Writing K and comparing Q with K

A reversible reaction in a closed container reaches dynamic equilibrium when the forward and reverse rates become equal. Both reactions keep running, so the concentrations stop changing. They are constant, but they are almost never equal to each other.

For $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$, the equilibrium expression is $K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$, with equilibrium molarities. $K_p$ has the same form with partial pressures of the gases. Pure solids and pure liquids (including water as the solvent) are left out. K is reported without units.

The size of K tells you where the equilibrium lies. If K is much greater than 1, the mixture at equilibrium is mostly products; if K is much less than 1, it is mostly reactants. K changes only when the temperature changes.

Changing the equation changes K. Reverse the equation and the new K is $1/K$. Multiply every coefficient by n and the new K is $K^n$ (so halving the coefficients gives $\sqrt{K}$). Add two equations and multiply their K values.

The reaction quotient Q has the same form as K but uses the concentrations present right now. If $Q < K$, the net reaction runs forward, making products, until Q rises to K. If $Q > K$, it runs in reverse. If $Q = K$, the system is already at equilibrium.

To find K from an experiment, build an ICE table: Initial molarities, the Change in each (tied together by the coefficients, using one unknown x), and Equilibrium molarities. Convert moles to molarity first by dividing by the volume in liters. Then put the equilibrium row into the K expression.

To predict a direction, compute Q from the concentrations given, then compare: Q smaller than K means the reaction makes more products; Q larger than K means it makes more reactants.