Acids, Bases & the pH Scale

You’ll be able to

Define acids and bases by the Arrhenius and Brønsted–Lowry models
Identify conjugate acid–base pairs in a proton-transfer reaction
Convert freely among [H⁺], [OH⁻], pH, and pOH using Kw

Two definitions, one idea: the proton

The Arrhenius model says an acid releases H⁺ in water and a base releases OH⁻. That works for simple cases but misses bases like ammonia that carry no OH⁻. The Brønsted–Lowry model is broader and more useful: an acid is a proton (H⁺) donor and a base is a proton acceptor. Every acid–base reaction is just an H⁺ handed from one species to another.

Conjugate acid–base pairs

When an acid donates its proton, what remains is a base — its conjugate base. When a base accepts a proton, the result is its conjugate acid. The two members of a pair differ by exactly one H⁺. In HF + H₂O ⇌ F⁻ + H₃O⁺, HF and F⁻ are one pair, and H₂O and H₃O⁺ are the other. Water plays both roles depending on its partner — it is amphoteric.

Water sets the scale: Kw

Water self-ionizes slightly: H₂O ⇌ H⁺ + OH⁻. At 25 °C the product of the ion concentrations is fixed at Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴. Because the product is constant, pushing [H⁺] up forces [OH⁻] down. In pure water the two are equal at 1.0 × 10⁻⁷ M, which is why neutral pH is 7.

Definition of pH

pH = −log[H⁺]

The minus sign makes pH positive for typical solutions. Each whole pH unit is a factor of 10 in [H⁺]: pH 3 is ten times more acidic than pH 4.

The pH–pOH relationship

pH + pOH = 14 (at 25 °C, since Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴)

pOH = −log[OH⁻]. Once you know any one of pH, pOH, [H⁺], or [OH⁻], you can reach the other three.

Worked example

A solution has [H⁺] = 1.0 × 10⁻³ M. Find its pH, pOH, and [OH⁻].

1.pH = −log[H⁺] = −log(1.0 × 10⁻³) = 3.00.
2.pOH = 14 − pH = 14 − 3.00 = 11.00.
3.[OH⁻] = Kw ÷ [H⁺] = (1.0 × 10⁻¹⁴) ÷ (1.0 × 10⁻³) = 1.0 × 10⁻¹¹ M.
4.Check: pOH = −log(1.0 × 10⁻¹¹) = 11.00 — consistent.

Answer: pH = 3.00, pOH = 11.00, [OH⁻] = 1.0 × 10⁻¹¹ M (acidic, as expected)

Watch out

Watch the sign of the log. For [H⁺] = 1.0 × 10⁻³, the exponent is −3, so pH = −(−3) = +3, not −3. A negative pH only appears for very concentrated strong acids where [H⁺] > 1 M.

Checkpoint

A solution has [H⁺] = 1.0 × 10⁻⁴ M. What is its pH?

Checkpoint

A solution has [OH⁻] = 1.0 × 10⁻² M. What is its pH?

On the exam

Identify conjugate pairs by counting protons: the acid always has exactly one more H⁺ than its conjugate base. HCO₃⁻ can be the conjugate base of H₂CO₃ or the conjugate acid of CO₃²⁻ — amphoteric species show up often on the exam.

Answer the 2 checkpoints as you read.