ICE Table & Equilibrium Solver
Set up the ICE table and solve it exactly. Enter a weak acid (Ka), a weak base (Kb), or a slightly-soluble salt (Ksp) and get the populated Initial–Change–Equilibrium table, the quadratic solved without the small-x shortcut, and the pH or molar solubility.
How to use this tool
An ICE table tracks the Initial, Change and Equilibrium concentrations of every species. Pick the equilibrium type, enter the constant and the starting concentration, and the table fills in and solves for x.
What to enter
- Weak acid: the acid's pKa (Ka = 10⁻ᵖᴷᵃ) and its initial molarity C₀. Solves HA ⇌ H⁺ + A⁻ for [H⁺] and pH.
- Weak base: the base's pKb and C₀. Solves B + H₂O ⇌ BH⁺ + OH⁻ for [OH⁻], then pH via Kw.
- Solubility: the Ksp (scientific notation OK, e.g. 1.8e-10) and the salt's dissolution stoichiometry. Solves for the molar solubility s.
Reading the result
The headline is the pH (acid/base) or the molar solubility s (Ksp). Below it, x is the equilibrium change solved from the quadratic, and the ICE table shows where every species ends up. The % ionization tells you whether the common "small-x" approximation was safe.
Worked example
Acetic acid, pKa 4.76, C₀ 0.1 M → x = [H⁺] ≈ 1.33×10⁻³ M, pH ≈ 2.87, about 1.3 % ionized.
Result
x is the equilibrium extent solved from the full quadratic — no small-x assumption. The ICE table shows the concentration of every species at equilibrium.
Methodology
Weak acid / weak base
For HA ⇌ H⁺ + A⁻, the equilibrium constant is Ka = x² / (C₀ − x) where x = [H⁺]. This is solved as the full quadratic x² + Ka·x − Ka·C₀ = 0 (positive root), so the answer is exact rather than relying on the common x ≈ √(Ka·C₀) shortcut — the tool flags when that shortcut would have introduced more than 5 % error. Weak bases use the analogous Kb = x² / (C₀ − x) with x = [OH⁻], and pH = 14 − pOH at 25 °C.
Solubility product
For a salt AₘBₙ ⇌ m A + n B, the molar solubility s satisfies Ksp = mᵐ · nⁿ · s^(m+n), giving s = (Ksp / (mᵐ·nⁿ))^(1/(m+n)). The ion concentrations are [A] = m·s and [B] = n·s.
Sources
- Atkins, P. & de Paula, J. Physical Chemistry — chemical equilibrium.
- NIST / CRC reference Ka, Kb and Ksp values.
Known limits
- Single-equilibrium model: it ignores the water autoionization contribution, so for very dilute or very weak systems (pH near 7) the result drifts.
- Activity coefficients are taken as 1 (ideal); at high ionic strength use activities.
- Ksp mode assumes no common-ion effect and no competing complexation.