Equilibrium

Notes

Dynamic equilibrium

At equilibrium, the forward and reverse rates are equal, so concentrations stay constant (not necessarily equal). Reactions still happen in both directions.

The equilibrium constant

For $aA + bB \rightleftharpoons cC + dD$:

• Leave out pure solids and liquids. $K_p$ uses partial pressures.
• $K \gg 1$: products favored. $K \ll 1$: reactants favored.
• Reverse the reaction: $\displaystyle K' = \frac{1}{K}$. Multiply by $n$: $K' = K^n$. Add reactions: multiply the $K$ values.

The reaction quotient $Q$

$Q$ has the same form as $K$ but uses current concentrations.

• $Q < K$: the reaction shifts right (toward products).
• $Q > K$: it shifts left.
• $Q = K$: at equilibrium.

ICE tables

Set up Initial, Change and Equilibrium rows. Use the changes from stoichiometry and solve for $x$. If $K$ is very small, you can often assume $x$ is negligible compared with the initial value.

Le Châtelier's principle

A system at equilibrium shifts to partly counteract a stress.

• Add reactant or remove product: shift right.
• Increase pressure by decreasing volume: shift toward fewer moles of gas.
• Raise temperature: shift in the endothermic direction. Only temperature changes the value of $K$.
• Adding a catalyst or an inert gas at constant volume: no shift.

Solubility

$K_{sp}$ for $AgCl(s) \rightleftharpoons Ag^+ + Cl^-$ is $[Ag^+][Cl^-] = s^2$. A common ion lowers solubility.