Unknown equilibrium concentrations can be determined from the initial concentration of the reactants and the equilibrium constant, K, for the reaction.

Consider the reaction where 0.30 molar nitrogen gas and 0.40 molar oxygen gas react to produce nitric oxide gas and where K is 0.10. To calculate the equilibrium concentrations, the known values are tabulated in an ICE table.

For the change in concentration, the increase or decrease for each product or reactant, respectively, is denoted by x times its stoichiometric coefficient. The sum or difference is used to find the equilibrium concentrations, which are then substituted into the equilibrium expression.

To solve for x, the expression is expanded and all the terms are put on one side to convert it into the form: ax² + bx + c. This equation can be solved using the quadratic formula.

Solving results in two values for x: 0.047 and −0.065. As the negative concentration of a substance is impossible, the value can be rejected.

Using 0.047 for x, the equilibrium concentrations of nitrogen, oxygen, and nitric oxide equal 0.25, 0.35, and 0.094 molar, respectively.

The perfect square condition is one situation where a shortcut can be used to avoid the quadratic formula.

For example, if the initial concentrations of nitrogen and oxygen in the above reaction were 0.30 molar each, the equation becomes a perfect square. In such cases, the equation can be simplified by taking the square root of both sides to solve for x.