pH of Mixtures and Dilutions

Diluting Strong Acids

When you dilute a strong acid, you increase the volume of solution without changing the number of moles of acid. Since pH depends on [H⁺], dilution changes the pH.

Worked Example: 50.0 cm³ of 0.10 mol dm⁻³ HCl is diluted to 500.0 cm³. Calculate the new pH.

Moles of HCl = 0.10 × (50.0/1000) = 5.00 × 10⁻³ mol

New concentration = 5.00 × 10⁻³ / (500.0/1000) = 0.010 mol dm⁻³

Since HCl fully dissociates, [H⁺] = 0.010 mol dm⁻³.

pH = -log₁₀(0.010) = 2.00

The original pH was -log₁₀(0.10) = 1.00, so the tenfold dilution increased the pH by exactly 1 unit. This is always the case for strong acids: a tenfold dilution raises pH by 1.

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Diluting Strong Bases

The same principle applies to bases, but you work through Kw.

Worked Example: 25.0 cm³ of 0.20 mol dm⁻³ NaOH is diluted to 250.0 cm³. Calculate the new pH at 25°C.

Moles of NaOH = 0.20 × (25.0/1000) = 5.00 × 10⁻³ mol

New [NaOH] = 5.00 × 10⁻³ / (250.0/1000) = 0.020 mol dm⁻³

[OH⁻] = 0.020 mol dm⁻³ (full dissociation)