ICE Table Equilibrium Calculator

What Is an ICE Table?

An ICE table is a systematic method for solving chemical equilibrium problems. ICE stands for Initial, Change, Equilibrium — the three rows of the table.

Weak Acid Dissociation: HA ⇌ H⁺ + A⁻

The equilibrium expression is: Ka = [H⁺][A⁻] / [HA] = x² / (Cₐ − x)

Rearranging: x² + Ka·x − Ka·Cₐ = 0

Solving the quadratic formula: x = (−Ka + √(Ka² + 4·Ka·Cₐ)) / 2

Then: pH = −log₁₀(x)

Weak Base: B + H₂O ⇌ BH⁺ + OH⁻

The same method applies using Kb. x = [OH⁻], then pOH = −log₁₀(x), then pH = 14 − pOH.

Percent Ionization

% Ionization = (x / Cₐ) × 100%

Weaker acids have lower Ka and lower percent ionization. Diluting a weak acid actually increases percent ionization (Le Chatelier’s principle).

Common Ka Values

5% Approximation Rule

If percent ionization is less than 5%, you can simplify Cₐ − x ≈ Cₐ. This gives x ≈ √(Ka × Cₐ) — a much faster calculation. This calculator always uses the exact quadratic formula for accuracy.

Worked example

Acetic acid at 0.1 mol/L with Ka = 1.8 × 10⁻⁵. The ICE table gives Ka = x²/(C − x), so:

x = (−Ka + √(Ka² + 4·Ka·C)) / 2 = 1.33 × 10⁻³

pH = −log₁₀(1.33 × 10⁻³) = 2.88, and the acid is 1.33% ionized.

Why this solves the quadratic rather than approximating

Most textbooks tell you to assume x is small compared with C, which turns Ka = x²/(C − x) into the far easier x ≈ √(Ka·C). For the example above that shortcut gives 1.342 × 10⁻³, a difference of well under 1%, and the resulting pH is identical to two decimal places.

The rule of thumb is that the approximation is safe when x comes out below 5% of C. It stops being safe in two situations: a relatively strong weak acid (Ka above about 10⁻³), and a very dilute solution. Take chloroacetic acid, Ka = 1.4 × 10⁻³, at 0.01 mol/L. The approximation gives x = 3.74 × 10⁻³, which is 37% of the starting concentration and plainly violates its own assumption. The quadratic gives 3.09 × 10⁻³, and the pH differs by 0.08 units.

Since solving the quadratic costs nothing on a computer, this calculator always does it. You get the right answer in both regimes without having to check first whether you were allowed to take the shortcut.

One limitation remains: the calculation ignores water’s own autoionization. For an extremely weak or extremely dilute acid the true pH cannot exceed 7, but this model will happily report a higher figure. If your result creeps toward neutral, the acid is too feeble for the simple treatment.