ICE Table Practice: Equilibrium Calculations

Fill in the missing initial, change, and equilibrium entries, then use your table to calculate equilibrium concentrations, constants, and pH. Symbolic answers like 0.200 - x and +2x are accepted with any spacing.

Use the ideal-gas/dilute-solution concentration model for these exercises. Gas flasks have fixed volume and temperature. All table concentrations are in M (mol/L); x also represents a concentration in M. Concentration answers may include M or mol/L. Enter Kc, Ka, and pH without units. Scientific notation such as 2.1e-3 is accepted. Keep extra digits until the final answer.

New to the method? Read the ICE tables lesson first.

1. HI formation: 1:1:2 stoichiometry

Intro

H₂(g) + I₂(g) ⇌ 2 HI(g)

A sealed flask is charged with 0.200 M H₂ and 0.200 M I₂. No HI is present initially. Let x be the decrease in [H₂], measured in M.

ICE table for H₂(g) + I₂(g) ⇌ 2 HI(g). Enter the missing values.
	H₂	I₂
Initial (M)	0.200	0.200
Change (M)	-x
Equilibrium (M)

Equilibrium questions

At equilibrium [HI] = 0.320 M. What is x (in M)?

Using x = 0.160 M, calculate K_c = [HI]² / ([H₂][I₂]). Enter a number without units.

2. Testing the small-x approximation

Core

N₂O₄(g) ⇌ 2 NO₂(g)

0.100 M N₂O₄ is placed in an empty flask at 298 K, where K_c = 4.6 × 10⁻³. Let x be the molarity of N₂O₄ that dissociates. Use the approximation only to estimate x first; then test whether that estimate is valid.

ICE table for N₂O₄(g) ⇌ 2 NO₂(g). Enter the missing values.
	N₂O₄	NO₂
Initial (M)	0.100
Change (M)
Equilibrium (M)

Equilibrium questions

First estimate x (in M) by using 0.100 - x ≈ 0.100 in K_c = 4x² / (0.100 - x).

Using your estimated x, calculate x / 0.100 × 100. Enter only the percentage (not the decimal fraction); the feedback will explain whether it meets the 5% criterion.

Because the 5% check fails, solve the exact expression 4x² / (0.100 - x) = 4.6 × 10⁻³ for the physically meaningful value of x (in M).

Using the exact value of x, what is [NO₂] at equilibrium (in M)?

3. Weak acid ionization

Core

CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq)

A 0.250 M acetic acid solution is at 25 °C, where K_a = 1.8 × 10⁻⁵. H⁺(aq) denotes hydrated protons. Neglect water autoionization, so the initial ion concentrations are treated as zero. Let x be the concentration of acid that ionizes, measured in M.

ICE table for CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq). Enter the missing values.
	CH₃COOH	H⁺
Initial (M)	0.250
Change (M)
Equilibrium (M)		x

Equilibrium questions

Solve for [H⁺] at equilibrium (in M), using the small-x approximation.

Using your approximate [H⁺], calculate the pH. Enter a number without units.

4. Equilibrium with an initial product

Challenge

PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

A flask initially contains 0.400 M PCl₅ and 0.100 M Cl₂, with no PCl₃. Let x be the molarity of PCl₅ that decomposes.

ICE table for PCl₅(g) ⇌ PCl₃(g) + Cl₂(g). Enter the missing values.
	PCl₅	Cl₂
Initial (M)	0.400	0.100
Change (M)
Equilibrium (M)

Equilibrium questions

If x = 0.150 M at equilibrium, what is [Cl₂] (in M)?

Using x = 0.150 M, calculate K_c = [PCl₃][Cl₂] / [PCl₅]. Enter a number without units.

5. Exact equilibrium by taking a square root

Challenge

CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g)

A flask initially contains 0.500 M CO and 0.500 M water vapor, with no CO₂ or H₂. At the fixed temperature, K_c = 4.00. Let x be the decrease in [CO], measured in M.

ICE table for CO(g) + H₂O(g) ⇌ CO₂(g) + H₂(g). Enter the missing values.
	CO	H₂O
Initial (M)	0.500	0.500
Change (M)	-x
Equilibrium (M)

Equilibrium questions

Solve x² / (0.500 - x)² = 4.00 for x (in M). Use the physical range 0 < x < 0.500 M to choose the positive square root first.

What is [CO] at equilibrium (in M)?

1. HI formation: 1:1:2 stoichiometry

Equilibrium questions

2. Testing the small-x approximation

Equilibrium questions

3. Weak acid ionization

Equilibrium questions

4. Equilibrium with an initial product

Equilibrium questions

5. Exact equilibrium by taking a square root

Equilibrium questions

Reference sheetPeriodic table and AP equations in a resizable window