ICE Tables and Equilibrium Concentrations

A reaction only has one extent of reaction at any moment, even though several species change amount at once. That single extent is x. Every species change is x times its own coefficient, because the stoichiometry of the balanced equation locks the species together: for every x mol/L of A that reacts, the same ratio of B must react and C must form. So one unknown describes the whole system, and the coefficients turn it into different numbers for different columns.

Setting up the table: write the balanced equation across the top. The Initial row holds the starting concentrations or pressures, usually zero for products. The Change row holds minus the coefficient times x for anything consumed, plus the coefficient times x for anything produced. The Equilibrium row adds Initial and Change for each column. Then write the equilibrium expression K using the Equilibrium row entries, and solve for x. Once you have x, plug it back into the Equilibrium row to get actual concentrations or pressures.

The algebra is often a quadratic, sometimes one that simplifies if you can take a square root of both sides, sometimes one needing the quadratic formula. Watch the physical limits on x: it cannot make any equilibrium amount negative, and that rule tells you which root of the quadratic is real. This topic is where the equilibrium constant from earlier becomes a tool for prediction rather than just a label, and it sets up the next idea: once a system is sitting at equilibrium, Le Chatelier's principle describes how it responds when you disturb it.