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equilibrium

Kc, Kp & Q, ICE tables, Le Chatelier, temperature dependence of K.

dynamic equilibrium · Kc & Kp · Q & ICE · Le Chatelier · temperature & K

Dynamic equilibrium

Definition. In a closed system: forward rate = reverse rate; concentrations constant.

Kc & Kp

Kc. For \(a\mathrm{A}+b\mathrm{B}\rightleftharpoons c\mathrm{C}+d\mathrm{D}\): \(K_c=\dfrac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b}\). Trap: omit pure solids and liquids; use equilibrium concentrations/pressures only.

Kp. \(K_p=\dfrac{(p_{\mathrm{C}})^c(p_{\mathrm{D}})^d}{(p_{\mathrm{A}})^a(p_{\mathrm{B}})^b}\); \(K_p=K_c(RT)^{\Delta n_g}\).

Magnitude. \(K\gg 1\): products dominate; \(K\ll 1\): reactants dominate. \(K\) changes only with temperature.

Q & ICE

Reaction quotient. \(Q\) is the same expression evaluated before equilibrium: \(Q\lt K\) forward proceeds; \(Q\gt K\) reverse; \(Q=K\) at equilibrium.

ICE tables. Initial–Change–Equilibrium bookkeeping; for the small-\(x\) approximation, check \(x/C\lt 5\%\).

Le Chatelier

Principle. The system shifts to oppose an imposed change. Catalyst: no shift. Inert gas at constant volume: no shift. Pressure increase: favors the side with fewer gas moles. Temperature increase: favors the endothermic direction.

Temperature & K

K vs T. Exothermic forward reaction: raising \(T\) shifts left and lowers \(K\). Endothermic forward reaction: raising \(T\) shifts right and raises \(K\).