All calculatorsEquilibrium ICE-Table Calculator
Calculate chemical equilibrium using an ICE table: determine direction with Q vs K, build the equilibrium expression, and compute equilibrium concentrations/partial pressures with optional step-by-step. Great for common General Chemistry exam setups.
Background
An ICE table tracks Initial, Change, and Equilibrium values. Using stoichiometric coefficients, we write changes in terms of one unknown x, then solve the equilibrium constant expression: K = \dfrac{\prod(\text{products})^{\nu}}{\prod(\text{reactants})^{\nu}}. The reaction’s direction comes from comparing Q (your starting ratio) to K.
How to use this calculator
- Choose Concentrations (Kc) or Partial pressures (Kp).
- Enter stoichiometric coefficients ν, species names, and initial values for up to 2 reactants and 2 products.
- Enter K, then click Calculate.
- Use Quick picks to load common equilibrium setups instantly.
How this calculator works
- Builds an ICE table using a single change variable x.
- Computes the reaction quotient Q from initial values and compares it to K to determine direction.
- Solves Q(x) = K numerically (robust bracketing + bisection), rejecting any solution that makes an equilibrium value negative.
- If enabled, tries a small-x approximation first and only accepts it if the % change check passes.
Formula & Equation Used
Reaction quotient: Q = \dfrac{\prod(\text{products})^{\nu}}{\prod(\text{reactants})^{\nu}}
Equilibrium condition: Q = K
ICE table idea: E = I + (\pm \nu)x (reactants decrease, products increase in the forward direction)
Example Problems & Step-by-Step Solutions
Example 1 — N₂O₄ ⇌ 2 NO₂
Given [N₂O₄]_0 = 0.200, [NO₂]_0 = 0, and K_c = 0.113, find equilibrium concentrations.
- Write ICE: [N₂O₄]=0.200 - x, [NO₂]=0 + 2x.
- Write K: K_c = \dfrac{[NO₂]^2}{[N₂O₄]}.
- Solve \dfrac{(2x)^2}{0.200-x} = 0.113 for x, then plug back into E-row values.
Example 2 — H₂ + I₂ ⇌ 2 HI
Start with [H₂]_0 = 0.500, [I₂]_0 = 0.500, [HI]_0 = 0, and K_c = 50.0.
- ICE: [H₂]=0.500-x, [I₂]=0.500-x, [HI]=2x.
- K: K_c = \dfrac{[HI]^2}{[H₂][I₂]}.
- Solve \dfrac{(2x)^2}{(0.500-x)(0.500-x)} = 50 and compute equilibrium values.
Example 3 — 2 SO₂ + O₂ ⇌ 2 SO₃ (Kp)
Given partial pressures P_{SO₂,0}=0.600, P_{O₂,0}=0.200, P_{SO₃,0}=0, and K_p=2.5.
- ICE: P_{SO₂}=0.600-2x, P_{O₂}=0.200-x, P_{SO₃}=2x.
- Kp: K_p=\dfrac{(P_{SO₃})^2}{(P_{SO₂})^2(P_{O₂})}.
- Solve Q(x)=K_p and compute equilibrium pressures.
Frequently Asked Questions
Q: What is the difference between Q and K?
Q uses current values (often the initial mixture). K is the equilibrium constant. If Q<K, the reaction proceeds forward; if Q>K, it shifts backward.
Q: What is “x” in an ICE table?
x is the extent of reaction needed to reach equilibrium. Each species changes by \pm \nu x (coefficient times x).
Q: When is the small-x approximation valid?
When the equilibrium shift is small compared to initial amounts (often checked by a % change test like ≤ 5%). This calculator only accepts the approximation if it passes a validation check.
Q: What if I enter a species with initial value 0?
That’s totally fine — it’s common. The calculator avoids invalid operations and finds a physically valid equilibrium solution where all equilibrium values are ≥ 0.
Q: Does this parse full chemical equations?
MVP: no. You enter coefficients and species names manually. (This keeps it reliable and avoids parser edge cases.)
