About the ICE Table Calculator
This ICE table calculator solves chemical equilibrium problems. Enter the balanced reaction as coefficients for up to two reactants and two products, the initial concentration of each species and the equilibrium constant K, and it finds the change x and every equilibrium concentration, then lays out the full Initial, Change, Equilibrium table you would write by hand.
It handles the problems general chemistry students meet most: gas-phase equilibria such as H₂ + I₂ ⇌ 2HI or N₂O₄ ⇌ 2NO₂, weak acid and weak base ionisation (enter Ka or Kb), solubility-style dissociations and reactions that run in reverse because products are present at the start. It compares the initial reaction quotient Q with K to tell you which way the reaction shifts.
The equation is solved numerically, so there is no need for the “x is small” approximation or the quadratic formula, and higher-order cases that would need a cubic are handled too. Concentrations are in mol/L and K is treated as Kc; set a coefficient to 0 to leave a species out. Pure solids and liquids should be omitted, as they do not appear in K.
With the default inputs, the change x is 0.779519 M. Change any value above to recalculate instantly.
How to use the ice table calculator
- 1Write the balanced equation and enter its coefficients; use 0 for an unused reactant or product slot.
- 2Optionally name each species so the ICE table is easy to read.
- 3Enter the initial concentration of each species in mol/L, including any products present at the start.
- 4Enter the equilibrium constant K (scientific notation such as 1.8e-5 works).
- 5Read x, the equilibrium concentrations and the completed ICE table.
Formula and method
An ICE table tracks each species from its Initial concentration, through the Change set by the stoichiometry (−a·x for reactants, +c·x for products), to its Equilibrium value. Substituting the equilibrium expressions into the law of mass action gives one equation in x. For simple cases it is a quadratic; with larger coefficients it becomes a cubic or higher.
The calculator solves that equation numerically by bisection on ln Q(x) − ln K, which increases steadily with x, inside the range where every concentration stays positive. That gives the unique physical root without approximations. Comparing the initial Q with K shows the direction: Q < K means the reaction moves forward (x > 0), Q > K means it moves in reverse (x < 0).
- a, b, c, d
- Stoichiometric coefficients of the balanced equation
- A₀ … D₀
- Initial molar concentrations (mol/L)
- x
- Change in concentration per unit of reaction (mol/L)
- K
- Equilibrium constant in terms of concentrations (Kc, Ka, Kb…)
- Q
- Reaction quotient using the initial concentrations
Worked examples
H₂ + I₂ ⇌ 2HI with K = 50
With 1.0 M H₂ and I₂ and no HI, (2x)² ÷ (1 − x)² = 50. Taking square roots, 2x ÷ (1 − x) = 7.071, so x = 0.7795 M. At equilibrium [H₂] = [I₂] = 0.2205 M and [HI] = 1.559 M.
Acetic acid, 0.10 M, Ka = 1.8 × 10⁻⁵
x² ÷ (0.10 − x) = 1.8 × 10⁻⁵ gives x = 1.333 × 10⁻³ M from the quadratic formula, so [H⁺] = 1.33 × 10⁻³ M (pH ≈ 2.88). Only 1.3% of the acid ionises, so the small-x approximation would also work.
N₂O₄ ⇌ 2NO₂, K = 4.63 × 10⁻³
(2x)² ÷ (0.050 − x) = 0.00463 rearranges to 4x² + 0.00463x − 0.0002315 = 0, whose positive root is x = 0.00705 M. Equilibrium [N₂O₄] = 0.0429 M and [NO₂] = 0.0141 M; 14.1% of the N₂O₄ dissociates.
Starting from products only: 1.0 M HI
Q is infinite, so the reaction runs in reverse and x is negative. (1 + 2x)² ÷ x² = 50 gives 1 + 2x = −7.071x, so x = −0.1102 M: [H₂] = [I₂] = 0.1102 M and [HI] = 0.7795 M.
Frequently asked questions
What does ICE stand for in chemistry?+
ICE stands for Initial, Change, Equilibrium. The table lists each species’ starting concentration, the change expressed in terms of x using the stoichiometric coefficients, and the resulting equilibrium concentration, which is then substituted into the K expression.
When can I use the “x is small” approximation?+
When K is small relative to the initial concentration, x is negligible next to the starting value and you can drop it from (C₀ − x). The usual test is the 5% rule: if x ÷ C₀ < 5%, the approximation is acceptable. This calculator solves exactly, so you can check.
How do I know which direction the reaction will shift?+
Compute the reaction quotient Q from the initial concentrations. If Q < K the reaction moves forward to make more products; if Q > K it moves in reverse; if Q = K the mixture is already at equilibrium.
Do solids and liquids go in the ICE table?+
No. Pure solids and pure liquids (including water as a solvent) have an activity of 1 and do not appear in the equilibrium expression, so leave them out and set their coefficient slots to 0.
Can I use this for Kp instead of Kc?+
Yes, if you enter partial pressures (in atm or bar) in place of concentrations and use Kp. The algebra is identical; just keep all values in the same pressure unit that Kp was defined with.