Acid-base Equilibria

Q: Do I need to solve quadratic equations for weak acid pH calculations?

No, Edexcel explicitly allows two approximations for IAL Chemistry Unit 4: 1) initial weak acid concentration, 2) . This simplifies the Ka expression to , so no quadratic solving is required.

Q: What value of Kw should I use in calculations?

At 298K (room temperature), . This value is provided in the data booklet if required for questions at non-standard temperatures.

Q: How do I find Ka from a titration curve?

Locate the half-neutralisation point: this is the volume of titrant exactly half of the equivalence point volume. At this point, , so substituting into the Ka expression gives , meaning . Read the pH directly from the curve at this point and calculate .

Edexcel International A-Level Chemistry· Spec 14.1–14.23· 45 min read

1. Fundamental Acid-Base Definitions and Strong Acid pH Calculations★★☆☆☆⏱ 10 min

📘 Definition

Brønsted-Lowry Acid-Base Pair

An acid is a proton (H⁺) donor, while a base is a proton acceptor. A conjugate pair consists of two species that differ by exactly one H⁺ ion: the conjugate base is the species left after an acid donates a proton, and the conjugate acid is the species formed when a base accepts a proton.

Example:

Hydrochloric acid (HCl, acid) donates H⁺ to form its conjugate base Cl⁻; ammonia (NH₃, base) accepts H⁺ to form its conjugate acid NH₄⁺.

Acid strength is determined by degree of dissociation, not concentration: strong acids dissociate 100% in aqueous solution, while weak acids only dissociate partially. pH is a logarithmic measure of hydrogen ion concentration, always reported to 2 decimal places in Edexcel exams.

pH = -\text{log}_{10}[H^+] \\ [H^+] = 10^{-pH}

📐 Worked Example

Calculate the pH of 0.005 mol dm⁻³ nitric acid (strong monoprotic acid) at 298K.

1
Strong monoprotic acids dissociate completely, so $[H^{+}] =$ initial acid concentration = 0.005 mol dm⁻³.
2
$pH = -\text{log}_{10}(0.005) = 2.30$

2. Ka, Kw and pH Calculations for Weak Acids & Strong Bases★★★☆☆⏱ 12 min

📘 Definition

Acid Dissociation Constant (Ka)

K_a

Equilibrium constant for the partial dissociation of a weak acid HA: $H A ⇌ H^{+} + A^{-}$ . The expression is: $K_{a} = \frac{[ H ^{+} ] [ A ^{-} ]}{[ H A ]}$ . $p K_{a} = - l o g_{10} K_{a}$ , so smaller pKa values correspond to stronger weak acids.

📘 Definition

Ionic Product of Water (Kw)

K_w

Equilibrium constant for the dissociation of water: $H_{2} O ⇌ H^{+} + O H^{-}$ . At 298K, $K_{w} = [H^{+}] [O H^{-}] = 1.0 \times 1 0^{- 14} m o l^{2} d m^{- 6}$ , so $p K_{w} = 14$ .

📐 Worked Example

Calculate the pH of 0.02 mol dm⁻³ propanoic acid, given $K_{a} = 1.35 \times 1 0^{- 5} m o l d m^{- 3}$ at 298K.

1
Apply allowed approximations to find $[H^{+}]$ :
2
$[H^+] = \sqrt{1.35 × 10^{-5} × 0.02} = \sqrt{2.7 × 10^{-7}} = 5.196 × 10^{-4} mol dm^{-3}$
3
Calculate pH to 2 decimal places:
4
$pH = -\text{log}_{10}(5.196 × 10^{-4}) = 3.28$

📐 Worked Example

Calculate the pH of 0.01 mol dm⁻³ barium hydroxide (strong dibasic base) at 298K.

1
Barium hydroxide dissociates completely: $B a (O H)_{2} \to B a^{2 +} + 2 O H^{-}$ , so $[O H^{-}] = 2 \times 0.01 = 0.02 m o l d m^{- 3}$ .
2
Use Kw to find $[H^{+}]$ :
3
$[H^+] = \frac{K_w}{[OH^-]} = \frac{1.0 × 10^{-14}}{0.02} = 5.0 × 10^{-13} mol dm^{-3}$
4
$pH = -\text{log}_{10}(5.0 × 10^{-13}) = 12.30$

3. Titration Curves and Indicator Selection★★★☆☆⏱ 10 min

Titration curves plot pH against volume of titrant added. Key features include: initial pH, a vertical section (rapid pH change near the equivalence point), equivalence point, and (for weak acid/strong base titrations) the half-neutralisation point. Diprotic acids have two separate vertical sections, one for each dissociable proton.

📐 Worked Example

A titration of ammonia (weak base) with hydrochloric acid (strong acid) has a vertical section from pH 3 to pH 7. State the suitable indicator for this titration.

1
Check indicator ranges against the vertical section:
2
Phenolphthalein (8.3–10.0) falls completely outside the vertical section, so is unsuitable.
3
Methyl orange (3.1–4.4) falls entirely inside the vertical section, so is the correct indicator.

4. Buffer Systems and Calculations★★★★☆⏱ 8 min

📘 Definition

Buffer Solution

A solution that resists changes in pH when small amounts of acid, base, or water are added. Acid buffers are made from a weak acid and its conjugate base (e.g. ethanoic acid + sodium ethanoate), while alkaline buffers are made from a weak base and its conjugate acid.

Example:

Human blood uses an acid buffer system of carbonic acid ( $H_{2} C O_{3}$ ) and hydrogencarbonate ions ( $H C O_{3}^{-}$ ) to maintain a constant pH of ~7.4.

Buffer action works by reacting added H⁺ or OH⁻ with buffer components: added H⁺ reacts with the conjugate base ( $H^{+} + A^{-} \to H A$ ), while added OH⁻ reacts with the weak acid ( $O H^{-} + H A \to A^{-} + H_{2} O$ ). The rearranged Ka expression is used to calculate buffer pH: $[H^{+}] = K_{a} \times \frac{[ H A ]}{[ A ^{-} ]}$ .

📐 Worked Example

A buffer is made by mixing equal volumes of 0.1 mol dm⁻³ ethanoic acid and 0.05 mol dm⁻³ sodium ethanoate. Given $K_{a} = 1.7 \times 1 0^{- 5} m o l d m^{- 3}$ , calculate the buffer pH.

1
Equal volumes halve both concentrations: $[H A] = 0.05 m o l d m^{- 3}$ , $[A^{-}] = 0.025 m o l d m^{- 3}$ .
2
Substitute into the buffer pH formula:
3
$[H^+] = 1.7 × 10^{-5} × \frac{0.05}{0.025} = 3.4 × 10^{-5} mol dm^{-3}$
4
$pH = -\text{log}_{10}(3.4 × 10^{-5}) = 4.47$

5. Experimental Ka Determination (Core Practical 11)★★★☆☆⏱ 5 min

There are two approved methods to determine the Ka of a weak acid for Core Practical 11: 1) Measure the pH of a known concentration of weak acid, then rearrange the Ka expression to calculate Ka. 2) Titrate the weak acid against a standard strong base, read the pH at the half-neutralisation point, where $p H = p K_{a}$ so $K_{a} = 1 0^{- p H}$ .

📐 Worked Example

25 cm³ of 0.1 mol dm⁻³ methanoic acid is titrated against 0.1 mol dm⁻³ NaOH. The pH at 12.5 cm³ of NaOH added is 3.75. Calculate the Ka of methanoic acid.

1
12.5 cm³ is exactly half the volume required to reach equivalence, so this is the half-neutralisation point.
2
At half-neutralisation, $p H = p K_{a} = 3.75$ .
3
$K_a = 10^{-3.75} = 1.8 × 10^{-4} mol dm^{-3}$

6. Common Pitfalls

Wrong move:

Confusing acid strength (strong/weak) with concentration (concentrated/dilute)

Why:

Strength refers only to degree of dissociation, not concentration: a dilute strong acid can have a higher pH than a concentrated weak acid.

Correct move:

Classify acid strength using degree of dissociation, and use concentration only for pH calculations.

Wrong move:

Attempting to solve quadratic equations for weak acid pH

Why:

Edexcel explicitly allows valid approximations for IAL Chemistry Unit 4, so quadratics are unnecessary and waste exam time.

Correct move:

Use $[H^{+}] = K_{a} \times c$ with the assumptions that $[H A] \approx$ initial concentration and $[H^{+}] \approx [A^{-}]$ .

Wrong move:

Assuming all titrations have an equivalence point at pH 7

Why:

Only strong acid + strong base titrations have equivalence at pH 7. Weak acid + strong base = pH >7, strong acid + weak base = pH <7.

Correct move:

Predict equivalence pH based on the relative strength of the acid and base used in the titration.

Wrong move:

Selecting an indicator with a range that only partially overlaps the titration curve vertical section

Why:

The indicator will change colour gradually outside the equivalence point, leading to inaccurate titre values.

Correct move:

Only select indicators whose full pH range lies entirely within the vertical section of the titration curve.

Wrong move:

Forgetting diprotic acids have two equivalence points on titration curves

Why:

Each proton in a diprotic acid dissociates separately, leading to two distinct vertical sections on the curve.

Correct move:

Count vertical sections to distinguish monoprotic and diprotic acids, and use the first half-neutralisation point to calculate Ka₁.

Wrong move:

Reporting pH values to 1 or 0 decimal places

Why:

Edexcel mark schemes explicitly require pH values to be reported to 2 decimal places for all calculations.

Correct move:

Always round pH to 2 decimal places, even for whole number values (e.g. pH 2 is written as 2.00).

7. Quick Reference Cheatsheet

Concept	Formula/Rule	Exam Notes
pH definition	$p H = - l o g_{10} [H^{+}]$ ; $[H^{+}] = 1 0^{- p H}$	Report pH to 2 decimal places
Strong acid pH	$[H^{+}] =$ initial monoprotic acid concentration	Complete dissociation, no approximations needed
Weak acid pH	$[H^{+}] = K_{a} \times c$	Approximations allowed, no quadratics required
Strong base pH	$[H^{+}] = \frac{K _{w}}{[ O H ^{-} ]}$	$K_{w} = 1.0 \times 1 0^{- 14} m o l^{2} d m^{- 6}$ at 298K
Buffer pH	$[H^{+}] = K_{a} \times \frac{[ H A ]}{[ A ^{-} ]}$	Assume no dissociation of buffer components
Half-neutralisation	$p H = p K_{a}$	Only for weak acid + strong base titrations
Indicator selection	Full indicator range inside curve vertical section	Ranges provided in data booklet

8. Frequently Asked

Do I need to solve quadratic equations for weak acid pH calculations?

No, Edexcel explicitly allows two approximations for IAL Chemistry Unit 4: 1) $[H A] \approx$ initial weak acid concentration, 2) $[H^{+}] \approx [A^{-}]$ . This simplifies the Ka expression to $[H^{+}] = K_{a} \times c$ , so no quadratic solving is required.

What value of Kw should I use in calculations?

At 298K (room temperature), $K_{w} = 1.0 \times 1 0^{- 14} m o l^{2} d m^{- 6}$ . This value is provided in the data booklet if required for questions at non-standard temperatures.

How do I find Ka from a titration curve?

Locate the half-neutralisation point: this is the volume of titrant exactly half of the equivalence point volume. At this point, $[H A] = [A^{-}]$ , so substituting into the Ka expression gives $K_{a} = [H^{+}]$ , meaning $p K_{a} = p H$ . Read the pH directly from the curve at this point and calculate $K_{a} = 1 0^{- p H}$ .

Going deeper

core_practical_guideCore Practical 11: Ka of a Weak AcidStep-by-step guide for required practical assessment

What's Next

Acid-base equilibria accounts for ~15% of the Edexcel IAL Chemistry Unit 4 written paper, so practice past paper questions on pH calculations, titration curve interpretation and buffer problems to consolidate your knowledge. Make sure you are fully confident with Core Practical 11, as practical-based questions on Ka determination are frequently tested, along with applications of the blood buffer system in biological contexts. Once you have mastered this topic, you are ready to move on to further organic chemistry and analytical techniques in the rest of Unit 4, or transition to Unit 5 transition metal chemistry.