Equilibrium Constants and Expressions

Chemical Equilibrium

A reversible reaction reaches dynamic equilibrium when the forward and reverse rates are equal, and concentrations stop changing.

Equilibrium Expression

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

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

Rules for Writing $K$ Expressions

1. Products over reactants, each raised to their stoichiometric coefficient
2. Omit pure solids and pure liquids (activities = 1)
3. Use molar concentrations for $K_c$, partial pressures for $K_p$

$K_c$ vs $K_p$

$K_p = K_c(RT)^{\Delta n}$

where $\Delta n = \text{moles gas products} - \text{moles gas reactants}$

Magnitude of $K$

| $K$ Value | Meaning | |-----------|---------| | $K \gg 1$ | Products favored at equilibrium | | $K \ll 1$ | Reactants favored at equilibrium | | $K \approx 1$ | Significant amounts of both |

Manipulating $K$

| Operation | New $K$ | |-----------|---------| | Reverse reaction | $K' = \frac{1}{K}$ | | Multiply by $n$ | $K' = K^n$ | | Add two reactions | $K' = K_1 \times K_2$ |

Reaction Quotient ($Q$)

Same form as $K$, but uses current concentrations:

$Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \quad \text{(at any moment)}$

| Comparison | Direction | |------------|-----------| | $Q < K$ | Reaction proceeds forward | | $Q > K$ | Reaction proceeds reverse | | $Q = K$ | At equilibrium |

AP Chemistry Tip: The equilibrium expression only includes species in the aqueous or gaseous phase.