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ICE Table Calculator and Equilibrium Solver
In short: This ICE table calculator takes a balanced reaction, the initial concentrations or pressures and K, then solves for x exactly. It shows the full I, C and E table, the equation, the 5% check for the small x shortcut, equilibrium amounts and which way the reaction shifts. It is free and works in your web browser.
Type a reaction such as N2O4(g) ⇌ 2NO2(g), enter starting amounts and K. Solids and pure liquids are left out of K for you. You can work in concentrations, moles in a volume or partial pressures, give K as Kc or Kp, and switch to Find K from equilibrium data to go the other way.
Fill in every equilibrium amount, or fill in all initial amounts plus the equilibrium amount of one species.
ICE table method and formulas
aA + bB ⇌ cC + dD Kc = [C]^c [D]^d / ([A]^a [B]^b) Kp = Kc (RT)^Δn
I: initial C: change (reactants −νx, products +νx) E: equilibrium = I + C
- Balance the equation and note the phase of each species. Solids (s) and pure liquids (l) such as solvent water are left out of K.
- Find the direction. Work out Q from the initial amounts. Q < K means the reaction goes forward, Q > K means it goes backward.
- Fill the ICE table. Each change is the stoichiometric coefficient times x.
- Substitute the E row into K and solve for x. The tool solves the full equation, which is a quadratic or higher polynomial, and keeps the only root that leaves every amount at zero or above.
- Check the 5% rule if you used the shortcut of ignoring x next to an initial amount.
When the small x approximation works
| Problem | K | Exact x | Approximate x | % of initial | Shortcut OK? |
|---|---|---|---|---|---|
| 0.10 M acetic acid | 1.8 × 10⁻⁵ | 1.33 × 10⁻³ M | 1.34 × 10⁻³ M | 1.3% | Yes |
| 0.0400 M N₂O₄ | 4.63 × 10⁻³ | 6.25 × 10⁻³ M | 6.80 × 10⁻³ M | 17% | No |
| 1.00 atm PCl₅ | 1.05 (Kp) | 0.626 atm | 1.02 atm | 102% | No |
A quick rule: if initial concentration ÷ K is more than about 400, x is usually under 5%.
Kp and Kc
Δn counts only gases. With R = 0.08206 L·atm/(mol·K), Kp is in atm units; with R = 0.08314 L·bar/(mol·K) it is in bar units. When Δn = 0, as for H₂ + I₂ ⇌ 2HI, Kp = Kc.
Worked examples
H₂ + I₂ ⇌ 2HI at 430 °C
0.500 M H₂ and 0.500 M I₂, Kc = 54.3.
54.3 = (2x)² / (0.500 − x)². Take the square root: 2x / (0.500 − x) = 7.369.
x = 0.393 M: [HI] = 0.787 M, [H₂] = [I₂] = 0.107 M
N₂O₄ ⇌ 2NO₂ at 25 °C
0.0400 M N₂O₄, Kc = 4.63 × 10⁻³.
4x² + 4.63 × 10⁻³ x − 1.852 × 10⁻⁴ = 0. The shortcut gives 6.80 × 10⁻³ M, which is 17% of 0.0400 M, so it fails.
x = 6.25 × 10⁻³ M: [NO₂] = 0.0125 M, [N₂O₄] = 0.0337 M
Weak acid: 0.10 M acetic acid
Ka = 1.8 × 10⁻⁵. Water is a liquid and is left out.
x² / (0.10 − x) = 1.8 × 10⁻⁵. Shortcut: x ≈ √(1.8 × 10⁻⁶) = 1.34 × 10⁻³ M (1.3%, valid).
[H₃O⁺] = 1.33 × 10⁻³ M, pH = 2.88
PCl₅ decomposition at 250 °C
P(PCl₅) = 1.00 atm at the start, Kp = 1.05.
x² / (1.00 − x) = 1.05, so x² + 1.05x − 1.05 = 0.
x = 0.626 atm: P(PCl₅) = 0.374 atm. Kc = 1.05 / (0.08206 × 523.15) = 0.0245
Haber process at 472 °C
1.00 M N₂, 3.00 M H₂, Kc = 0.105.
0.105 = (2x)² / [(1.00 − x)(3.00 − 3x)³]. This is a quartic, so solve it numerically.
x = 0.353 M: [NH₃] = 0.705 M, [N₂] = 0.647 M, [H₂] = 1.94 M
Find K from one equilibrium amount
1.00 mol H₂ and 1.00 mol I₂ in 2.00 L give 1.56 mol HI at equilibrium.
[HI] = 0.780 M so x = 0.390 M and [H₂] = [I₂] = 0.110 M.
Kc = 0.780² / 0.110² = 50.3
Common mistakes
- Forgetting coefficients in the C row. For 2HI the change is +2x, and the term in K is (2x)², not 2x².
- Putting solids or solvent water in K. CaCO₃(s), CaO(s) and H₂O(l) never appear in the expression.
- Using moles instead of concentrations. Divide moles by the volume in litres first, unless Δn = 0 and the volumes cancel.
- Skipping the 5% check. The shortcut only works for small K. Always compare x with the initial amount.
- Picking the wrong root. A quadratic gives two roots. Only one keeps all amounts at zero or above.
- Wrong Δn or units in Kp = Kc(RT)^Δn. Count gases only, use T in kelvin and the R that matches your pressure unit.
- Assuming the reaction goes forward. If products are present at the start, work out Q first. x can be negative.
Drawing the molecules in your equilibrium? Sketch reactants, products and reaction arrows in MolDraw, a free online chemical structure editor.
Open MolDraw editorFrequently asked questions
How do I set up an ICE table?
Write the balanced equation. Fill the I row with initial concentrations or pressures. In the C row, each species changes by its coefficient times x: minus for reactants and plus for products. The E row is I plus C. Put the E row into the K expression and solve for x.
When can I use the small x approximation?
Only when K is small compared with the starting amounts. Solve with x neglected, then check that x is less than 5% of each initial amount it was subtracted from. For 0.10 M acetic acid with Ka = 1.8 × 10⁻⁵, x is 1.3% of 0.10 M, so the shortcut is fine. For 0.0400 M N2O4 with Kc = 4.63 × 10⁻³ it is 17%, so you must solve the quadratic.
Why are solids and pure liquids left out of K?
Their activity is 1 because their concentration does not change during the reaction. So CaCO3(s), CaO(s) and H2O(l) as the solvent do not appear in the K expression, though some solid must still be present for the equilibrium to exist.
How do I convert Kp to Kc?
Use Kp = Kc(RT)^Δn, where Δn is moles of gaseous products minus moles of gaseous reactants, R = 0.08206 L·atm/(mol·K) and T is in kelvin. For N2 + 3H2 ⇌ 2NH3 at 745 K, Δn = −2, so Kp = 0.105 × (61.15)^−2 = 2.81 × 10⁻⁵.
What does comparing Q and K tell me?
Q is the same ratio as K but uses the current amounts. If Q is less than K the reaction moves forward to make more products. If Q is greater than K it moves backward. If Q equals K the mixture is already at equilibrium.
How do I find K from equilibrium amounts?
Put the equilibrium concentrations into the K expression. If you only know the initial amounts and one equilibrium amount, use that species to find x, fill in the rest of the ICE table, and then calculate K. Example: 1.00 mol H2 and 1.00 mol I2 in 2.00 L give 1.56 mol HI, so Kc = 0.780² / 0.110² = 50.3.
Related chemistry tools
Want the full method with more examples? Read the ICE table and equilibrium guide. Need to sketch molecules for a report? Draw chemical structures online with MolDraw.
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