How do you calculate the pH of a weak acid?

Find the free H+ concentration from the acid's Ka: [H+] is about the square root of Ka times the concentration, when little of the acid ionises. Then pH is minus the log base 10 of that.

Why does a weak acid have a higher pH than a strong acid at the same concentration?

Because only a small fraction of its molecules give up H+, so the concentration of free H+ is much lower, and pH counts free H+ only.

It sounds like this“A 0.1 mol per litre solution of any acid has a pH of 1.”

Thinking equal concentrations give the same pH

2 min readBy the Cognosc teamPart of How can you tell whether a molecule is an acid or a base?

Why it feels right

If a bottle says 0.1 mol per litre acid, it seems you could work out the pH from that alone: 0.1 is 10 to the minus 1, so pH 1. School examples use hydrochloric acid so often that the shortcut feels like the rule.

Why it’s wrong

pH only counts the H+ that is actually free. Hydrochloric acid at 0.1 mol per litre gives free H+ of 0.1 and a pH of 1. Acetic acid at the same concentration frees only about 0.0013, which is a pH of 2.87, because most of it stays as whole molecules.

A worked example

pH is defined as minus the base-10 logarithm of the hydrogen ion concentration: pH = -log10 [H+]. It counts free H+ ions, not acid molecules. The number of acid molecules matters only through how many of them give up their H+.

For hydrochloric acid, a strong acid, every molecule does. At 0.1 mol per litre, [H+] = 0.1, so pH = -log10(0.1) = 1.

For acetic acid, a weak acid with Ka = 1.8 x 10^-5, only a small fraction does. The equilibrium gives [H+] = the square root of (Ka x concentration) = the square root of (1.8 x 10^-5 x 0.1), which is about 1.34 x 10^-3 mol per litre. The pH is -log10(0.00134) = 2.87.

Because pH is a logarithm, 2.87 against 1 is a difference of nearly 2 units, which is about 75 times fewer free hydrogen ions. Two solutions with the same amount of acid can differ in acidity by a factor of tens or hundreds.

How to catch yourself

You compute pH from the concentration of a weak acid directly.
You assume every acid at the same concentration has the same pH.
You forget that pH measures free H+.

What to hold instead

The better idea

pH is minus the logarithm of the free H+ concentration. A strong acid frees all its hydrogen, so 0.1 mol per litre gives pH 1. A weak acid at the same concentration frees only about 1.3%, giving pH 2.87.

Where you’ll meet it

Calculating the pH of vinegar.
Comparing hydrochloric acid and acetic acid at the same concentration.
Reading why pH is on a logarithmic scale.

Questions people ask

How do you calculate the pH of a weak acid?: Find the free H+ concentration from the acid's Ka: [H+] is about the square root of Ka times the concentration, when little of the acid ionises. Then pH is minus the log base 10 of that.
Why does a weak acid have a higher pH than a strong acid at the same concentration?: Because only a small fraction of its molecules give up H+, so the concentration of free H+ is much lower, and pH counts free H+ only.

Where it’s taken apart

pH counts the free hydrogen ions, on a log scalepH is minus the base-10 log of the free H+ concentration. 0.1 mol per litre of HCl frees all of it, so pH 1. 0.1 mol per litre of acetic acid frees about 1.3%, [H+] = 0.00134, so pH 2.87. Each pH unit is a tenfold change, so the same amount of two acids can differ in acidity by tens of times.How can you tell whether a molecule is an acid or a base? →