How to use the ice table equilibrium calculator
- List each species with its coefficient from the balanced equation, whether it is a reactant or a product, and its starting concentration.
- Enter the equilibrium constant K. Leave pure solids and liquids out of the table.
- Read the extent of reaction x, every equilibrium concentration and the check that K is recovered.
- Study the initial, change and equilibrium table, and the direction the reaction runs.
Formula
Change: reactants lose coefficient x x; products gain coefficient x x
K = (product concentrations raised to their coefficients) / (reactant concentrations raised to theirs)
Reaction quotient Q at the start: the same expression with starting values
Q rises steadily with x, so exactly one x gives Q = K
If Q is less than K the reaction runs forward, to the right. If Q is greater than K it runs backward. The page solves for x with a safe repeated-halving search.
A weak acid, ammonia and a reverse reaction
For HA <-> H+ + A- starting with 0.10 mol/L of HA and K = 1.8e-5, the extent is x = 0.0013327 mol/L, so [H+] = [A-] = 0.0013327 and [HA] = 0.098667. About 1.333 percent of the acid has reacted. The default table A + B <-> C + D with 1.0 mol/L of A and B and K = 4 gives x = 2/3, so [A] = [B] = 0.33333 and [C] = [D] = 0.66667.
For N2 + 3 H2 <-> 2 NH3 with 1.0 mol/L of N2, 3.0 of H2 and K = 0.5 the extent is x = 0.48578, leaving 0.51422 of N2, 1.5427 of H2 and making 0.97156 of NH3. Starting only with C in A + B <-> 2 C with 1.0 mol/L of C and K = 4, Q is infinite, so the reaction runs backward by x = -0.25, ending with 0.25 of A and B and 0.5 of C.
How the solve works
Between the point where a reactant runs out and the point where a product runs out, making more product always raises Q, so the equation Q = K has exactly one solution. The page finds it by repeated halving, in a form that keeps full precision even when K is huge or tiny and a concentration is nearly zero. No guessing a root of a polynomial or checking for a negative concentration is needed.
For a quick weak acid or base result use the pH and weak acid calculator. To balance an equation first, use the chemical equation balancer, and for amounts by mass see the limiting reagent calculator and the moles to grams calculator.
Reading the table
The table has a row per species. Initial is what you entered. Change is plus or minus the coefficient times x, and equilibrium is initial plus change. When x is negative the reaction runs backward, consuming products. The share of the limiting reactant used tells you how far the reaction has gone.
Assumptions and limits
- K is a concentration-based constant at one temperature. Partial pressures work if you use a Kp consistently.
- Pure solids and liquids, and the solvent, are left out of both the table and the K expression.
- Coefficients are whole numbers from 1 to 10. Up to six species can be entered.
- Activity effects, changing volume and temperature shifts are not modeled.
Frequently asked questions
What does ICE stand for?
It stands for initial, change, equilibrium. The table tracks how much of each species starts, how much it changes by in terms of x, and what is left at equilibrium.
How do I know which way the reaction goes?
Compare the reaction quotient Q at the start with K. Q smaller than K means the reaction runs forward to make more products. Q larger than K means it runs backward.
Why do I not need the small x approximation?
The page solves the equation exactly, so there is no need to assume x is small or to check the 5 percent rule. The share of the limiting reactant used is still shown for context.
What if a reactant starts at zero?
Then the reaction cannot run forward until some product breaks down. If products are present the reaction runs backward to make reactants, as in the last example. If all species start at zero there is nothing to react.