pH Calculations: GCSE Chemistry Step-by-Step Guide

What is the pH scale?

The pH scale runs from 0 to 14 under standard conditions, though values outside this range are possible in extreme concentrations. It is a measure of the concentration of hydrogen ions (H⁺, or more precisely hydronium ions H₃O⁺) in solution:

• pH below 7: acidic solution; [H⁺] > 1 × 10⁻⁷ mol/dm³
• pH = 7: neutral at 25 °C; [H⁺] = 1 × 10⁻⁷ mol/dm³
• pH above 7: alkaline solution; [H⁺] < 1 × 10⁻⁷ mol/dm³

The scale is logarithmic: each unit change in pH corresponds to a tenfold change in [H⁺]. A solution of pH 3 has 10 times the hydrogen ion concentration of a pH 4 solution, and 100 times that of a pH 5 solution.

What is the pH formula?

pH = −log₁₀[H⁺]

Where [H⁺] is the hydrogen ion concentration in mol/dm³ (moles per cubic decimetre, equivalent to moles per litre).

The negative logarithm is used so that acids (which have high [H⁺] and thus a very small number, often written in standard form like 1 × 10⁻³) produce positive, manageable pH values. Without the negative sign, strong acids would have negative pH values expressed as awkward decimals.

To find [H⁺] from pH, rearrange:

[H⁺] = 10⁻ᵖᴴ

What are the pH values of common solutions?

How to calculate pH from [H⁺] step by step

1. Identify the hydrogen ion concentration. Read [H⁺] from the question. Make sure the units are mol/dm³.

2. Check whether to work with standard form. [H⁺] values are often given in standard form (e.g. 1 × 10⁻³ mol/dm³). If so, remember that log₁₀(1 × 10⁻ⁿ) = −n.

3. Apply the formula. pH = −log₁₀[H⁺]

4. Evaluate the logarithm. Use the log button on your calculator (labelled "log" — this is log base 10, not "ln" which is natural logarithm).

5. Apply the negative sign and round. pH values are normally quoted to 2 decimal places.

Worked Example 1: A solution has [H⁺] = 0.01 mol/dm³. Calculate its pH.

[H⁺] = 0.01 = 1 × 10⁻² mol/dm³

pH = −log₁₀(1 × 10⁻²) = −(−2) = 2

This solution is strongly acidic. A pH of 2 corresponds to a concentration of 0.01 mol/dm³ of hydrogen ions.

Worked Example 2: A solution has [H⁺] = 3.5 × 10⁻⁴ mol/dm³. Calculate its pH.

pH = −log₁₀(3.5 × 10⁻⁴)

On a calculator: log(3.5 × 10⁻⁴) = −3.456

pH = −(−3.456) = 3.46 (to 2 decimal places)

How to find [H⁺] from pH step by step

1. Identify the pH value. Read it from the question.

2. Apply the inverse formula. [H⁺] = 10⁻ᵖᴴ

3. Evaluate using a calculator. Use the 10^x button (sometimes written as "10ˣ" or found by pressing "shift" then "log").

4. State the answer with correct units. Units are mol/dm³. Express in standard form for small values.

Worked Example 3: A solution has pH = 4.3. Calculate [H⁺].

[H⁺] = 10⁻⁴·³

On a calculator: 10^(−4.3) = 5.01 × 10⁻⁵ mol/dm³

[H⁺] = 5.0 × 10⁻⁵ mol/dm³ (to 2 significant figures)

Worked Example 4: Calculate the [H⁺] in a solution with pH = 11.

[H⁺] = 10⁻¹¹ = 1 × 10⁻¹¹ mol/dm³

This is a strongly alkaline solution with a very low hydrogen ion concentration.

How does the logarithmic scale affect pH comparisons?

Because pH is logarithmic, a change of 1 pH unit represents a tenfold change in [H⁺]:

This means a solution of pH 1 is 10 times more acidic than pH 2, but 1000 times more acidic than pH 4. Exam questions often ask you to state the factor by which [H⁺] changes when pH changes by a given number of units — use this table.

What are Ka and weak acids? (Higher level)

Strong acids (HCl, HNO₃, H₂SO₄) completely dissociate in water, so [H⁺] equals the starting concentration of the acid. For example, 0.1 mol/dm³ HCl gives [H⁺] = 0.1 mol/dm³ and pH = 1.

Weak acids (ethanoic acid, carbonic acid, citric acid) only partially dissociate. At equilibrium, most acid molecules remain intact:

HA ⇌ H⁺ + A⁻

The acid dissociation constant Ka measures how far this equilibrium lies to the right:

Ka = [H⁺][A⁻] / [HA] (units: mol/dm³)

A higher Ka means a stronger weak acid (more dissociation). Ethanoic acid has Ka ≈ 1.8 × 10⁻⁵ mol/dm³ at 25 °C — far smaller than a strong acid's complete dissociation. At GCSE, you are not usually required to calculate pH for weak acids using Ka, but knowing the concept explains why 0.1 mol/dm³ ethanoic acid has a pH of about 2.9 rather than the pH 1 a strong acid of the same concentration would give.

Frequently asked questions

Q: Why is pH defined using a negative logarithm?

Hydrogen ion concentrations in typical solutions range from 1 mol/dm³ (very acidic) to 10⁻¹⁴ mol/dm³ (very alkaline). Writing and comparing these as raw numbers is awkward. Taking −log₁₀ converts this range into a manageable scale from 0 to 14, where each unit is a tenfold change. The negative sign ensures that more acidic solutions (higher [H⁺]) give lower, more intuitive pH numbers rather than larger negative numbers.

Q: What happens to pH when you dilute an acid?

Diluting an acid reduces [H⁺] by increasing the volume of solvent. If you dilute a solution tenfold (e.g. add 9 volumes of water to 1 volume of acid), [H⁺] decreases by a factor of 10 and pH increases by 1 unit. However, for a strong acid, you can never dilute far enough to reach pH 7 — the minimum [H⁺] contribution from the water itself sets the practical lower bound for dilution. Adding water to an acid increases pH; adding water to an alkali decreases pH, in both cases moving towards pH 7.

Q: How do I know which "log" button to use on my calculator?

pH calculations use log base 10, written as log₁₀ or simply "log" on most calculators. Do not use the "ln" button, which is the natural logarithm (base e ≈ 2.718). To calculate [H⁺] = 10⁻ᵖᴴ, use the 10ˣ function, which is usually obtained by pressing "shift" or "2nd" followed by "log".

Q: If an acid has a low Ka, does that mean it is safe?

Not necessarily. Hydrofluoric acid (HF) has a relatively low Ka (about 6.6 × 10⁻⁴ mol/dm³), making it a weak acid, but it is extremely hazardous because HF penetrates skin and reacts with calcium in bone tissue. Safety depends on many factors beyond acid strength, including concentration, reactivity with biological tissue, and volatility. Never infer safety from Ka alone.

Q: Can pH be below 0 or above 14?

Yes. pH = −log₁₀[H⁺], so if [H⁺] > 1 mol/dm³, pH is negative. Concentrated sulfuric acid at 18 mol/dm³ has a pH of approximately −1.26. Similarly, pH values above 14 are possible for very concentrated strong alkalis. These extreme values are less commonly encountered in GCSE work, but the formula applies throughout.

Let Professor Pi guide you through pH calculations — visit aitutors.me.