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Chemistry · General chemistry II · Worked example

Find the pH of a weak base

Find the pH of 0.100 M sodium acetate, NaC₂H₃O₂, at 25 °C. Acetic acid has Ka = 1.8 × 10⁻⁵.

Identify the base

Sodium acetate dissolves completely into Na⁺, a spectator ion, and acetate, the conjugate base of acetic acid. Acetate takes a proton from water: C₂H₃O₂⁻ + H₂O ⇌ HC₂H₃O₂ + OH⁻.

Find Kb from Ka

For a conjugate pair, Ka × Kb = Kw.

Kb=KwKa=1.0×10−141.8×10−5=5.6×10−10

Solve for [OH⁻]

With x = [OH⁻] and the small-x approximation, x² = (5.6 × 10⁻¹⁰)(0.100). Keep a guard digit: x = 7.48 × 10⁻⁶ M, far under 5% of 0.100.

x=(5.6×10−10)⁢(0.100)=7.48×10−6
x=(5.6×10−10)⁢(0.100)=7.48×10−6

Convert to pH

pOH = −log(7.48 × 10⁻⁶) = 5.13, and pH = 14.00 − 5.13.

pH=14.00−5.13=8.87

Result

pH = 8.87: sodium acetate solution is slightly basic.

Your turn

Find the pH of 0.500 M sodium acetate.

Show the answer and explanation

pH = 9.22.

[OH⁻] = √((5.6 × 10⁻¹⁰)(0.500)) = 1.67 × 10⁻⁵ M, so pOH = 4.78 and pH = 14.00 − 4.78 = 9.22.

14.00−4.78=9.22

Keep exploring

In Acid, base & pH, raise the concentration tenfold, to 1.00 M. The pH rises by only half a unit, to 9.37, because [OH⁻] grows with the square root of the concentration.

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