Equilibrium
High-Yield Summary
- Kinetics = how fast a reaction runs; equilibrium = how far it goes. Chemical equilibrium: forward rate = reverse rate, so concentrations stay constant (dynamic, not stopped).
- K = [C]^c[D]^d/[A]^a[B]^b for aA+bB⇌cC+dD, from the Law of Mass Action — uses stoichiometric coefficients as exponents (unlike a rate law).
- Keq is general; Kc uses concentrations (= Keq for dilute solutions); Kp uses partial pressures (gas-phase).
- ICE table (Initial, Change, Equilibrium) finds equilibrium concentrations; the 5% rule skips the quadratic formula when x < 5% of the initial concentration.
- Q uses the same expression as K but at any moment: Q<Keq shifts forward (ΔG<0), Q=Keq is equilibrium (ΔG=0), Q>Keq shifts reverse (ΔG>0).
Equilibrium Constant Expression
K = [C]^c[D]^d / [A]^a[B]^b (for aA + bB ⇌ cC + dD)
- K = Equilibrium constant, from the Law of Mass Action
- a, b, c, d = Stoichiometric coefficients, used directly as exponents
- Pure solids and pure liquids are excluded (activity = 1).
Keq vs. Kc vs. Kp
| Constant | Context |
|---|---|
| Keq | General equilibrium constant, any reaction |
| Kc | Molar concentrations, solution-phase; Keq = Kc for dilute solutions |
| Kp | Partial pressures, gas-phase reactions |
ICE Table Method
- 1Initial (I): write down starting concentrations of reactants and products.
- 2Change (C): assign a variable x for how much concentration changes as the system moves to equilibrium.
- 3Equilibrium (E): equilibrium concentration = initial ± change (I ± C = E).
- 4Plug equilibrium expressions into K and solve for x — apply the 5% rule (x < 5% of initial concentration) to avoid the quadratic formula when valid.
Reaction Quotient Q vs. Keq
| Comparison | Direction / ΔG |
|---|---|
| Q < Keq | More reactants than equilibrium → shifts forward → ΔG < 0 |
| Q = Keq | At equilibrium → no net shift → ΔG = 0 |
| Q > Keq | More products than equilibrium → shifts reverse → ΔG > 0 |
Rules Governing K
- Pure solids and pure liquids are excluded from K (activity defined as 1).
- K is temperature-dependent — changing temperature changes K's value.
- Larger Keq favors products (right); smaller Keq favors reactants (left).
- The reverse reaction's equilibrium constant is 1/Keq of the forward reaction.
Common MCAT Trap
- The 5% rule only applies when x truly is negligible (K much smaller/larger than initial concentrations, or a large excess of reactant) — if K is similar in magnitude to initial concentrations, you must solve exactly (quadratic), not approximate.
- Don't confuse the equilibrium constant expression (uses stoichiometric coefficients as exponents, valid only at equilibrium) with a kinetic rate law (uses experimentally determined orders, valid at any time).
- Reaching equilibrium is not a single 'end of the reaction' event — the forward/reverse rates can equalize (and Q can equal Keq) well before a reaction visibly stops changing.
Quick Recall
If Q > Keq, which direction does the reaction shift, and what is the sign of ΔG?
Why are pure solids and liquids left out of the equilibrium constant expression?
If the forward reaction's Keq is 4.0, what is the reverse reaction's equilibrium constant?