Chemical Equilibrium (ICE Table) Calculator
Solve an equilibrium from K and the starting amounts. Type the reaction, and the calculator builds the ICE table and finds x exactly, not with the small-x shortcut, which it shows beside the exact answer with the 5% test. It also compares Q with K, converts Kc and Kp, and finds K from equilibrium data.
How to Use
- Type the reaction, such as N2(g) + 3H2(g) = 2NH3(g). Use =, -> or ⇌ for the arrow; if you leave out the coefficients it is balanced for you. Mark solids and liquids with (s) or (l) to leave them out of K.
- Choose Solve equilibrium, Find K from equilibrium amounts, or Kc ⇄ Kp.
- Enter K and say whether it is Kc or Kp. Choose whether your amounts are concentrations (M) or partial pressures (atm or bar); the calculator converts K with Kp = Kc(RT)^Δn when they do not match, using the temperature.
- Enter the starting amount of each species; leave products at 0 if there are none yet.
- Read x, the direction from Q against K, and the ICE table. Show Work gives the equation for x, its exact root, the small-x shortcut and the 5% test, and Le Chatelier hints.
Worked Example
Hydrogen iodide. H₂ + I₂ ⇌ 2HI with K = 50 (an example value; textbooks quote about 50 near 450 °C), starting from 0.100 M H₂ and 0.100 M I₂. The ICE table gives [H₂] = [I₂] = 0.100 − x and [HI] = 2x, so 50 = (2x)² ÷ (0.100 − x)². Taking the square root, 2x ÷ (0.100 − x) = 7.071, so x = 0.07795 M: [HI] = 0.1559 M and [H₂] = [I₂] = 0.02205 M. The small-x shortcut cannot work here: it would give x = 0.3536 M and use up 354% of the hydrogen.
Kc to Kp. For N₂ + 3H₂ ⇌ 2NH₃, Δn = 2 − 4 = −2. At 500 °C (773.15 K), RT = 0.08206 × 773.15 = 63.44 L·atm/mol, so Kp = 0.060 × 63.44⁻² = 1.491 × 10⁻⁵ atm⁻².
The common mistake: trusting the small-x shortcut without the 5% test. For 0.100 M N₂O₄ with Kc = 4.6 × 10⁻³, dropping x from 0.100 − x gives 4x² = 4.6 × 10⁻⁴ and x = 0.01072 M. That is 10.7% of the starting 0.100 M, so the shortcut fails; the exact root of 4x² = 4.6 × 10⁻³ (0.100 − x) is x = 0.01016 M, 5.5% lower, giving [NO₂] = 0.02033 M, not 0.02145 M.
Show Work
Formulas
The Law of Mass Action
The idea that a reaction stops short of completion, with reactants and products balanced against each other, was put on a quantitative footing by the Norwegian chemists Cato Guldberg and Peter Waage, who published the law of mass action in 1864. Their starting point included the esterification measurements of Marcellin Berthelot and Léon Péan de Saint-Gilles, who found in the early 1860s that acetic acid and ethanol in equal amounts stop at about two-thirds conversion, which is K ≈ 4.
In 1884 Henri Le Chatelier stated the rule that an equilibrium shifts to oppose a change imposed on it, and in the same decade Jacobus van ’t Hoff and Josiah Willard Gibbs connected K to thermodynamics, which is where ΔG° = −RT ln K comes from. Fritz Haber’s ammonia synthesis, worked out from 1909, is the best-known industrial use of both ideas: high pressure favours the side with fewer gas moles.
About This Tool
This calculator reads a reaction as you would write it, balances it if needed, and solves the equilibrium from K and the starting amounts. Instead of the quadratic formula, which only covers some reactions, it finds x by bisection inside the range where no amount goes negative; Q rises steadily across that range, so the root is unique and found to full precision, whether the reaction barely starts or almost completes. The small-x shortcut and the 5% test are shown beside the exact answer so you can see when the shortcut is safe.
The K values in the presets are example values of a realistic size, except acetic acid’s Ka (pKa 4.76 at 25 °C, from data tables such as the CRC Handbook) and the esterification K ≈ 4 found by Berthelot. Ideal behaviour is assumed: concentrations and partial pressures stand in for activities. Everything runs in your browser; nothing is sent anywhere.
Related tools: Gibbs Free Energy Calculator, pH Calculator, and Stoichiometry & Limiting Reagent Calculator.
Frequently Asked Questions
How do you solve an ICE table?
Write Initial amounts, the Change in terms of x from the coefficients, and the Equilibrium amounts, then put them into K. For N₂O₄ ⇌ 2NO₂ with Kc = 4.6 × 10⁻³ and 0.100 M N₂O₄: (2x)² ÷ (0.100 − x) = 4.6 × 10⁻³, so x = 0.01016 M, [NO₂] = 0.02033 M and [N₂O₄] = 0.08984 M.
When can I use the small-x approximation?
When x turns out to be under 5% of every starting amount it is taken from. For 0.100 M acetic acid (K = 1.74 × 10⁻⁵) the shortcut gives x = 0.001319 M, 1.32% of 0.100, against the exact 0.001310 M: fine. For 0.100 M N₂O₄ it gives 0.01072 M, 10.7%, so it fails, and it is 5.5% off the exact 0.01016 M.
What is the difference between Kc and Kp?
Kc uses concentrations in mol/L and Kp uses partial pressures. They are linked by Kp = Kc(RT)^Δn, with R = 0.08206 L·atm/(mol·K) and Δn the change in moles of gas. For N₂O₄ ⇌ 2NO₂ at 25 °C, Δn = 1 and Kc = 4.6 × 10⁻³ gives Kp = 0.1125 atm. For N₂ + 3H₂ ⇌ 2NH₃ at 500 °C, Δn = −2 and Kc = 0.060 gives Kp = 1.491 × 10⁻⁵ atm⁻².
How do I know which way a reaction will go?
Compare the reaction quotient Q, worked out from the starting amounts, with K. If Q < K the reaction runs forward; if Q > K it runs in reverse. Starting from 1.0 M HI alone with K = 50, Q is infinite, so HI breaks down until [H₂] = [I₂] = 0.1102 M and [HI] = 0.7795 M.
How does Le Chatelier’s principle change the answer?
Adding a reactant pushes the reaction forward. In an esterification with K = 4.0, 1.00 M acid and 1.00 M alcohol give 66.67% of the acid converted; tripling the alcohol to 3.00 M raises that to 90.28%. Squeezing a gas reaction favours the side with fewer gas moles: doubling every concentration in the ammonia example raises the share of N₂ converted from 30.63% to 42.33%.
How do I use the Chemical Equilibrium (ICE Table) Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Esterification yield
Acetic acid and ethanol, 1.00 M each, with K = 4.0 reach 0.667 M ethyl acetate: two-thirds conversion, the classic result.
Weak acid ionisation
0.100 M acetic acid with K = 1.74 × 10⁻⁵ gives [H⁺] = 0.001310 M, pH 2.88, with 1.31% ionised.
Hydrogen iodide
H₂ and I₂ at 0.100 M each with K = 50 end at 0.02205 M each and 0.1559 M HI.
Ammonia synthesis
1.00 M N₂ and 3.00 M H₂ with Kc = 0.060 make 0.6125 M NH₃, 30.63% conversion of the nitrogen.
Kc to Kp
Kc = 0.060 for the ammonia synthesis at 500 °C is Kp = 1.491 × 10⁻⁵ atm⁻², because (RT)⁻² = 2.484 × 10⁻⁴.
Last updated: