Chemistry · General chemistry II · Concept
pH of strong and weak acids and bases
pH measures the hydronium-ion concentration on a logarithmic scale: pH = −log[H₃O⁺]. A strong acid ionizes completely, so its concentration is [H₃O⁺]. A weak acid ionizes only partly, so [H₃O⁺] comes from Ka and an ICE table. At 25 °C water’s ion product, Kw = 1.0 × 10⁻¹⁴, links acids and bases, and pH + pOH = 14.00.
pH and pOH
pH = −log[H₃O⁺] and pOH = −log[OH⁻]. Each pH unit is a factor of ten in [H₃O⁺]: a solution at pH 3 has ten times the [H₃O⁺] of one at pH 4. Only the digits after the decimal point of a pH are significant, so [H₃O⁺] = 2.5 × 10⁻³ M, with two significant figures, gives pH 2.60, with two decimal places.
Water links acids and bases
Water ionizes slightly, 2H₂O ⇌ H₃O⁺ + OH⁻. At 25 °C the product of the ion concentrations is Kw = 1.0 × 10⁻¹⁴, so pH + pOH = 14.00, and a neutral solution has pH 7.00. At other temperatures Kw, and the neutral pH, are different.
Strong acids and bases
Strong acids such as HCl and HNO₃ ionize completely, so [H₃O⁺] equals the acid’s concentration. A strong base such as NaOH gives [OH⁻] equal to its concentration; Ca(OH)₂ gives twice its concentration.
Weak acids and Ka
A weak acid HA reaches an equilibrium with its ions, and its small Ka means most of it stays as HA. In an ICE table, let x = [H₃O⁺] = [A⁻], so [HA] = C − x, where C is the acid’s starting concentration.
The small-x approximation
When Ka is small next to C, x is tiny compared with C, so C − x ≈ C and x ≈ √(Ka·C). Check afterward: if x is under 5% of C, the approximation holds; if not, solve the quadratic.
Weak bases and conjugate pairs
A weak base B takes a proton from water, B + H₂O ⇌ BH⁺ + OH⁻, with constant Kb, and the same method gives [OH⁻]. For a conjugate acid–base pair, Ka × Kb = Kw, so the conjugate base of a weak acid is a weak base: acetate, from acetic acid, makes water slightly basic.
Common mistakes
- Taking −log of a weak acid’s concentration: only a small fraction ionizes, so [H₃O⁺] is much smaller than C.
- Using pH + pOH = 14.00 away from 25 °C, where Kw is different.
- Reporting a pH with the wrong number of decimal places: they match the significant figures of [H₃O⁺].
- Skipping the 5% check after the small-x approximation.
- Forgetting that Ca(OH)₂ releases two hydroxide ions per formula unit.
Key terms
- pH
- pH = −log[H₃O⁺], a measure of acidity. At 25 °C, pH 7 is neutral, lower is acidic and higher is basic; each unit is a tenfold change in [H₃O⁺].
- pOH
- pOH = −log[OH⁻]. At 25 °C, pH + pOH = 14; the sum changes with temperature because Kw does.
- Water ion product
- Kw = [H₃O⁺][OH⁻], the equilibrium constant for water’s self-ionization: 1.0 × 10⁻¹⁴ at 25 °C. It changes with temperature, so neutral pH is exactly 7 only at 25 °C.
- Acid dissociation constant
- Ka, the equilibrium constant for an acid giving a proton to water: HA + H₂O ⇌ H₃O⁺ + A⁻. A larger Ka means a stronger acid.
- Base dissociation constant
- Kb, the equilibrium constant for a base taking a proton from water: B + H₂O ⇌ BH⁺ + OH⁻. For a conjugate pair, Ka × Kb = Kw.
- Weak acid or base
- An acid or base that reacts only partly with water, so most of it stays in its original form at equilibrium, such as acetic acid or ammonia. Its pH depends on both its K and its concentration.
- Percent ionization
- The share of a weak acid that ionizes: [H₃O⁺] at equilibrium ÷ starting acid concentration × 100 (and likewise for a weak base). It rises as the solution gets more dilute.
- Conjugate acid-base pair
- Two species differing by one proton. An acid loses that proton to form its conjugate base; the base gains it to reform the acid.
Work through an example
Calculate the pH, [OH⁻] and pOH of 0.0025 M hydrochloric acid at 25 °C.
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