7.4 Calculating the Equilibrium Constant

Setting up the ICE table

To calculate K, use an ICE table (Initial, Change, Equilibrium) with concentrations or partial pressures. Start with known initial amounts, use stoichiometric coefficients to define changes (±x), then sum each column to get equilibrium values. Plug equilibrium values into the equilibrium expression to solve for K.

Using given equilibrium data

If you're given the equilibrium concentrations directly, just substitute them into the law of mass action: K = [products]^coeff / [reactants]^coeff. If only some concentrations are given, use stoichiometry and initial conditions to find the missing values before calculating K.

Working backward from K

Sometimes you know K and initial concentrations, and must solve for x (the change) using algebra, often requiring the quadratic formula or approximations when K is very small. Once x is found, calculate equilibrium concentrations. Always check that concentrations are non-negative and chemically reasonable.

Key terms

ICE table

A table organizing Initial, Change, and Equilibrium concentrations to solve equilibrium problems.

Law of mass action

K = [products]^coefficients / [reactants]^coefficients at equilibrium.

Change row (ICE table)

Determined by stoichiometric coefficients, expressed as multiples of x (e.g., -x, +2x).

Solving for x

Often requires algebra, factoring, or the quadratic formula when K and initial concentrations are known.

Checking equilibrium answers

Verify all equilibrium concentrations are positive and chemically reasonable before finalizing K or concentration values.

Try an AP-style question

At equilibrium [H₂] = 0.10 M, [I₂] = 0.10 M, and [HI] = 0.80 M. What is K for H₂ + I₂ ⇌ 2HI?

1. 8
2. 64
3. 0.016
4. 80