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II-09: Equilibrium expressions and ICE tables

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Module II-09 · Recommended before: Before equilibrium concentrations

Equilibrium expressions and ICE tables

An ICE table tracks initial values, stoichiometric changes and final equilibrium values. Concentration ratios are evaluated at equilibrium, not necessarily initially.

Learn the method

K_c = products/reactants, each raised to stoichiometric powers

  1. Write the balanced reaction and the correct K expression.
  2. List initial concentrations.
  3. Represent change using x with coefficients.
  4. Substitute equilibrium expressions into K.
  5. Solve and check nonnegative concentrations.

Common mistake: Do not use initial concentrations to evaluate an equilibrium constant unless they are equilibrium values.

Worked example

Problem: For A ⇌ B, [A]eq = 0.20 M and [B]eq = 0.60 M. Find Kc.

Step-by-step solution: Kc = [B]/[A] = 0.60/0.20 = 3.0.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

One-step ICE example

For A ⇌ B starting with 0.100 M A and K=3.00, x/(0.100−x)=3 gives x=0.075 M B and 0.025 M A.

Equilibrium coefficient powers

For 2A ⇌ B, Kc = [B]/[A]²; the coefficient of A becomes an exponent of its activity or approximate concentration ratio.

Reaction quotient and Kp

The expression for Q uses the same form as K but current concentrations or pressures. At equilibrium Q=K. For gas equilibria under ideal conditions, Kp=Kc(RT)^Δn using a consistent standard-state convention.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. For A ⇌ B, [A]eq=0.5 M and [B]eq=1.5 M. What is Kc?
Hint for question 1

Use equilibrium, not initial, concentrations.

Question 2. For A ⇌ B, [A]eq=0.6 M and [B]eq=1.8 M. What is Kc?
Hint for question 2

Use equilibrium, not initial, concentrations.

Question 3. For A ⇌ B, [A]eq=0.8 M and [B]eq=2.4 M. What is Kc?
Hint for question 3

Use equilibrium, not initial, concentrations.

Question 4. For A ⇌ B, [A]eq=1 M and [B]eq=3 M. What is Kc?
Hint for question 4

Use equilibrium, not initial, concentrations.

Question 5. For A ⇌ B, [A]eq=1.2 M and [B]eq=3.6 M. What is Kc?
Hint for question 5

Use equilibrium, not initial, concentrations.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

W3C WCAG 2.2 accessibility guidance.

Applied practice: Predicting direction and using an ICE table

These additional, ungraded problems cover skills beyond the scored five-question check above. Try each before expanding its solution. Your existing score and progress records are unchanged.

  1. Challenge 1. For A ⇌ B with K = 3.0, the initial mixture has [A] = 0.500 M and [B] = 0.100 M. Which direction will the reaction proceed?

    Show worked solution for challenge 1

    Q = [B]/[A] = 0.100/0.500 = 0.200. Because Q is less than K (3.0), the reaction proceeds forward, producing more B.

  2. Challenge 2. For A ⇌ B with K = 3.0, start with [A] = 0.400 M and [B] = 0 M. Find both equilibrium concentrations.

    Show worked solution for challenge 2

    Let x be the amount of B formed. K = x/(0.400 − x) = 3.0, so x = 0.300 M. Therefore [B]eq = 0.300 M and [A]eq = 0.100 M.

IntoChemistry original instructional content, 2026. Formative feedback is not an official course grade. Sources are linked for independent reading. Accessibility testing with your institution and assistive technology is still recommended.