About the Ka & pKa Calculator
This Ka and pKa calculator converts any one of the four acid–base constants — Ka, pKa, Kb or pKb — into the other three, using pKa = −log₁₀ Ka and pKa + pKb = 14 for a conjugate acid–base pair at 25 °C. Add the solution concentration and it also solves for the pH, [H⁺] or [OH⁻], and percent ionization.
It is designed for chemistry students working weak-acid and weak-base problems, for lab work where you need to know how ionized a buffer component is, and for quick lookups when a data table gives Ka but your problem uses pKa. Enter Ka or pKa to treat the solution as a weak acid; enter Kb or pKb to treat it as a weak base such as ammonia.
The pH is solved exactly from the charge balance rather than with the “x is small” shortcut, so it stays accurate for moderately strong weak acids. Water’s own ionization is included, so very dilute or extremely weak solutions correctly approach pH 7 instead of giving impossible values. Activities are taken as concentrations (ideal behaviour) at 25 °C.
How to use the ka & pka calculator
- 1Choose which constant you know: Ka, pKa, Kb or pKb.
- 2Enter its value (Ka/Kb accept scientific notation such as 1.8e-5).
- 3Enter the solution concentration if you want the pH.
- 4Read the converted constants, pH and percent ionization.
Formula and method
pKa is the negative base-10 logarithm of the acid dissociation constant, so a lower pKa means a stronger acid; each unit lower is ten times stronger. For a conjugate acid–base pair Ka × Kb = Kw = 1.0 × 10⁻¹⁴ at 25 °C, which gives pKa + pKb = 14.
For a weak acid HA at initial concentration C, the equilibrium Ka = x²/(C − x) rearranges to the quadratic x² + Ka·x − Ka·C = 0, whose positive root is [H⁺]. The calculator solves the slightly fuller charge balance [H⁺] = Ka·C/(Ka + [H⁺]) + Kw/[H⁺] numerically, which reduces to that quadratic whenever water’s contribution is negligible but stays correct for very dilute solutions. The same equations with Kb give [OH⁻] for a weak base, and pH = 14 − pOH. Percent ionization is the fraction present as the ionized form, Ka/(Ka + [H⁺]) × 100.
- Ka, Kb
- Acid and base dissociation constants
- pKa, pKb
- Negative base-10 logarithms of Ka and Kb
- C
- Initial concentration of the weak acid or base (mol/L)
- x
- [H⁺] for an acid or [OH⁻] for a base at equilibrium
Worked examples
Acetic acid, pKa 4.76, 0.10 M
Ka = 10⁻⁴·⁷⁶ = 1.738 × 10⁻⁵ and the conjugate base acetate has pKb = 14 − 4.76 = 9.24. Solving x² + Ka·x − Ka(0.10) = 0 gives [H⁺] = 1.31 × 10⁻³ M, pH ≈ 2.88, with 1.31% of the acid ionized.
Hydrofluoric acid, Ka 6.8 × 10⁻⁴, 0.050 M
pKa = −log(6.8 × 10⁻⁴) = 3.167. HF is 11% ionized at 0.05 M, so the quadratic matters: [H⁺] = 5.50 × 10⁻³ M and pH ≈ 2.26 (the shortcut would give 2.23).
Ammonia, Kb 1.8 × 10⁻⁵, 0.20 M
pKb = −log(1.8 × 10⁻⁵) = 4.745, so the ammonium ion has pKa = 9.255. For 0.20 M NH₃, [OH⁻] = 1.89 × 10⁻³ M, pOH = 2.724 and pH ≈ 11.28.
Frequently asked questions
How do you convert Ka to pKa?+
Take the negative base-10 logarithm: pKa = −log₁₀(Ka). For example Ka = 1.8 × 10⁻⁵ gives pKa = 4.74. To go back, Ka = 10^(−pKa).
What is the relationship between pKa and pKb?+
For a conjugate acid–base pair in water at 25 °C, Ka × Kb = Kw = 1.0 × 10⁻¹⁴, so pKa + pKb = 14. Ammonium (pKa 9.25) and ammonia (pKb 4.75) are an example.
Does a lower pKa mean a stronger acid?+
Yes. A lower pKa means a larger Ka and more dissociation. Each one-unit drop in pKa corresponds to a tenfold increase in acid strength; acids with pKa below about 0 are considered strong.
How do you calculate the pH of a weak acid?+
Set up Ka = x²/(C − x), where x is [H⁺], and solve the quadratic x = (−Ka + √(Ka² + 4KaC))/2. Then pH = −log₁₀ x. If ionization is under about 5%, the shortcut x ≈ √(Ka·C) gives nearly the same answer.
What does pKa tell you about buffers?+
A weak acid buffers best within about ±1 pH unit of its pKa, where both the acid and its conjugate base are present in significant amounts. At pH = pKa they are present in equal concentrations.
Is pKa + pKb = 14 true at every temperature?+
No. The 14 comes from Kw at 25 °C. Kw increases with temperature (pKw is about 13.26 at 50 °C), so the sum changes. This calculator uses the standard 25 °C value.