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How do we calculate the pH of strong and weak acids, and how do buffers resist changes in pH?

The pH scale, Ka and pKa for weak acids, the ionic product of water Kw, calculating the pH of strong and weak acids and bases, buffer solutions and titration curves with indicators.

An Eduqas A-Level Chemistry PI5.2 answer on the pH scale, Ka and pKa, the ionic product of water, calculating pH for strong and weak acids and bases, buffers and titration curves.

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  1. What this topic is asking
  2. The pH scale and Kw
  3. Strong acids and bases
  4. Weak acids: Ka and pKa
  5. Buffer solutions
  6. Titration curves and indicators
  7. Examples in context
  8. Try this

What this topic is asking

Eduqas topic PI5.2 covers the quantitative chemistry of acids and bases: the pH scale, the acid dissociation constant KaK_a and pKapK_a for weak acids, the ionic product of water KwK_w, calculating the pH of strong and weak acids and bases, the action and calculation of buffer solutions, and titration curves with the choice of indicator. It is one of the most calculation-heavy topics in the specification.

The pH scale and Kw

Strong acids and bases

A strong acid (such as HCl) is fully dissociated, so [H+][\text{H}^+] equals the acid concentration and pH follows directly. For a strong base (such as NaOH), [OH−][\text{OH}^-] equals the base concentration, and [H+]=Kw[OH−][\text{H}^+] = \dfrac{K_w}{[\text{OH}^-]} gives the pH.

Weak acids: Ka and pKa

Buffer solutions

The pH of a buffer is found from [H+]=Ka×[HA][A−][\text{H}^+] = K_a \times \dfrac{[\text{HA}]}{[\text{A}^-]}.

Titration curves and indicators

A pH-against-volume titration curve has a near-vertical section at the equivalence point. The indicator must change colour within that vertical range: methyl orange for strong-acid/weak-base, phenolphthalein for weak-acid/strong-base, and either for strong-acid/strong-base. A weak-acid/weak-base titration has no sharp vertical section, so no indicator is suitable.

Examples in context

Example 1. Blood pH. The hydrogencarbonate buffer system keeps blood pH near 7.4; added acid is removed by HCO3−\text{HCO}_3^- and added base by H2CO3\text{H}_2\text{CO}_3, a direct biological application of buffering.

Example 2. Choosing an indicator in the lab. When titrating ethanoic acid (weak) with sodium hydroxide (strong), phenolphthalein is chosen because its colour change (pH≈8\text{pH} \approx 8 to 1010) lies within the vertical section of the curve, giving a sharp end point.

Try this

Q1. Calculate the pH of 0.0500 mol dm−30.0500\ \text{mol dm}^{-3} hydrochloric acid. [1 mark]

  • Cue. HCl is strong, so [H+]=0.0500[\text{H}^+] = 0.0500; pH=−log⁡10(0.0500)=1.30\text{pH} = -\log_{10}(0.0500) = 1.30.

Q2. Calculate the pH of 0.100 mol dm−30.100\ \text{mol dm}^{-3} sodium hydroxide (Kw=1.0×10−14K_w = 1.0 \times 10^{-14}). [2 marks]

  • Cue. [OH−]=0.100[\text{OH}^-] = 0.100, so [H+]=1.0×10−140.100=1.0×10−13[\text{H}^+] = \dfrac{1.0 \times 10^{-14}}{0.100} = 1.0 \times 10^{-13}; pH=13.0\text{pH} = 13.0.

Exam-style practice questions

Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Eduqas 20194 marksEthanoic acid has Ka=1.8×10−5 mol dm−3K_a = 1.8 \times 10^{-5}\ \text{mol dm}^{-3}. Calculate the pH of a 0.100 mol dm−30.100\ \text{mol dm}^{-3} solution of ethanoic acid.
Show worked answer →

For a weak acid, [H+]=Ka×[HA][\text{H}^+] = \sqrt{K_a \times [\text{HA}]} (assuming [H+]=[A−][\text{H}^+] = [\text{A}^-] and that dissociation is small) (1).

[H+]=1.8×10−5×0.100=1.8×10−6=1.34×10−3 mol dm−3[\text{H}^+] = \sqrt{1.8 \times 10^{-5} \times 0.100} = \sqrt{1.8 \times 10^{-6}} = 1.34 \times 10^{-3}\ \text{mol dm}^{-3} (2).

pH=−log⁡10(1.34×10−3)=2.87\text{pH} = -\log_{10}(1.34 \times 10^{-3}) = 2.87 (1).

Eduqas 20214 marks(a) Explain how a buffer solution made from ethanoic acid and sodium ethanoate resists a change in pH when a small amount of acid is added. (b) State one use of buffer solutions.
Show worked answer →

(a) The buffer contains a high concentration of the weak acid CH3COOH\text{CH}_3\text{COOH} and its conjugate base CH3COO−\text{CH}_3\text{COO}^- (1). When acid (H+\text{H}^+) is added, the ethanoate ions react with it (CH3COO−+H+→CH3COOH\text{CH}_3\text{COO}^- + \text{H}^+ \rightarrow \text{CH}_3\text{COOH}) (1), removing most of the added H+\text{H}^+, so the pH changes only slightly (1).

(b) Any one (1): controlling the pH of blood, shampoos, or biochemical or industrial processes where a stable pH is needed.

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