The concentrations or partial pressures of species at equilibrium can be predicted from the balanced reaction, the initial concentrations, and the appropriate K. The tool is the ICE table.

Initial — Change — Equilibrium. Fill the Initial row from the problem, express the Change row in terms of x scaled by the coefficients, add the two rows to get Equilibrium, then substitute into the K expression and solve for x.

The "x is small" approximation. When K is very small (roughly K < 10⁻⁴) the reaction barely proceeds, so x is negligible compared to the initial concentration and terms like (0.100 − x) can be approximated as 0.100. This turns an unwieldy polynomial into a simple root extraction.

The 5% rule: the approximation is valid if x is less than 5% of the initial concentration you approximated. Always check it. If it fails, you must use the quadratic formula.

When the approximation fails — typically for K near or above 10⁻³, or for very dilute solutions — set up the quadratic and use x = (−b ± √(b² − 4ac))/(2a). Discard the root that gives a negative concentration.

A useful shortcut for large K. If K is very large, it is easier to assume the reaction goes to completion first, then let it come back a small amount. Build the ICE table from the "all products" side.

Sanity checks before you write down an answer: no concentration may be negative, and substituting your equilibrium values back into the K expression must reproduce K.