0.333333
M
0.666667
M
0.333333
M
33.33
%
0.333333
M
0
0.333333
M
0.666667
M
0.333333
M
33.33
%
0.333333
M
0
The ICE Table Calculator solves Initial-Change-Equilibrium problems for chemical reactions approaching equilibrium. ICE tables are a systematic method for determining equilibrium concentrations from initial concentrations and the equilibrium constant. The calculator finds the change variable x that satisfies the equilibrium expression, then computes final concentrations for all species. This tool is invaluable for general chemistry and analytical chemistry courses, handling the algebra that often challenges students. It also reports the percent dissociation, which indicates how much of the reactant has converted to product at equilibrium.
The ICE table method follows three steps for a reaction aA ⇌ bB:
Initial: Start with known initial concentrations [A]₀ and [B]₀.
Change: Define x as the amount of reaction progress. Reactant decreases by ax, product increases by bx:
$$[A] = [A]_0 - ax, \quad [B] = [B]_0 + bx$$
Equilibrium: Substitute into the equilibrium expression:
$$K = \frac{[B]_0 + bx)^b}{([A]_0 - ax)^a}$$
For the simplest case (a = b = 1): K = ([B]₀ + x)/([A]₀ − x), solving gives:
$$x = \frac{K \cdot [A]_0 - [B]_0}{K + 1}$$
The percent dissociation is calculated as:
$$\% \text{dissociation} = \frac{a \cdot x}{[A]_0} \times 100$$
The change x represents how far the reaction proceeds toward equilibrium. A larger x means more reaction has occurred. The equilibrium concentrations show the final state. Percent dissociation indicates the fraction of original reactant consumed — higher values mean the reaction goes closer to completion. If percent dissociation is close to 100%, the equilibrium strongly favors products. Low values indicate reactants are favored.
Inputs
Results
K = (0 + x)/(1.0 − x) = 4. Solving: x = 4(1 − x), x = 4 − 4x, 5x = 4, x = 0.8. Equilibrium: [A] = 0.2 M, [B] = 0.8 M. Check: 0.8/0.2 = 4 ✓. 80% of A dissociated.
Inputs
Results
K = (0.2 + x)/(0.5 − x) = 2. Solving: 0.2 + x = 2(0.5 − x) = 1 − 2x. 3x = 0.8, x = 0.267. [A] = 0.233, [B] = 0.467. Check: 0.467/0.233 ≈ 2.0 ✓.
ICE stands for Initial, Change, and Equilibrium. These are the three rows of the table that track concentrations as a reaction approaches equilibrium.
Use an ICE table when you know initial concentrations and the equilibrium constant, and need to find equilibrium concentrations. It is the standard method for solving equilibrium problems in chemistry.
If K is very small (K << initial concentration), you can approximate [A]₀ − x ≈ [A]₀ to simplify the algebra. This is valid when x is less than 5% of the initial concentration.
Yes. For aA + bB ⇌ cC + dD, each species has its own column. Changes are linked through stoichiometry: if A decreases by ax, B decreases by bx, C increases by cx, D increases by dx.
The ICE table handles non-zero initial product concentrations. The change x can be positive or negative depending on whether Q < K or Q > K.
When coefficients are not all 1, the equilibrium expression may yield a quadratic (or higher order) equation. Use the quadratic formula: x = (−b ± √(b² − 4ac))/2a, choosing the physically meaningful root.
Percent dissociation is the fraction of the initial reactant that has reacted at equilibrium, expressed as a percentage. It equals (moles reacted / initial moles) × 100%.
Yes. For weak acids and bases, dilution increases percent dissociation. This is because the equilibrium expression favors more dissociation at lower total concentrations.
Yes. If Q > K (too much product initially), the reaction shifts in reverse, and x becomes negative in the conventional setup. The calculator handles this automatically.
This calculator uses an analytical solution for 1:1 stoichiometry and an approximate iterative method for other cases. For complex stoichiometries, the exact solution may require numerical methods.
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