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Calculating the equilibrium constant

An ICE table is the bookkeeping that turns starting amounts and one measurement into K. The catch: K is computed from the bottom row, and the changes in the middle row follow the stoichiometry.

§1

Initial, Change, Equilibrium.

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An ICE table organizes an equilibrium calculation into three rows: Initial concentrations, the Change as the reaction proceeds, and the Equilibrium concentrations.

The change row follows the stoichiometry: reactants change by −(coefficient × x) and products by +(coefficient × x), so the changes are in the coefficient ratio and carry signs. The equilibrium row is initial plus change.

K is then computed from the equilibrium row only — never from the initial concentrations. Fill the table, find the equilibrium concentrations, and substitute them into the K expression.

UNIT 7 TOPIC 7.4 • CALCULATING THE EQUILIBRIUM CONSTANT ICE TABLE BUILDER EXAMPLE: Kc FROM CONCENTRATIONS N₂O₄(g) ⇌ 2 NO₂(g) [N₂O₄] [NO₂] Initial 0.100 0 Change −x +2x Equil. 0.100 − x 2x Kc = [NO₂]² / [N₂O₄] Kp FOR GASES Kp uses partial pressures Kp = (PNO₂)² / PN₂O₄ Use Kc for molarity and Kp for gas partial pressures. Do not mix units inside one expression. RULES WHILE BUILDING ICE Coefficients become exponents in K. Coefficients also scale changes in the ICE row. Pure solids and liquids are omitted. NO COLUMN COEFFICIENTS Column header: [NO₂] NOT: [2 NO₂] The coefficient belongs in the balanced equation and in the change row. It tracks the concentration of one species. CED ANCHOR An ICE table tracks initial, change, and equilibrium amounts. K expressions use equilibrium amounts only, with coefficients as exponents. AP Chemistry · Unit 7 · Equilibrium
Fig. 7.4.1 An ICE table tracks Initial, Change, and Equilibrium concentrations. The changes follow the stoichiometry (in the coefficient ratio, with signs); the equilibrium row is initial plus change. K is calculated from the equilibrium row.
§2

Filling the table for K.

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Build the equilibrium row, then compute K.

  1. Write the initial concentrations. The starting values before any reaction.
  2. Express the change with signs. Reactants −(coefficient·x), products +(coefficient·x).
  3. Add to get equilibrium. Equilibrium = initial + change for each species.
  4. Compute K from the equilibrium row. Substitute the equilibrium concentrations into the K expression.
§3

The pieces you'll meet.

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Three rows, one target: the equilibrium row.

ICE
ICE table
Initial, Change, Equilibrium rows.
initial
Initial
Starting concentrations.
change
Change
In the coefficient ratio, with signs.
equilibrium
Equilibrium
Initial plus change; used to compute K.
x
x
The variable tracking the extent of change.
from eq row
K source
K comes from the equilibrium row, not the initial.
§4

Worked example: K from an ICE table.

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Reaction. N₂O₄(g) ⇌ 2NO₂(g). Initial: [N₂O₄] = 0.10 M, [NO₂] = 0. At equilibrium, [NO₂] is measured as 0.040 M.

Change. NO₂ increased by 0.040, and by stoichiometry (2:1) N₂O₄ decreased by 0.020.

Equilibrium row. [N₂O₄] = 0.10 − 0.020 = 0.080 M; [NO₂] = 0.040 M.

Compute K. K = [NO₂]² / [N₂O₄] = (0.040)² / 0.080 = 0.020, using the equilibrium row — not the initial 0.10.

§5

Mistakes that cost real points.

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Pitfall · 01

"Calculate K from the initial concentrations."

K must be computed from the equilibrium concentrations (the E row), not the initial ones. Using the initial row gives the reaction quotient at the start (Q), not the equilibrium constant.

Fix. Always substitute the equilibrium row into the K expression, never the initial row.

Pitfall · 02

"The change for every species is the same value."

Changes follow the stoichiometry: they are in the ratio of the coefficients and carry signs (reactants negative, products positive). In N₂O₄ ⇌ 2NO₂, NO₂ changes twice as much as N₂O₄. Using one identical change for all species is wrong.

Fix. Scale each change by its coefficient and give reactants a minus, products a plus.

Pitfall · 03

"x is the final answer."

x is the extent of change, not the equilibrium concentration itself. You must substitute x back into 'initial + change' to get each equilibrium concentration before computing K. Stopping at x skips the last step.

Fix. Substitute x into the equilibrium row to get the actual concentrations, then compute K.

§6

Skill Check.

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Ten scenarios. Pick the chips that match your answer, then check. A scenario marks complete the first time every part is right. Progress saves on this device.

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