The pH scale — measuring acidity

By the end of this lesson

By the end you can state that water has pH 7, acidic solutions have pH < 7, alkaline solutions have pH > 7, and calculate pH from [H⁺] using pH = –log₁₀[H⁺].

Why we need pH

[H⁺] in solutions ranges from ~10 mol dm⁻³ (concentrated acid) down to 10⁻¹⁴ mol dm⁻³ (strong base). That's 15 orders of magnitude — impossible to compare directly.

Sørensen (1909) invented pH: $\text{pH} = -\log_{10}[\text{H}^+]$

The "p" stands for potenz (German for power/exponent). It compresses the huge range into a manageable 0–14 scale (usually).

Definition

$\text{pH} = -\log_{10}[\text{H}^+]$ where [H⁺] is the hydrogen ion concentration in mol dm⁻³.

Logarithmic = each step is 10×

pH	[H⁺] (mol dm⁻³)	Relative acidity
0	1	10⁷ × more acidic than pH 7
1	0.1	10⁶ ×
2	0.01	10⁵ ×
3	0.001	10⁴ ×
4	10⁻⁴	10³ ×
5	10⁻⁵	10² ×
6	10⁻⁶	10 ×
7	10⁻⁷	neutral
8	10⁻⁸	10 × more alkaline
9	10⁻⁹	10² ×
10	10⁻¹⁰	10³ ×
11	10⁻¹¹	10⁴ ×
12	10⁻¹²	10⁵ ×
13	10⁻¹³	10⁶ ×
14	10⁻¹⁴	10⁷ ×

A change of 1 pH unit = 10× change in [H⁺]. A change of 2 units = 100×. This is why "small" pH changes matter enormously in biology.

Worked example: Calculating pH from [H⁺]

Calculate the pH of a solution with [H⁺] = 2.5 × 10⁻³ mol dm⁻³.

Have a go first?

Calculate pH

CalculateQuestion 1 · Recall

CalculateQuestion 2 · Apply

Answer the 2 questions above to continue.