Definition and determination of pH (A-level only) — AQA A-Level Chemistry
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Definition and determination of pH (A-level only) explained
Hydrogen ion concentrations in aqueous solution span an enormous range.
Read the full explanation
Concentrated hydrochloric acid can exceed 10 mol dm⁻³; pure water at 298 K is 1.00 × 10⁻⁷ mol dm⁻³; a concentrated alkali can be below 1 × 10⁻¹⁵ mol dm⁻³. That is sixteen powers of ten, and no linear axis can show it. On a scale where 1 mol dm⁻³ is drawn a metre long, pure water would be a ten-millionth of a metre. The differences matter even between similar solutions: dissolve SO₂ in water and you reach pH 2 to 3, dissolve SO₃ and you reach pH 0 to 1, a hundredfold difference in [H⁺] from two oxides of the same element. Comparing quantities that differ by powers of ten is exactly the job a logarithm does.
Therefore, a logarithmic scale, the pH scale, is used as a measure of hydrogen ion concentration.
The pH scale compresses that huge range by taking a logarithm: pH = −log₁₀[H⁺], with the concentration in mol dm⁻³. Because the logarithm is to base 10, one whole pH unit corresponds to a factor of ten in hydrogen ion concentration, and the minus sign makes acidic solutions, which have large [H⁺], have small pH values. Nothing restricts pH to the range 0 to 14: 2 mol dm⁻³ hydrochloric acid has a negative pH and concentrated sodium hydroxide exceeds 14. pH 7 is neutral only at 298 K, because neutrality means [H⁺] = [OH⁻] and the concentration at which that happens depends on Kw, which rises as temperature rises. Since a logarithm is being taken, answers are normally quoted to two decimal places.
+ pH = –log [H ] Students should be able to: convert concentration of hydrogen ions into pH and vice versa calculate the pH of a solution of a strong acid from its concentration.
For a strong monoprotic acid the dissociation is complete, so every mole of acid delivers a mole of H⁺ and [H⁺] is simply the acid concentration. Then pH = −log₁₀[H⁺]: for 0.0500 mol dm⁻³ hydrochloric acid, pH = −log(0.0500) = 1.30. Working backwards, [H⁺] = 10⁻ᵖᴴ, so a solution of pH 3.40 has [H⁺] = 3.98 × 10⁻⁴ mol dm⁻³. Two traps recur. A diprotic strong acid supplies two protons per molecule, so 0.0200 mol dm⁻³ H₂SO₄ gives [H⁺] = 0.0400 mol dm⁻³ and pH = 1.40. And if the acid has been diluted or mixed, recalculate the concentration from the moles and the new total volume before taking the logarithm.
Your focus
- Compare the hydrogen ion concentrations of solutions at pH 1 and pH 3 as a factor of 100.
- Explain why 2.0 mol dm⁻³ hydrochloric acid can have a pH below zero.
- Deduce, from measured pH values of 0 to 1 and 2 to 3, which of two aqueous oxides is the stronger acid.
Show all 9 objectives
- Calculate the pH of a solution in which [H⁺] is 2.5 × 10⁻³ mol dm⁻³, giving the answer to two decimal places.
- Explain why pure water at 323 K has a pH below 7 and is still neutral.
- Deduce the change in [H⁺] when the pH of a solution falls from 4.0 to 2.0.
- Calculate the pH of 0.0500 mol dm⁻³ hydrochloric acid as 1.30.
- Convert a pH of 3.40 into a hydrogen ion concentration of 3.98 × 10⁻⁴ mol dm⁻³.
- Calculate the pH of 0.0200 mol dm⁻³ sulfuric acid, doubling the concentration before taking the logarithm.
Definition and determination of pH (A-level only) exam tips
Marking Points
- one mark for stating that [H⁺] covers many powers of ten, roughly 10 to 10⁻¹⁵ mol dm⁻³
- one mark for explaining that a linear scale cannot conveniently display such a range
- one mark for relating a tenfold change in [H⁺] to a change of one pH unit
- one mark for comparing two solutions using the ratio of their hydrogen ion concentrations
- one mark for pH = −log₁₀[H⁺] with the concentration in mol dm⁻³
- one mark for stating that a fall of one pH unit means a tenfold rise in [H⁺]
- one mark for stating that a neutral solution has pH 7 only at 298 K
- one mark for quoting the pH to two decimal places
- one mark for stating that [H⁺] equals the acid concentration for a strong monoprotic acid
- one mark for substituting correctly into pH = −log₁₀[H⁺]
- one mark for the pH quoted to two decimal places
- one mark for using [H⁺] = 10⁻ᵖᴴ when converting a pH back to a concentration
- one mark for doubling the concentration when the strong acid is diprotic
Examiner Tips
- 💡Whenever a question compares acidity, convert everything to [H⁺] or everything to pH before you compare.
- 💡A difference of n pH units is a factor of 10ⁿ in hydrogen ion concentration.
- 💡Sanity-check every answer: an acid should give a small pH and an alkali a large one.
- 💡Give pH to two decimal places unless the question says otherwise; whole numbers lose marks.
- 💡Write [H⁺] on its own line before you touch the log button; most lost marks happen before the calculator, not on it.
- 💡For 'concentration from pH', use the 10ˣ key with a negative exponent and keep three significant figures.
Common Mistakes
- saying a solution at pH 1 is twice as acidic as one at pH 2 rather than ten times
- believing pH cannot fall below 0 or rise above 14
- comparing a concentration in mol dm⁻³ with a pH value without converting one to the other
- assuming a strong acid and a weak acid of equal concentration have the same [H⁺]
- using ln rather than log₁₀ on the calculator
- omitting the minus sign, so the pH of an acid comes out negative
- calling any solution of pH 7 neutral regardless of temperature
- rounding pH to a whole number, when 0.1 of a pH unit is already a 26% change in [H⁺]
- using a number of moles rather than a concentration in mol dm⁻³ inside the logarithm
- forgetting that 0.100 mol dm⁻³ H₂SO₄ provides 0.200 mol dm⁻³ H⁺
- giving the pH to a whole number when two decimal places are expected
- using Ka for a strong acid, which is unnecessary because dissociation is complete
- failing to recalculate the concentration after dilution before taking the logarithm