7.7 Calculating Equilibrium Concentrations

Setting up the ICE table

To find equilibrium concentrations, use an ICE table (Initial, Change, Equilibrium). Write initial concentrations, define the change using x based on stoichiometric coefficients, then express equilibrium amounts. Substitute equilibrium expressions into the K expression and solve for x. This method organizes reversible reaction data systematically.

Simplifying assumptions

When K is very small compared to initial concentrations, you can often assume x is negligible (5% rule) to avoid solving a quadratic. Check validity by calculating percent change: if x is less than 5% of the initial concentration, the approximation is valid; otherwise, solve the quadratic equation exactly.

Using the quadratic formula

When approximations fail, expand the K expression into a quadratic equation in x and solve using the quadratic formula. Always discard physically impossible roots (like negative concentrations). Then plug x back into equilibrium expressions to find final concentrations, and verify by substituting into the K expression.

Key terms

ICE table

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

5% rule

A guideline stating that the simplifying assumption (x is negligible) is valid if x is less than 5% of the initial concentration.

When to solve a quadratic in equilibrium problems

When the 5% approximation fails, requiring the full quadratic equation to accurately solve for x.

Discarding extraneous roots

When solving a quadratic for x, reject roots that produce negative or physically impossible concentrations.

Verifying equilibrium concentrations

Substitute calculated concentrations back into the K expression to confirm they yield the correct equilibrium constant.

Try an AP-style question

A ⇌ B with K = 4. Starting with [A] = 1.0 M and no B, what is [B] at equilibrium?

1. 4.0 M
2. 0.25 M
3. 0.50 M
4. 0.80 M