Conjugate Acid-Base Calculator Formula

Understand the math behind the conjugate acid-base calculator. Each variable explained with a worked example.

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Formulas Used

Conjugate K Value

k_conjugate = kw / k_known

pK of Known

pk_known = -log10(k_known)

pK of Conjugate

pk_conjugate = -log10(kw / k_known)

Variables

VariableDescriptionDefault
k_knownKnown K Value (Ka or Kb)0.000018
kwKw (Ion Product of Water)1e-14

How It Works

Conjugate Acid-Base Relationship

Formula

Ka × Kb = Kw

Therefore:

  • Ka = Kw / Kb (find Ka of conjugate acid from Kb of base)
  • Kb = Kw / Ka (find Kb of conjugate base from Ka of acid)

    • At 25°C, Kw = 1.0 × 10⁻¹⁴. This means pKa + pKb = 14.

    Worked Example

    Ammonia has Kb = 1.8 × 10⁻⁵. Find Ka of its conjugate acid NH₄⁺.

    k_known = 0.000018kw = 1e-14
    1. 01Ka = Kw / Kb
    2. 02Ka = 1.0 × 10⁻¹⁴ / 1.8 × 10⁻⁵
    3. 03Ka = 5.56 × 10⁻¹⁰
    4. 04pKa = -log₁₀(5.56 × 10⁻¹⁰) = 9.26

    Frequently Asked Questions

    What is a conjugate acid-base pair?

    A conjugate pair differs by one proton (H⁺). When a base accepts a proton, it forms its conjugate acid. When an acid donates a proton, it forms its conjugate base.

    Why does Ka × Kb = Kw?

    The dissociation of the acid and the protonation of the base combine to give the autoionization of water: H₂O ⇌ H⁺ + OH⁻.

    Does Kw change with temperature?

    Yes. Kw = 1.0 × 10⁻¹⁴ at 25°C but increases with temperature (e.g., 5.5 × 10⁻¹³ at 100°C).

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