pH from Hydrogen Ion Concentration

Quick answer: For dilute aqueous solutions in school calculations, pH ≈ −log₁₀[H⁺], using the numerical concentration in mol/L. More precisely pH is defined using hydrogen-ion activity. At 25°C, pH 7 is neutral; below 7 is acidic and above 7 basic.

Worked example

Find pH when [H⁺] = 1.0×10⁻³ mol/L.

1. log₁₀(10⁻³) = −3.
2. Apply the leading minus sign: pH = −(−3) = 3.
3. At 25°C this is acidic.
4. If [H⁺] becomes 10⁻⁴ mol/L, the pH becomes 4: lower hydrogen-ion concentration means higher pH.

Check the result

Reverse the calculation: [H⁺] ≈ 10⁻pH = 10⁻³ mol/L for pH 3.

Common mistake to avoid

pH has no concentration unit. Neutral pH depends on temperature; the familiar neutral value 7 assumes about 25°C. A tenfold concentration change changes pH by one, not ten.

Try it yourself

1. Find pH for [H⁺] = 10⁻⁵ mol/L. 2. Compare [H⁺] at pH 2 and pH 4.

Answers and reasoning

1. pH = 5. 2. 10⁻²/10⁻⁴ = 100: the pH-2 solution has 100 times the hydrogen-ion concentration under the approximation.

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