pH Calculator — Strong & Weak Acid, Strong & Weak Base

The pH scale measures the free hydrogen-ion activity in aqueous solution. This calculator handles strong acids, strong bases, weak acids (via Ka or pKa), and weak bases (via Kb or pKb) — with the full mass-balance quadratic that keeps very dilute solutions in the physical range.

Definitions

pH = −log₁₀[H⁺] and pOH = −log₁₀[OH⁻]. At 25 °C, K_w = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴, so pH + pOH = 14.00.

Strong acids and bases

For a strong acid at C ≳ 10⁻⁶ M, essentially every molecule ionises, so [H⁺] ≈ C and pH ≈ −log₁₀(C). Below that concentration, water’s own autoionisation matters and the full mass balance is needed: [H⁺]² − C·[H⁺] − K_w = 0. The positive root [H⁺] = (C + √(C² + 4K_w))/2 is what this calculator uses uniformly — no branch on concentration, no slip out of the physical range for 10⁻⁸ M HCl.

Weak acids — the ICE quadratic

For a weak acid HA with dissociation constant $K_a$, let x = [H⁺] = [A⁻]. Mass balance says [HA] = C − x, and $K_a = \dfrac{x^2}{C - x}$. Rearranging gives $x^2 + K_a x - K_a C = 0$, whose positive root is $x = \dfrac{-K_a + \sqrt{K_a^2 + 4 K_a C}}{2}$. Then pH = −log₁₀(x). Weak bases follow the same form in [OH⁻].

When the ICE approximation breaks

The exact quadratic above always solves correctly, but three regimes warrant care:

• Dissociation exceeds ~5 % — the acid is behaving like a strong acid at that concentration. The calculator warns; the answer is still right.
• $K_a \cdot C \lesssim 10 K_w$ — water autoionization contributes to $[\mathrm{H^+}]$. Uncommon for typical bench concentrations.
• Multiple ionizable protons (H₂SO₄, H₃PO₄, H₂CO₃) — treat each pKa separately, or handle as a coupled system. This calculator does the single-ionization case; use it iteratively for polyprotic acids at your discretion.

Reference pKa values (25 °C)

Values from Harris QCA 10e Table 9-2 and the CRC Handbook 97th ed. dissociation-constant tables.

Common mistakes

1. Using $-\log(C)$ for very dilute strong acids. Below $10^{-6}$ M, water’s autoionization contributes. The full quadratic keeps you in the physical range.
2. Confusing $K_a$ and $\mathrm{p}K_a$. $K_a$ is dimensionless (activity ratio); $\mathrm{p}K_a = -\log_{10} K_a$. This calculator accepts pKa/pKb — enter the value, not its negative log.
3. Applying pKa to a base. A weak base uses $K_b$ (or pKb). If you only have pKa of the conjugate acid, convert: $\mathrm{p}K_a + \mathrm{p}K_b = \mathrm{p}K_w = 14.00$ at 25 °C.
4. Ignoring temperature. $K_w$ roughly doubles every 15 °C. All values in this calculator are 25 °C — meaningful for cold-room work.