ICE Tables for Equilibrium (Step by Step)

ICE tables are the single most repeated calculation in the equilibrium unit, and once the setup is automatic, the actual algebra is usually the easy part.

Setting up the table

ICE stands for Initial, Change, and Equilibrium, the three rows of the table. Each column is one species in the equilibrium expression. The Initial row is the starting concentration of each species. The Change row uses a variable, usually x, scaled by that species' coefficient in the balanced equation, with a negative sign for anything being consumed and a positive sign for anything being produced. The Equilibrium row is simply Initial plus Change for each column.

Worked example

Problem

A 0.100 M solution of a weak acid HA has Ka = 1.8 × 10⁻⁵. Find the equilibrium [H+].

Set up the ICE table for HA ⇌ H+ + A−

Initial: [HA] = 0.100, [H+] = 0, [A−] = 0

Change: [HA] = −x, [H+] = +x, [A−] = +x

Equilibrium: [HA] = 0.100 − x, [H+] = x, [A−] = x

Apply the small x approximation

Ka = x² / (0.100 − x) ≈ x² / 0.100, since x is expected to be small relative to 0.100

Solve

x² = (1.8 × 10⁻⁵)(0.100) = 1.8 × 10⁻⁶ → x = 1.3 × 10⁻³ M = [H+]

Check the approximation

1.3 × 10⁻³ ÷ 0.100 = 1.3%, well under the usual 5% threshold, so the approximation was valid

Where students actually lose points here

Forgetting to scale the change by the coefficient

If a species has a coefficient of 2 in the balanced equation, its change is 2x, not x. Skipping this scaling is a common setup error before any math even happens.

Using the small x approximation without checking it

The approximation is only valid when x turns out to be small compared to the initial concentration, usually under about 5%. Skipping the check can mean reporting an answer that isn't actually accurate enough.

Sign errors on the change row

Reactants decrease (negative x) and products increase (positive x). Mixing up which species are reactants versus products in a less familiar reaction leads to the wrong sign.

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The calculation underneath the whole unit

Once ICE tables are automatic, equilibrium constant problems, buffer problems, and solubility problems all start to feel like variations on the same theme.

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Common questions

What does ICE stand for in an ICE table?

Initial, Change, and Equilibrium, the three rows used to track how the concentration of each species in a reaction changes as it moves toward equilibrium.

When is it valid to use the small x approximation?

When the calculated x turns out to be small relative to the initial concentration it was subtracted from or added to, commonly under about 5%. If it's larger than that, the quadratic formula should be used instead for an accurate answer.

Why does the change row use the equation's coefficients?

Because the amounts of each species change in the same ratio the balanced equation describes. A species with a coefficient of 2 changes twice as fast as one with a coefficient of 1.