14.9The pH and pOH Scales

The idea

• Calculate pH from [H₃O⁺] and the reverse.
• Use pOH and the relationship to 14.

pH = −log[H₃O⁺], where the concentration is in mol/L. pOH = −log[OH⁻]. At 25 °C, pH + pOH = 14.00. Neutral is 7.00, acidic is below 7, basic is above 7. Because of the negative log, a smaller pH is a more acidic solution, and a change from pH 3 to pH 1 is a hundredfold rise in [H₃O⁺], not a rise of “2 units” in a linear sense. The number of decimal places in the pH matches the number of significant figures in the concentration: 1.0 × 10⁻³ has two significant figures, so pH 3.00.

To go backward, [H₃O⁺] = 10^(−pH). For a strong acid, [H₃O⁺] equals the acid molarity (watch sulfuric acid’s two protons as a special case often simplified in intro problems). For a strong base, find [OH⁻] first, then pOH, then pH. Do not take −log of a hydroxide concentration and call it pH.

Worked path

Find the pH of 0.020 M HCl, a strong acid, and of 0.020 M NaOH.

1. Observe

   HCl: [H₃O⁺] = 0.020. NaOH: [OH⁻] = 0.020.

Check yourself