [H₃O⁺] = 2.5 × 10⁻³.

2

METHOD (a): In pure water, [H₃O⁺] = [OH⁻] = √Kw = √(5.5 × 10⁻¹⁴) = 2.35 × 10⁻⁷ mol/L. pH = −log(2.35 × 10⁻⁷) = 6.63. Pure water at 50°C is neutral (by definition — [H₃O⁺] = [OH⁻]) but has pH 6.63, not 7.

3

METHOD (b): Neutral pH at 50°C = 6.63. A solution with pH 6.8 has [H₃O⁺] = 10⁻⁶·⁸ = 1.58 × 10⁻⁷ mol/L. Since pH 6.8 > 6.63 (neutral pH at 50°C), [H₃O⁺] < [OH⁻] → the solution is basic — even though its pH is below 7. At temperatures above 25°C, neutral pH < 7, so solutions with pH between neutral pH and 7 are actually basic.

4

METHOD (c): [OH⁻] = Kw / [H₃O⁺] = (5.5 × 10⁻¹⁴) / (2.5 × 10⁻³) = 2.2 × 10⁻¹¹ mol/L. Compare: [H₃O⁺] = 2.5 × 10⁻³ >> [OH⁻] = 2.2 × 10⁻¹¹ → acidic. pH = −log(2.5 × 10⁻³) = 2.60 — well below neutral pH 6.63 at 50°C.

ANSWER: (a) pH of pure water at 50°C = 6.63 (neutral but not pH 7). (b) pH 6.8 at 50°C is basic — neutral pH is 6.63 at 50°C, so pH 6.8 > 6.63 means [H₃O⁺] < [OH⁻]. (c) [OH⁻] = 2.2 × 10⁻¹¹ mol/L; solution is acidic ([H₃O⁺] >> [OH⁻]).

Worked Example 3 — Band 6: Amphiprotic Behaviour and Kw Synthesis
Evaluate Band 6 (7 marks)

Sodium hydrogen phosphate (Na₂HPO₄) is used in phosphate buffer solutions for biological research. (a) Explain why HPO₄²⁻ is amphiprotic, writing equations to support your answer. (b) In a buffer at pH 7.4 and 25°C, calculate [OH⁻] and determine whether [H₃O⁺] or [OH⁻] is greater. (c) A researcher claims that because the buffer is used at 37°C, the neutral pH at that temperature is 7.0. Evaluate this claim (Kw = 2.4 × 10⁻¹⁴ at 37°C). (d) Explain why HPO₄²⁻ in this buffer predominantly acts as a base at pH 7.4, using Ka values.

1

GIVEN: Na₂HPO₄; pH 7.4 at 25°C; Kw = 2.4 × 10⁻¹⁴ at 37°C; Ka3(HPO₄²⁻) = 4.8 × 10⁻¹³; Ka2 = 6.2 × 10⁻⁸.

2

METHOD (a — amphiprotic definition): Amphiprotic means a substance can both donate and accept a proton depending on its reaction partner. HPO₄²⁻ is amphiprotic because it retains one ionisable H⁺ (can act as acid) and has lone pairs on oxygen atoms (can act as base).

Acting as acid: HPO₄²⁻(aq) ⇌ H⁺(aq) + PO₄³⁻(aq)   Ka3 = 4.8 × 10⁻¹³

Acting as base: HPO₄²⁻(aq) + H⁺(aq) ⇌ H₂PO₄⁻(aq)   (reverse of Ka2)

3

METHOD (b — [OH⁻] at pH 7.4): [H₃O⁺] = 10⁻⁷·⁴ = 3.98 × 10⁻⁸ mol/L. [OH⁻] = Kw/[H₃O⁺] = (1.0 × 10⁻¹⁴)/(3.98 × 10⁻⁸) = 2.51 × 10⁻⁷ mol/L. [OH⁻] > [H₃O⁺] → the buffer is basic at 25°C (pH 7.4 > 7.0).

4

METHOD (c — evaluate claim at 37°C): Neutral pH at 37°C = −log(√(2.4 × 10⁻¹⁴)) = −log(1.549 × 10⁻⁷) = 6.81. The researcher's claim is incorrect — neutral pH at 37°C is 6.81, not 7.0. pKw = −log(2.4 × 10⁻¹⁴) = 13.62, so pH + pOH = 13.62 at 37°C (not 14). A solution with pH 7.0 at 37°C is actually slightly basic (pH 7.0 > 6.81).

5

METHOD (d — why HPO₄²⁻ acts as base at pH 7.4): At pH 7.4, [H₃O⁺] = 3.98 × 10⁻⁸ mol/L. HPO₄²⁻ as acid: Ka3 = 4.8 × 10⁻¹³ — extremely small, meaning HPO₄²⁻ has very little tendency to donate H⁺. [H₃O⁺] = 3.98 × 10⁻⁸ >> Ka3 = 4.8 × 10⁻¹³ — far more H₃O⁺ available than HPO₄²⁻ can generate, so HPO₄²⁻ preferentially accepts H⁺. The reverse of Ka2 gives Kb = Kw/Ka2 = 1.0 × 10⁻¹⁴/6.2 × 10⁻⁸ = 1.6 × 10⁻⁷ — significantly larger than Ka3, so HPO₄²⁻ is a stronger base than it is an acid.

ANSWER: (a) HPO₄²⁻ is amphiprotic: as acid HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ (Ka3 = 4.8 × 10⁻¹³); as base HPO₄²⁻ + H⁺ ⇌ H₂PO₄⁻. (b) [OH⁻] = 2.51 × 10⁻⁷ mol/L; [OH⁻] > [H₃O⁺] — basic. (c) Claim incorrect — neutral pH at 37°C = 6.81; pH + pOH = 13.62 at 37°C. (d) Ka3 = 4.8 × 10⁻¹³ is extremely small — HPO₄²⁻ has minimal acid tendency; its Kb = 1.6 × 10⁻⁷ >> Ka3, so it predominantly accepts protons at pH 7.4.

08

📓 Copy Into Your Books

These are the minimum facts and equations to have in your notes for Lesson 7.

  • Conjugate pair rule: differ by exactly one H⁺; opposite sides of equation; charge differs by exactly 1
  • Conjugate base of H₂SO₄ = HSO₄⁻ (NOT SO₄²⁻ — that removes two protons)
  • Amphiprotic = can both donate and accept H⁺ (Brønsted-Lowry); use this term, not "amphoteric"
  • NESA-named salts: Na₂HPO₄ (amphiprotic ion = HPO₄²⁻) and KH₂PO₄ (amphiprotic ion = H₂PO₄⁻)
  • Phosphate chain: H₃PO₄ → H₂PO₄⁻ → HPO₄²⁻ → PO₄³⁻ (acid = move right; base = move left)
  • Water self-ionisation: 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq); Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C
  • Neutral pH = −log(√Kw) — equals 7.00 ONLY at 25°C; at 37°C neutral pH ≈ 6.81
  • pH + pOH = 14 at 25°C only; [OH⁻] = Kw/[H₃O⁺]
09

Activities

Activity A — Sort & Classify: Conjugate Pairs and Amphiprotic Species

For each species listed, (i) state whether it is amphiprotic (yes/no) and give a reason, and (ii) write its equation acting as an acid AND as a base where amphiprotic, or explain why it cannot act in one mode. One row contains a deliberate error — identify and correct it.

SpeciesAmphiprotic?As acid (if applicable)As base (if applicable)
HCO₃⁻
HPO₄²⁻
H₂O
Cl⁻
OH⁻
H₂PO₄⁻
NH₄⁺
H₂SO₄ → SO₄²⁻ + 2H⁺   (conjugate base is SO₄²⁻)⚠ This row contains a deliberate error — identify and correct it

Activity B — Analyse & Connect: Kw at Non-Standard Temperatures

Use the Kw data provided to answer the questions below.

TemperatureKwNeutral pHAt this temperature, is a solution with pH 7.0 acidic, basic, or neutral?
10°C2.9 × 10⁻¹⁵
25°C1.0 × 10⁻¹⁴
37°C2.4 × 10⁻¹⁴
60°C9.6 × 10⁻¹⁴
  1. Calculate the neutral pH at each temperature and complete column 3.
  2. Determine whether a solution with pH 7.0 is acidic, basic, or neutral at each temperature. Complete column 4.
  3. Explain why neutral pH decreases as temperature increases, using Le Chatelier's principle and the self-ionisation equation: 2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq).
  4. A student states: "At 60°C, pure water must be acidic because its pH is only 6.51 — below 7." Explain the error in this reasoning.
Interactive — Conjugate Pair Matcher
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?

10

Multiple Choice Questions

Select the best answer for each question.

Understand Band 3

1. Which of the following species is amphiprotic?

Apply Band 3

2. At 25°C, Kw = 1.0 × 10⁻¹⁴. A solution has [OH⁻] = 2.0 × 10⁻³ mol/L. Which of the following correctly identifies [H₃O⁺] and the nature of the solution?

Analyse Band 4

3. The salt Na₂HPO₄ is dissolved in water. A student writes: Equation 1: HPO₄²⁻(aq) ⇌ H⁺(aq) + PO₄³⁻(aq). Equation 2: HPO₄²⁻(aq) + H⁺(aq) ⇌ H₂PO₄⁻(aq). Which statement correctly evaluates these equations?

Analyse Band 4

4. At 37°C, Kw = 2.4 × 10⁻¹⁴. A student measures the pH of a physiological buffer and obtains pH 6.8. Which statement correctly describes the classification of this solution at 37°C?

Analyse Band 5

5. A student is asked to identify the two conjugate pairs in the reaction: NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq). The student writes: "Pair 1: NH₃/NH₄⁺. Pair 2: H₂O/OH⁻." Which evaluation is correct?

11

Short Answer Questions

Apply Band 3–4 (4 marks)

Question 6. For each of the following species, state whether it is amphiprotic and write equations showing its amphiprotic behaviour where applicable. If it is not amphiprotic, explain why not.

(a) H₂PO₄⁻   (b) HPO₄²⁻   (c) PO₄³⁻   (d) Cl⁻

Apply Band 4 (4 marks)

Question 7. At 60°C, Kw = 9.6 × 10⁻¹⁴.

(a) Calculate the pH of pure water at 60°C. (b) State whether a solution with pH 6.8 at 60°C is acidic, basic, or neutral. Justify your answer with a calculation. (c) Calculate [OH⁻] in a solution at 60°C with pH 5.2. (d) Does pH + pOH = 14 apply at 60°C? Explain your reasoning.

Evaluate Band 6 (7 marks)

Question 8. Potassium dihydrogen phosphate (KH₂PO₄) is used as a pH buffer in food preservation. (a) Identify the amphiprotic ion in KH₂PO₄ and write equations showing its behaviour as both a Brønsted-Lowry acid and a Brønsted-Lowry base. (2 marks) (b) When KH₂PO₄ is dissolved in water at 25°C, the pH of the solution is 4.4. Calculate [OH⁻] at this pH and state whether [H₃O⁺] or [OH⁻] is greater. (2 marks) (c) A food scientist claims: "Adding KH₂PO₄ to a strongly acidic food preservative will make it less acidic, because H₂PO₄⁻ will act as a base and accept the excess H⁺." Evaluate this claim using Brønsted-Lowry theory and relevant Ka values. (3 marks)

12

Revisit — Think First

Return to your Think First response. The chemist observed NaHCO₃ acting as a base with HCl and as an acid with NaOH. You now have the framework to explain this precisely:

  • NaHCO₃ + HCl: HCl is a strong acid — Cl⁻ is an extremely weak base. HCO₃⁻ acts as a base, accepting H⁺ from HCl: HCO₃⁻ + HCl → H₂CO₃ + Cl⁻. H₂CO₃ then decomposes to CO₂ + H₂O (the bubbles observed). The solution becomes less acidic.
  • NaHCO₃ + NaOH: OH⁻ is a strong base. HCO₃⁻ acts as an acid, donating H⁺ to OH⁻: HCO₃⁻ + OH⁻ → CO₃²⁻ + H₂O. No CO₂ is produced because H₂CO₃ is not formed. The solution becomes less basic.
  • The key insight: HCO₃⁻ is amphiprotic. Whether it acts as acid or base depends entirely on which is stronger — its reaction partner as a base (relative to CO₃²⁻) or as an acid (relative to H₂CO₃). With a stronger acid (HCl), it acts as a base. With a stronger base (OH⁻), it acts as an acid. This is not a contradiction — it is the defining feature of amphiprotic behaviour.

Review your original response. Did you identify the role of the reaction partner? Did you use the terms amphiprotic or conjugate pair? Update your notes with any missing reasoning.

13

Answers

MC Answers & Explanations

Q1: C — HCO₃⁻
HCO₃⁻ can donate H⁺ to a base (HCO₃⁻ ⇌ H⁺ + CO₃²⁻, acting as acid) and accept H⁺ from an acid (HCO₃⁻ + H⁺ ⇌ H₂CO₃, acting as base) — amphiprotic. Cl⁻ (conjugate of strong acid HCl) cannot donate H⁺ and has negligible base tendency. OH⁻ can only accept H⁺ (base only). SO₄²⁻ has no ionisable H⁺ and is a very weak base — not meaningfully amphiprotic at HSC level.

Q2: B
[H₃O⁺] = Kw/[OH⁻] = (1.0 × 10⁻¹⁴)/(2.0 × 10⁻³) = 5.0 × 10⁻¹² mol/L. [OH⁻] = 2.0 × 10⁻³ >> [H₃O⁺] = 5.0 × 10⁻¹² → basic. pH = −log(5.0 × 10⁻¹²) = 11.3 > 7, confirms basic. Option A wrong — equal concentrations would be neutral, but [OH⁻] = 2.0 × 10⁻³ ≠ 1.0 × 10⁻⁷. Option C correct [H₃O⁺] but wrong classification. Option D uses incorrect calculation.

Q3: C
Both equations are chemically correct. Equation 1: HPO₄²⁻ acts as BL acid (proton donor → PO₄³⁻, Ka3 step). Equation 2: HPO₄²⁻ acts as BL base (proton acceptor → H₂PO₄⁻, reverse Ka2). Together they demonstrate amphiprotic character. Option A wrong — having lost two protons does not prevent further amphiprotic behaviour; one H⁺ remains. Option B wrong — negative charge does not prevent proton donation. Option D wrong — PO₄³⁻ is a stable, well-characterised ion.

Q4: D
Neutral pH at 37°C = −log(√(2.4 × 10⁻¹⁴)) = −log(1.549 × 10⁻⁷) = 6.81. pH 6.8 < 6.81 → [H₃O⁺] > [OH⁻] → acidic. Option A is correct reasoning but incomplete (doesn't use Kw). Option B uses same numbers but classifies as basic — incorrect direction. Option C invents an incorrect neutral pH value.

Q5: A
Both pairs are correctly identified. NH₃ (base) accepts H⁺ from H₂O → NH₄⁺ (conjugate acid of NH₃). H₂O (acid) donates H⁺ → OH⁻ (conjugate base of H₂O). Pair 1: NH₃/NH₄⁺ on opposite sides, differ by one H⁺ ✓. Pair 2: H₂O/OH⁻ on opposite sides, differ by one H⁺ ✓. Option B confuses direction — NH₄⁺ is the conjugate acid (NH₃ + H⁺, not NH₃ − H⁺). Option C wrong — H₂O and OH⁻ are on opposite sides (reactant and product).

Short Answer — Q6 Sample Answer

(a) H₂PO₄⁻ — YES, amphiprotic. It retains ionisable H⁺ (can act as acid) and has lone pairs on oxygen (can act as base).
As acid: H₂PO₄⁻(aq) ⇌ H⁺(aq) + HPO₄²⁻(aq)   (Ka2 = 6.2 × 10⁻⁸)
As base: H₂PO₄⁻(aq) + H⁺(aq) ⇌ H₃PO₄(aq)   (reverse of Ka1)

(b) HPO₄²⁻ — YES, amphiprotic.
As acid: HPO₄²⁻(aq) ⇌ H⁺(aq) + PO₄³⁻(aq)   (Ka3 = 4.8 × 10⁻¹³)
As base: HPO₄²⁻(aq) + H⁺(aq) ⇌ H₂PO₄⁻(aq)   (reverse of Ka2)

(c) PO₄³⁻ — NOT amphiprotic. PO₄³⁻ has no ionisable H⁺ remaining — it cannot act as a Brønsted-Lowry acid (no proton to donate). It can only act as a base (accepting H⁺). It is the final conjugate base of the phosphate system.

(d) Cl⁻ — NOT amphiprotic. Cl⁻ is the conjugate base of HCl (a strong acid). It has no ionisable H⁺ (cannot act as acid) and its tendency to accept H⁺ is essentially zero (the inverse strength rule means the conjugate of a very strong acid is a very weak base). Cl⁻ is a neutral spectator ion in aqueous solution.

Short Answer — Q7 Sample Answer

(a) pH of pure water at 60°C:
[H₃O⁺] = [OH⁻] = √Kw = √(9.6 × 10⁻¹⁴) = 3.10 × 10⁻⁷ mol/L
pH = −log(3.10 × 10⁻⁷) = 6.51
Pure water at 60°C is neutral (by definition — [H₃O⁺] = [OH⁻]) but has pH 6.51, not 7.

(b) Classification of pH 6.8 at 60°C:
Neutral pH at 60°C = 6.51. pH 6.8 > 6.51 → [H₃O⁺] < [OH⁻].
Therefore pH 6.8 at 60°C is basic. Even though pH 6.8 < 7, the relevant reference at 60°C is 6.51 (not 7).

(c) [OH⁻] at pH 5.2:
[H₃O⁺] = 10⁻⁵·² = 6.31 × 10⁻⁶ mol/L
[OH⁻] = Kw/[H₃O⁺] = (9.6 × 10⁻¹⁴)/(6.31 × 10⁻⁶) = 1.52 × 10⁻⁸ mol/L

(d) pH + pOH at 60°C:
pKw = −log(9.6 × 10⁻¹⁴) = 13.02
pH + pOH = pKw = 13.02 at 60°C — NOT 14. The relationship pH + pOH = 14 applies only at 25°C because that is the temperature at which Kw = 1.0 × 10⁻¹⁴ exactly. At other temperatures, Kw changes and so does pKw.

Short Answer — Q8 Sample Answer (Band 6)

(a) Amphiprotic ion in KH₂PO₄ = H₂PO₄⁻
KH₂PO₄ dissolves: K⁺ (neutral spectator, conjugate of KOH strong base) + H₂PO₄⁻ (amphiprotic ion).
As acid (proton donor): H₂PO₄⁻(aq) ⇌ H⁺(aq) + HPO₄²⁻(aq)   Ka2 = 6.2 × 10⁻⁸
As base (proton acceptor): H₂PO₄⁻(aq) + H⁺(aq) ⇌ H₃PO₄(aq)   (reverse of Ka1)

(b) [OH⁻] at pH 4.4:
[H₃O⁺] = 10⁻⁴·⁴ = 3.98 × 10⁻⁵ mol/L
[OH⁻] = (1.0 × 10⁻¹⁴)/(3.98 × 10⁻⁵) = 2.51 × 10⁻¹⁰ mol/L
[H₃O⁺] = 3.98 × 10⁻⁵ >> [OH⁻] = 2.51 × 10⁻¹⁰ → [H₃O⁺] is greater. The solution is acidic (pH 4.4 < 7).

(c) Evaluate the food scientist's claim:
The claim is partially correct but oversimplified. H₂PO₄⁻ can indeed act as a Brønsted-Lowry base, accepting H⁺ from a stronger acid to form H₃PO₄ (reverse of Ka1 = 7.5 × 10⁻³). If the "strongly acidic preservative" has [H⁺] significantly greater than Ka1 (i.e., the acid is stronger than H₃PO₄), then H₂PO₄⁻ would accept the H⁺ and reduce acidity — the claim would be correct in principle.
However, the claim is limited because: (1) If [H⁺] is very high (e.g., from a strong acid like HCl at low pH), the buffer capacity of H₂PO₄⁻ is finite — adding excess strong acid will eventually overwhelm it; (2) At very low pH, H₂PO₄⁻ may already be fully protonated to H₃PO₄ and unable to accept more H⁺; (3) Whether H₂PO₄⁻ acts as acid or base depends on the relative strength of the reaction partner — with a very strong acid, it acts as base (correct), but this does not mean it will always neutralise all excess H⁺ in a "strongly acidic" system.
Conclusion: The scientist correctly identifies the base behaviour of H₂PO₄⁻, but overstates its effectiveness in strongly acidic conditions without specifying concentrations and Ka values.

🏎️
Speed Race

Race Through Conjugate Pairs!

Answer questions on conjugate acid-base pairs, amphiprotic substances and Kw before your opponents cross the line. Fast answers = faster car. Pool: lessons 1–7.

Lesson 7 Complete

You can now identify conjugate pairs using the one-proton rule, define amphiprotic substances, write all four NESA-required equations for Na₂HPO₄ and KH₂PO₄, derive and apply Kw, and classify solutions at non-standard temperatures. These skills underpin every calculation in Lessons 8–10.