✓ Revise Right course
pH is calculated using pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol dm⁻³. Free A Level AQA Chemistry notes and 11 questions answered.
Understanding and Calculating pH is part of Acids and bases (A-level only) in A Level AQA Chemistry.
5 min
Reading time
68
Lessons in this topic
A Level AQA
Pathway
Reviewed by Revise Right
Content review
pH is calculated using pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol dm⁻³. Free A Level AQA Chemistry notes and 11 questions answered.
AQA A-Level Chemistry mock draft, 26–31 Oct. Draft coverage: Chemistry 7405/1 · Paper 1. Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
Use this lesson to stay inside Acids and bases (A-level only) while connecting the detail back to the wider Physical chemistry topic.
Read the core explanations from Understanding and Calculating pH before testing yourself from memory.
Picture two solutions side by side. One is concentrated hydrochloric acid with a hydrogen ion concentration of 1 mol dm-3. The other is a dilute solution where [H+] is 0.000001 mol dm-3. Both are acids, but their concentrations differ by a factor of one million.
Writing out numbers like 0.0000001 mol dm-3 repeatedly is impractical and error-prone. The concentration of hydrogen ions in aqueous solution covers a very wide range, so chemists use a logarithmic scale — the pH scale — as a more manageable measure of hydrogen ion concentration.
A logarithmic scale compresses that enormous range into a small set of numbers. Each whole-number step on the pH scale corresponds to a tenfold change in [H+]. A solution at pH 3 has ten times the hydrogen ion concentration of a solution at pH 4, and one hundred times that of a solution at pH 5.
This logarithmic compression is why pH 7 is described as neutral, pH values below 7 indicate acidic conditions, and pH values above 7 indicate alkaline conditions — all within a scale that typically runs from 0 to 14 for common laboratory solutions.
Now that you can see why the scale exists, here is the tool that makes it work. The relationship between pH and hydrogen ion concentration is captured in a single formula.
The negative sign is deliberate. Because [H+] is always a small positive number (less than 1 mol dm-3 for most solutions), its log10 is negative. Multiplying by -1 converts that negative value into the positive pH numbers you are familiar with.
To reverse the process — converting a pH back into [H+] — rearrange the formula. If pH = -log10[H+], then $[\text{H}^+] = 10^{-\text{pH}}$. This inverse operation is called the antilog, and it is the key to working backwards from pH to concentration.
Strong acids — such as hydrochloric acid (HCl), nitric acid (HNO3), and sulphuric acid (H2SO4) — dissociate completely in aqueous solution. This complete dissociation is the critical assumption that makes the pH calculation straightforward.
For a monoprotic strong acid like HCl, complete dissociation means every mole of HCl produces exactly one mole of H+ ions. So the concentration of H+ equals the initial concentration of the acid. You can substitute that concentration directly into the pH formula.
Sulphuric acid is diprotic. In this worked example we treat each mole of H2SO4 as contributing two moles of H+ for the pH calculation, so a 0.025 mol dm-3 solution gives [H+] = 0.050 mol dm-3. Always state the proton assumption you are using before substituting into the pH formula.
Worked example: Calculating the pH of a Strong Monoprotic Acid
Calculate the pH of a 0.050 mol dm-3 solution of hydrochloric acid, HCl(aq). [2 marks]
Answer: pH = 1.30
The reverse calculation — finding [H+] from a given pH — appears regularly in AQA questions. The operation needed is the inverse power of ten: raise 10 to the power of negative pH.
Worked example: Converting pH to Hydrogen Ion Concentration
The pH of a solution is 3.40. Calculate the concentration of hydrogen ions in this solution. Give your answer in mol dm-3. [2 marks]
Answer: [H+] = 3.98 × 10^-4 mol dm^-3
Notice the pattern: a pH of 3.40 gives [H+] = 3.98 × 10-4 mol dm-3. The integer part of the pH (3) determines the power of ten (10-4 because of the negative sign), and the decimal part (0.40) shifts the coefficient away from 1.00.
One of the most powerful ways to consolidate this topic is to compare pH values across a range of concentrations. The table below shows how [H+] and pH relate for a strong monoprotic acid — notice how each tenfold decrease in concentration increases pH by exactly 1.
| [H+] / mol dm-3 | log10[H+] | pH = -log10[H+] |
|---|---|---|
| 1.0 | 0 | 0.00 |
| 0.10 (= 10-1) | -1 | 1.00 |
| 0.010 (= 10-2) | -2 | 2.00 |
| 1.0 × 10-3 | -3 | 3.00 |
| 1.0 × 10-7 | -7 | 7.00 |
The table confirms the logarithmic relationship: each factor of 10 in concentration corresponds to a change of exactly 1 pH unit. This is the core insight that makes the pH scale so useful — and it is also the source of a common exam trap.
Worked example: Calculating pH of a Diprotic Strong Acid
Calculate the pH of a 0.025 mol dm-3 solution of sulphuric acid, H2SO4(aq). In this worked example, treat each mole of H2SO4 as providing 2 moles of H+ for the pH calculation. [3 marks]
Answer: pH = 1.30
pH calculations are reliable mark-winners once you know the traps. The mistakes below appear repeatedly in mark-scheme reports — recognising them before the exam is the most efficient preparation you can do.
AQA mark schemes for pH calculations typically award one mark for a correct method (showing the formula and substitution) and one accuracy mark for the correct final answer. Even if you make an arithmetic slip, a clearly shown method can still earn the method mark.
These three specification requirements — converting [H+] to pH, converting pH to [H+], and calculating pH for strong acids — are all variations of the same core skill. Master the formula, apply the dissociation logic correctly, and use the bracket-check every time, and this topic becomes one of the most reliable sources of marks in the Physical Chemistry paper.
Worked example: Safe pH-Calculation Workflow
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-09-05.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
pH is calculated using pH = −log₁₀[H⁺], where [H⁺] is the hydrogen ion concentration in mol dm⁻³. For a strong monoprotic acid such as 0.050 mol dm⁻³ HCl, complete dissociation means [H⁺] = 0.050 mol dm⁻³, so pH = −log₁₀(0.050) = 1.30.
Examples of strong acids are hydrochloric acid, HCl, nitric acid, HNO₃, and sulphuric acid, H₂SO₄. They dissociate completely in aqueous solution, so for a monoprotic strong acid the H⁺ concentration equals the acid concentration.
For a diprotic strong acid such as sulphuric acid, treat each mole of H₂SO₄ as giving two moles of H⁺. A 0.025 mol dm⁻³ solution therefore has [H⁺] = 2 × 0.025 = 0.050 mol dm⁻³ and pH = −log₁₀(0.050) = 1.30.
pH can be zero: a strong monoprotic acid with [H⁺] = 1.0 mol dm⁻³ has pH = −log₁₀(1.0) = 0.00. The pH scale typically runs from 0 to 14 for common laboratory solutions, with each tenfold drop in concentration raising pH by exactly 1.
The hydrogen ion concentration is found from pH using the antilog: [H⁺] is 10 raised to the power −pH. For a pH of 3.40, [H⁺] = 3.98 × 10⁻⁴ mol dm⁻³; substituting this back into pH = −log₁₀[H⁺] should return the original pH.
pH uses a logarithmic scale because hydrogen ion concentrations in aqueous solution cover a very wide range, and a logarithmic scale compresses this into a small set of numbers. Each whole-number step on the pH scale is a tenfold change in [H⁺], so pH 3 has ten times the [H⁺] of pH 4.
For a strong monoprotic acid, each tenfold decrease in concentration increases the pH by exactly 1. A 0.10 mol dm⁻³ solution has pH 1.00 and a 0.010 mol dm⁻³ solution has pH 2.00, because each factor of 10 in [H⁺] corresponds to one pH unit.
The pH formula, pH = −log₁₀[H⁺], has a negative sign because [H⁺] is usually a small positive number less than 1 mol dm⁻³, so its log₁₀ is negative. Multiplying by −1 turns that into the familiar positive pH values.
A pH answer is checked by bracketing [H⁺] between two powers of ten. For example, [H⁺] = 0.050 mol dm⁻³ lies between 10⁻¹ and 10⁻², so the pH must be between 1 and 2, and pH = 1.30 fits. Substituting [H⁺] back into the formula is another check.
pH is usually given to 2 decimal places when the concentration has 2 or 3 significant figures, so the precision matches the data. For example, 0.050 mol dm⁻³ HCl gives pH 1.30, and a pH of 3.40 gives [H⁺] to 3 significant figures, 3.98 × 10⁻⁴ mol dm⁻³.
For a diprotic strong acid such as sulphuric acid, each mole is treated as giving 2 moles of H⁺, so [H⁺] is twice the acid concentration; for a monoprotic acid like HCl, [H⁺] equals the acid concentration. The proton assumption should be stated before using the pH formula.