ICE Table Calculator – Solving Equilibrium Problems Step by Step
An ICE table organises an equilibrium problem into three rows: Initial amounts, the Change as the reaction runs, and the Equilibrium amounts. This ICE table calculator builds the table from any balanced reaction, solves for x exactly, and also works the problem in reverse to find K from one measured value.
Why one x describes every species
Stoichiometry ties every species together. In H₂ + I₂ ⇌ 2HI, each mole of H₂ that reacts uses one mole of I₂ and makes two moles of HI. So if H₂ falls by x, I₂ also falls by x and HI rises by 2x. The C row is just the coefficients times x. Starting from 0.500 M H₂ and I₂ with Kc = 54.3, the E row is 0.500 − x, 0.500 − x and 2x, and K fixes x at 0.393 M.
Setting up the C row: which way does it go?
Compare the starting quotient Q₀ with K. If Q₀ < K the reaction runs forward, so reactants get a minus sign. If Q₀ > K it runs backward and the products are used up instead. A mixture of 0.500 M N₂, 0.800 M H₂ and 0.200 M NH₃ has Q₀ = 0.156, larger than Kc = 0.0603, so ammonia decomposes. Starting from 1.00 M HI alone reaches exactly the same equilibrium as 0.500 M H₂ plus 0.500 M I₂, because both starts contain the same atoms.
Solving for x
Some problems are perfect squares: taking √54.3 on both sides gives a linear equation. Most give a quadratic, which always has two roots. Only one keeps every concentration positive; the other would leave, for example, [H₂] = −0.186 M, so it is rejected. Reactions with larger coefficients give cubic or quartic equations. Rather than juggle those formulas, the calculator uses the fact that Q rises steadily with x, so there is exactly one crossing with K inside the allowed range. It brackets that crossing and narrows it down numerically, which also works for fractional coefficients.
The "x is small" shortcut and the 5 % rule
For a weak acid such as 0.100 M acetic acid with Ka = 1.8 × 10⁻⁵, x is tiny next to 0.100, so 0.100 − x ≈ 0.100 and x ≈ √(Ka·c₀). The shortcut is a test, not a habit: check that x is under about 5 % of the starting amount. Here it is 1.3 %, so it passes. For 0.0500 M N₂O₄ with Kc = 4.63 × 10⁻³, x is 15 % of the start and the shortcut overestimates x by almost 8 %. Books quote the equivalent rule of thumb as c₀/K > 100, 400 or 1000.
Large K: go to completion, then back off
When K is huge, as for the silver–ammonia complex (K ≈ 10⁷), assuming x is small fails badly. Instead, treat the reaction as going to completion, which is a limiting-reagent step, and then let a small amount y run back. The leftover Ag⁺ comes out near 6 × 10⁻¹⁰ M, and the shortcut matches the exact answer to better than 0.001 %.
Solids, liquids and limits
Pure solids and liquids are left out of K because their activity is 1, but they still matter. In CaCO₃(s) ⇌ CaO(s) + CO₂(g), the CO₂ pressure at equilibrium equals Kp only while some limestone is left. If too little CaCO₃ is present it all decomposes first and the pressure stays below Kp. Amounts here are in moles; to start from a mass, use the Grams to Moles Converter first.
Working backwards to K
If you know the starting amounts and measure one thing at equilibrium, such as a concentration, the pH, the percent dissociated or the total pressure, that measurement fixes x and therefore K. Watch the significant figures: a total pressure of 1.30 atm from a start of 1.00 atm gives x = 0.30 atm, which has only two significant figures, so K does too. If you already have every equilibrium amount, the Equilibrium Constant Calculator is the quicker route, and the Kp to Kc Converter switches between pressure and concentration constants.