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pKa, Ka, pKb and Kb Converter

Convert between an acid's Ka and pKa and its conjugate base's Kb and pKb, using Ka × Kb = Kw and pKa + pKb = 14 at 25 °C.

Formula

pKa=−log⁡10Ka;pKb=−log⁡10Kb\mathrm{p}K_{\mathrm{a}} = -\log_{10}K_{\mathrm{a}};\quad \mathrm{p}K_{\mathrm{b}} = -\log_{10}K_{\mathrm{b}}
Ka×Kb=Kw=1.0×10−14K_{\mathrm{a}} \times K_{\mathrm{b}} = K_{\mathrm{w}} = 1.0\times 10^{-14}
pKa+pKb=14.00\mathrm{p}K_{\mathrm{a}} + \mathrm{p}K_{\mathrm{b}} = 14.00
KaK_{\mathrm{a}}
acid dissociation constant
KbK_{\mathrm{b}}
base dissociation constant of the conjugate base

How it works

The strength of a weak acid is given by its dissociation constant Ka, or more conveniently by pKa, which is its negative logarithm. A smaller pKa is a stronger acid. The conjugate base has its own constant, Kb, and the two are linked through the ion product of water: Ka × Kb = Kw. A strong acid has a very weak conjugate base, and the reverse.

So a base is often described by the pKa of its conjugate acid instead of by its own pKb. Acetic acid (pKa 4.76) has acetate as its conjugate base, with pKb 9.24; ammonia has a pKb of 4.75, which corresponds to a pKa of 9.25 for the ammonium ion.

Worked example

Acetic acid with pKa 4.76.

  1. Ka = 10^−4.76 = 1.74 × 10⁻⁵.
  2. pKb of acetate = 14.00 − 4.76 = 9.24, so Kb = 5.75 × 10⁻¹⁰.

Ka = 1.74 × 10⁻⁵, pKb = 9.24, Kb = 5.75 × 10⁻¹⁰: a weak acid with a correspondingly very weak conjugate base.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • A conjugate acid-base pair in water at 25 °C.
  • Kw = 1.0 × 10⁻¹⁴. The value changes with temperature, and so does the relationship pKa + pKb = 14.

Common mistakes

  • Using the pKb of a base where its conjugate acid's pKa is needed in the Henderson-Hasselbalch equation.
  • Mixing up the direction of the scale: a larger pKa is a weaker acid.
  • Comparing pKa values measured at different temperatures or ionic strengths.

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