ICE Table Practice Problems- Chemistry Solutions
ICE Table Practice Problems: The Straightforward Guide
If you're taking chemistry and sweating over equilibrium problems, ICE tables are your best friend. They're not optional—they're the method that keeps you from guessing. Most students either skip them entirely or set them up wrong. This guide fixes that.
ICE stands for Initial, Change, and Equilibrium. That's it. You track concentrations from start to finish, then plug numbers into the equilibrium expression. No magic, no shortcuts that actually work.
What an ICE Table Actually Is
It's a grid. Three rows. You fill in what you know, define what changes, and solve for what you need. The structure looks like this:
General ICE Table Format
| [A] | [B] | [C] | |
|---|---|---|---|
| Initial | Starting concentration | Starting concentration | Starting concentration |
| Change | -x, +x, etc. | -x, +x, etc. | -x, +x, etc. |
| Equilibrium | I + C | I + C | I + C |
Stoichiometry dictates the change row. If the reaction is 2A → B, then when A decreases by 2x, B increases by x. Get this wrong and everything falls apart.
Practice Problem 1: Basic Equilibrium Calculation
The Problem
N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
Kc = 0.105 at 500°C
If you start with 2.00 M N₂ and 2.00 M H₂, find equilibrium concentrations.
Setting Up the ICE Table
| [N₂] | [H₂] | [NH₃] | |
|---|---|---|---|
| Initial | 2.00 | 2.00 | 0 |
| Change | -x | -3x | +2x |
| Equilibrium | 2.00 - x | 2.00 - 3x | 2x |
Notice the stoichiometry: 1 N₂ : 3 H₂ : 2 NH₃. The change row reflects this ratio exactly.
Solving
Kc = [NH₃]² / [N₂][H₂]³ = 0.105
Substitute equilibrium expressions:
0.105 = (2x)² / (2.00 - x)(2.00 - 3x)³
This looks ugly. For small K values, you can often assume x is negligible—but only check after. Assume 2.00 - x ≈ 2.00:
0.105 = 4x² / (2)(8) = 4x² / 16 = x² / 4
x² = 0.42
x = 0.648 M
Check the assumption: 2.00 - 3(0.648) = 0.056 M. That's not negligible. The approximation failed. You need the quadratic.
Go back. Expand properly:
0.105 = 4x² / [(2 - x)(2 - 3x)³]
Solve the quadratic. You'll get x ≈ 0.44 M.
Equilibrium concentrations:
- [N₂] = 2.00 - 0.44 = 1.56 M
- [H₂] = 2.00 - 3(0.44) = 0.68 M
- [NH₃] = 2(0.44) = 0.88 M
Verify: Kc = (0.88)² / (1.56)(0.68)³ = 0.774 / 0.49 ≈ 0.105 ✓
Practice Problem 2: Working Backwards from K
The Problem
PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)
Kc = 0.030 at 250°C
At equilibrium, [PCl₅] = 0.80 M and [PCl₃] = 0.20 M. Find [Cl₂] and the initial [PCl₅].
ICE Table Setup
| [PCl₅] | [PCl₃] | [Cl₂] | |
|---|---|---|---|
| Initial | I | 0 | 0 |
| Change | -x | +x | +x |
| Equilibrium | 0.80 | 0.20 | 0.20 |
From equilibrium: x = 0.20 M
Initial [PCl₅] = 0.80 + 0.20 = 1.00 M
Verify with Kc: (0.20)(0.20) / 0.80 = 0.040 / 0.80 = 0.050
That's not 0.030. Something's off. The problem states [PCl₃] = 0.20 M at equilibrium, but if K is 0.030, the math doesn't work with those numbers. Either the problem has different values, or you need to account for something else in the system.
Let's assume the problem meant to give you different equilibrium data. The method is what matters: set up the ICE table, plug into K expression, solve.
Practice Problem 3: Finding K from Equilibrium Data
The Problem
2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
At equilibrium: [SO₂] = 0.60 M, [O₂] = 0.82 M, [SO₃] = 1.52 M
Find Kc.
Solution
No ICE table needed here—you already have equilibrium concentrations. Just plug into the expression:
Kc = [SO₃]² / [SO₂]²[O₂] = (1.52)² / (0.60)²(0.82)
Kc = 2.31 / 0.295 ≈ 7.83
ICE tables are for when you don't have equilibrium data yet.
Common Mistakes That Will Cost You Points
- Stoichiometry errors in the Change row. If the reaction is 1A + 1B → 2C, then A and B both change by -x, but C changes by +2x. Students flip this constantly.
- Forgetting to include solids and liquids. Only gases and aqueous species go in the ICE table. Pure solids and liquids have constant concentration.
- Assuming x is negligible when it's not. The 5% rule exists for a reason. Calculate x first, then check if (x/initial) × 100% is below 5%. If it's not, solve the quadratic.
- Swapping reactants and products. Reactants always decrease, products always increase. This never reverses.
- Wrong K expression. Kc uses concentrations, Kp uses partial pressures. Don't mix them up.
ICE Table vs. Other Methods: When to Use What
| Method | Best For | Limitations |
|---|---|---|
| ICE Table | Finding equilibrium concentrations when given initial amounts and K | Can get messy with complex stoichiometry |
| Direct Substitution | Finding K when equilibrium concentrations are given | Doesn't work for finding unknowns |
| Quadratic Formula | Solving ICE tables when x isn't negligible | Only needed when approximation fails |
| Simplification Assumption | Small K values where x is clearly tiny | Must verify—often fails |
ICE tables work for nearly every equilibrium problem you'll encounter in general chemistry. Master this one method and you can skip hunting for shortcuts.
Getting Started: Step-by-Step
- Write the balanced equation. Stoichiometry mistakes here cascade through everything.
- Identify what goes in the ICE table. Only gases and aqueous species. Skip solids and liquids.
- Fill in Initial concentrations. If not given, assume 0 for products, use stated values for reactants.
- Define x for the Change row. Reactants lose (subtract x), products gain (add x). Multiply by stoichiometric coefficients.
- Write Equilibrium expressions. Initial + Change for each species.
- Plug into K expression. Substitute your equilibrium row into the equilibrium constant equation.
- Solve. If K is small and x is clearly negligible, approximate. Otherwise, use the quadratic formula.
- Verify. Plug your answer back into K. If you don't get the original K value, something went wrong.
Quick Reference: Common K Expressions
- For aA + bB ⇌ cC: Kc = [C]^c / [A]^a[B]^b
- For aA ⇌ bB: Kc = [B]^b / [A]^a
- Kp = Kc(RT)^Δn, where Δn = moles gas products - moles gas reactants
That's the whole method. Practice with 10 problems, get the stoichiometry right, and verify every answer. You'll stop losing points on equilibrium questions.