The pH scale

This page covers one Form 4 content standard: the pH scale. It builds directly on the previous standard, where you learnt that acidic properties come from hydrogen ions, H⁺, and alkaline properties from hydroxide ions, OH⁻. The pH scale turns the concentration of those hydrogen ions into a single, easy number, so you can compare solutions at a glance and answer the calculation questions the exam sets.

What the pH scale measures

The pH scale is a numerical scale, normally running from 0 to 14, that measures the degree of acidity or alkalinity of an aqueous solution. It reflects the concentration of hydrogen ions, [H⁺], in the solution.

• pH less than 7, acidic. The smaller the pH, the more acidic the solution and the higher its [H⁺].
• pH equal to 7, neutral. Pure water is neutral; [H⁺] equals [OH⁻].
• pH greater than 7, alkaline. The larger the pH, the more alkaline the solution and the higher its [OH⁻].

A change of one unit on the pH scale corresponds to a tenfold change in [H⁺], because the scale is logarithmic. So a solution of pH 2 has ten times the hydrogen ion concentration of one at pH 3, and a hundred times that of pH 4.

The defining relationship

The formula that connects pH to hydrogen ion concentration is:

pH = −log₁₀[H⁺]

where [H⁺] is the hydrogen ion concentration in mol dm⁻³. You can rearrange it to find the concentration from the pH:

[H⁺] = 10⁻ᵖᴴ mol dm⁻³

These two forms are all you need for the Form 4 calculations. Reading [H⁺] straight off a power of ten is the quickest route: if [H⁺] = 1 × 10⁻³ mol dm⁻³, the pH is simply 3.

Measuring pH: indicators

pH is estimated in the laboratory with a universal indicator (which shows a range of colours mapped to a pH chart) or read precisely with a pH meter. A single indicator such as litmus, methyl orange or phenolphthalein only tells you whether a solution is acidic or alkaline, not the exact pH; universal indicator and a pH meter give the value. Knowing which tool gives a value and which gives only a direction is a common short-answer mark.

Strength versus concentration

The pH scale exposes a distinction students often blur. Strength is the degree of ionisation; concentration is how much acid is dissolved per unit volume.

• A strong acid (e.g. hydrochloric acid) ionises completely, so at a given concentration it has the highest [H⁺] and therefore the lowest pH.
• A weak acid (e.g. ethanoic acid) ionises only partially at the same concentration, so it has a lower [H⁺] and a higher pH.
• Diluting any acid with water lowers [H⁺], so the pH rises toward 7 (it never crosses 7 by dilution alone).

Getting this straight prevents the classic wrong answer that a concentrated weak acid must have a lower pH than a dilute strong acid.

Worked example

Question. A hydrochloric acid solution has a hydrogen ion concentration of [H⁺] = 1 × 10⁻² mol dm⁻³. (a) Calculate its pH. (b) The solution is then diluted with water until [H⁺] = 1 × 10⁻⁴ mol dm⁻³. State the new pH and explain the change.

Step 1, Apply the formula for part (a). pH = −log₁₀[H⁺] = −log₁₀(1 × 10⁻²) = −(−2) = 2.

Step 2, Apply it again for the diluted solution. pH = −log₁₀(1 × 10⁻⁴) = −(−4) = 4.

Step 3, Explain the change. Adding water lowers the hydrogen ion concentration (from 10⁻² to 10⁻⁴ mol dm⁻³), so the pH rises from 2 to 4, moving closer to neutral.

Answer. (a) The pH is 2. (b) After dilution the pH is 4; the pH increases because dilution reduces [H⁺] by a factor of 100, which is two pH units.

Practice question

Question. A solution of sodium hydroxide has a pH of 13. Another solution, of ethanoic acid, has a pH of 4. (a) State which is acidic and which is alkaline. (b) Calculate [H⁺] for the ethanoic acid solution. (c) If the ethanoic acid were replaced by hydrochloric acid of the same concentration, would you expect its pH to be higher, lower, or the same? Explain.

Answer. (a) The sodium hydroxide solution (pH 13) is alkaline; the ethanoic acid solution (pH 4) is acidic. (b) [H⁺] = 10⁻ᵖᴴ = 10⁻⁴ = 1 × 10⁻⁴ mol dm⁻³. (c) Lower. Hydrochloric acid is a strong acid and ionises completely, so at the same concentration it produces a higher [H⁺] than the weak ethanoic acid, giving a lower pH.

Exam tip

For pH calculations, read the power of ten: if [H⁺] = 1 × 10⁻ⁿ, then pH = n, and if you are given the pH, then [H⁺] = 10⁻ᵖᴴ. Always attach the unit mol dm⁻³ to a concentration. When a question compares two solutions, decide first whether it is testing direction (acidic/alkaline) or magnitude ([H⁺] and strength). And never say that diluting an acid makes it alkaline, dilution only moves the pH toward 7, never past it.

Reading pH questions well

Many pH questions describe an everyday situation, rainwater, soil, a soft drink, stomach fluid, and ask you to place it on the scale or to say what would happen if it were diluted or neutralised. Approach these in two moves. First, translate the description into a position on the scale: below 7, at 7, or above 7. Second, use the logarithmic idea to reason about size: each step of one pH unit is a factor of ten in [H⁺]. That single fact answers a surprising number of Paper 1 items, for instance ordering three solutions by acidity or working out how [H⁺] changes when the pH shifts by two.

A further favourite is the strength-versus-concentration comparison. If two acids share the same concentration but have different pH values, the one with the lower pH is the stronger acid because it has ionised more fully. If the same acid is compared at two concentrations, the more concentrated sample has the lower pH. Keeping these two variables, strength and concentration, separate in your mind is exactly the discipline the pH standard is designed to reward.

Where this fits

This is content standard 6.2 of the Acids, Bases and Salts chapter. It follows directly from the properties of acids and bases and leads into concentration, molarity and neutralisation, where the same [H⁺] idea is used quantitatively. Reinforce it with the chapter revision notes and practise the calculations in the worked examples. In our online 1-to-1 SPM Chemistry lessons, taught in English, from RM50/hr, our teachers make the strength-versus-concentration distinction concrete with side-by-side examples, because it is the single most common misconception in this standard.

Quick recap

• pH scale 0–14: below 7 acidic, 7 neutral, above 7 alkaline.
• pH = −log₁₀[H⁺] and [H⁺] = 10⁻ᵖᴴ mol dm⁻³.
• One pH unit = a tenfold change in [H⁺] (logarithmic scale).
• Strength = degree of ionisation; concentration = amount per volume; dilution raises pH toward 7.