Chemical Equilibrium

A Balance of Rates, Not of Amounts

A reversible reaction reaches equilibrium when forward and reverse rates become equal. Concentrations then stop changing, but both reactions continue, equilibrium is dynamic, not static.

For $aA + bB \rightleftharpoons cC + dD$ the equilibrium constant is

$$K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Pure solids and pure liquids are omitted, because their concentrations cannot change. $K$ depends on temperature and on nothing else, not on starting amounts, not on pressure, not on the presence of a catalyst.

The reaction quotient $Q$ has the identical form but is evaluated at any moment, and comparing the two predicts the direction of change:

Le Chatelier's principle says a system at equilibrium responds to a disturbance in the direction that partially offsets it. Adding a reactant drives the reaction forward; removing a product does the same. Raising the pressure on a gaseous equilibrium shifts it toward the side with fewer gas molecules. Raising the temperature shifts an endothermic reaction forward, and temperature is the only disturbance that actually changes $K$; everything else merely moves the system to a different point on the same constant.

The temperature dependence is the Van 't Hoff equation:

$$\ln \frac{K_2}{K_1} = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$

Quantitative problems use an ICE table — Initial, Change, Equilibrium — where the changes are in the ratio of the stoichiometric coefficients.

Common pitfall: thinking a catalyst increases yield. A catalyst speeds the forward and reverse reactions by identical factors, so $Q$ still meets the same $K$. It changes only how soon equilibrium arrives, never where it sits, which is why industrial catalysts are paired with pressure and temperature choices that do move the equilibrium.