AP Chemistry: ICE Tables for Equilibrium Problems (with 2 worked examples)
Equilibrium problems are the single highest point-value section of the AP Chemistry exam, and ICE tables (Initial, Change, Equilibrium) are the standard tool for them. Most students lose points by setting up the table sloppily — not by getting the math wrong. Here’s the discipline Tae teaches his AP Chem students, plus two worked examples.
The ICE table format
Every equilibrium problem gets a 3-row table for each species in the reaction:
- I — Initial concentration (or pressure) of each species
- C — Change during the reaction, written as +x or −x based on stoichiometry
- E — Equilibrium concentration = Initial + Change
Then you plug the Equilibrium row into the Kc or Kp expression and solve for x.
Example 1: simple equilibrium
For the reaction H2(g) + I2(g) ⇄ 2 HI(g), Kc = 50 at 700 K. If you start with 0.20 M H2 and 0.20 M I2, what are the equilibrium concentrations?
Setup:
| H2 | I2 | HI | |
|---|---|---|---|
| I | 0.20 | 0.20 | 0 |
| C | −x | −x | +2x |
| E | 0.20−x | 0.20−x | 2x |
Equation: Kc = [HI]² / ([H2][I2]) = (2x)² / (0.20−x)² = 50
Taking the square root of both sides: 2x / (0.20−x) = √50 ≈ 7.07. Solve: x ≈ 0.156. So [H2] = [I2] = 0.044 M and [HI] = 0.31 M.
Example 2: when you can use the small-x approximation
If Kc is very small (less than about 10−4), and the initial concentrations are large, you can assume x is negligible compared to the initial values. That simplifies the math dramatically: instead of solving a quadratic, you treat (initial − x) as just the initial.
Rule of thumb: the approximation is valid if the initial concentration is at least 500× larger than the expected x. If after solving x is more than 5% of the initial, redo without the approximation.
Common mistakes that cost AP exam points
- Wrong sign on the Change row. Reactants decrease (−x), products increase (+x). Reversing them is the #1 setup error.
- Missing stoichiometric coefficient. If the balanced equation has 2 HI, the change is +2x, not +x.
- Using mass-action expression with the Initial row instead of Equilibrium. Kc is defined at equilibrium — only the E row goes into the expression.
- Forgetting that pure solids and liquids don't appear in K.
- Reporting x as the answer when the question asks for [species]. Plug x back into the E row.
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