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General chemistry · Equilibrium

ICE table practice problems

An ICE table tracks Initial concentrations, the Change as the reaction shifts by x, and the Equilibrium amounts. Put the equilibrium row into the K expression and solve for x.

How to set one up

  1. Write the balanced equation and the K expression. Leave out pure solids and liquids.
  2. Fill the I row with starting molarities.
  3. Fill the C row with ±x times each coefficient. Reactants lose and products gain if the reaction moves forward.
  4. Add rows to get E, substitute into K, and solve.
  5. Check your answer: no concentration can be negative.

If you are not sure which way the reaction shifts, compare Q with K. If Q < K it moves forward; if Q > K it moves in reverse.

Worked example 1: a perfect square

H2 + I2 ⇌ 2 HI at a temperature where Kc = 49.0. Start with 1.00 M H2 and 1.00 M I2.

ICE table for H2 + I2
RowH2I2HI
I1.001.000
C−x−x+2x
E1.00 − x1.00 − x2x

(2x)2 / (1.00 − x)2 = 49.0. Take the square root: 2x / (1.00 − x) = 7.00, so x = 0.778.

At equilibrium: [HI] = 1.56 M, [H2] = [I2] = 0.222 M. Check: 1.5562 ÷ 0.2222 ≈ 49.

Worked example 2: when the shortcut fails

PCl5 ⇌ PCl3 + Cl2, Kc = 0.040, starting with 0.50 M PCl5. Then x2 / (0.50 − x) = 0.040.

If you drop the x in the denominator you get x = 0.14, which is 28% of 0.50. That is far above the usual 5% limit, so the shortcut is not valid. Solve the quadratic x2 + 0.040x − 0.020 = 0 instead: x = 0.123.

At equilibrium: [PCl3] = [Cl2] = 0.123 M and [PCl5] = 0.377 M.

Practice problems

1. Find the pH of 0.10 M acetic acid (Ka = 1.8 × 10−5).

Show answer

x2 / (0.10 − x) = 1.8 × 10−5. With the shortcut, x = √(1.8 × 10−6) = 1.34 × 10−3 M, which is 1.3% of 0.10, so the shortcut is fine. pH = −log(1.34 × 10−3) = 2.87.

2. For a reaction with K = 2.5, a mixture has Q = 0.8. Which way does it shift?

Show answer

Q < K, so it shifts forward (toward products) until Q = K.

3. Why is water left out of the K expression for a reaction in aqueous solution?

Show answer

Water is the solvent. Its concentration barely changes, so it is treated as a pure liquid with an activity of 1.

Frequently asked questions

When can I ignore x in the denominator?

When K is small compared with the starting concentration. Check afterward: if x is under about 5% of the starting value, the shortcut is acceptable.

Do solids go in an ICE table?

No. Pure solids and liquids are left out of K, so they are left out of the table too.

Reference: OpenStax Chemistry 2e, chapter 13 (Fundamental Equilibrium Concepts, especially 13.4 Equilibrium Calculations) and section 14.3.

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