Chemical Equilibrium

Core Review

Dynamic Equilibrium

At equilibrium, the forward and reverse reactions occur at equal rates — there is no net change in concentrations, but reactions continue at the molecular level (dynamic, not static). Equilibrium can be approached from either direction.

Equilibrium Constants

For a general reaction: aA + bB ⇌ cC + dD

K_c = [C]^c[D]^d / [A]^a[B]^b
K_p = (P_C)^c(P_D)^d / (P_A)^a(P_B)^b

• Products in numerator, reactants in denominator, each raised to its stoichiometric coefficient.
• Pure solids and pure liquids are omitted from K expressions (their "concentration" is constant).
• K_c uses molar concentrations; K_p uses partial pressures (atm).

Relationship between K_p and K_c:

K_p = K_c (RT)^(Δn)

Δn = moles gaseous products − moles gaseous reactants. R = 0.08206 L·atm/mol·K. If Δn = 0, K_p = K_c.

Interpreting K:

• K >> 1: products favored at equilibrium.
• K << 1: reactants favored at equilibrium.
• K ≈ 1: significant amounts of both.

Reaction Quotient Q

Q has the same form as K but uses current (non-equilibrium) concentrations:

• Q < K: reaction proceeds forward (→) to produce more products.
• Q > K: reaction proceeds in reverse (←) to produce more reactants.
• Q = K: at equilibrium.

Le Chatelier's Principle

When a system at equilibrium is disturbed, it shifts to partially counteract the disturbance and re-establish equilibrium.

1. Concentration change: Adding reactant → shifts right (forward). Adding product → shifts left (reverse). Removing reactant → shifts left. K does NOT change.

2. Pressure/Volume change (gases only): Decreasing volume (increasing pressure) favors the side with fewer gas molecules. Increasing volume (decreasing pressure) favors the side with more gas molecules. If Δn = 0, pressure changes have no effect. K does NOT change.

3. Temperature change: This is the ONLY disturbance that changes K.

• Exothermic (ΔH < 0): K decreases with increasing T (heat is a product; adding heat shifts left).
• Endothermic (ΔH > 0): K increases with increasing T (heat is a reactant; adding heat shifts right).

4. Catalysts: Catalysts speed up BOTH forward and reverse rates equally — they do NOT affect K or equilibrium position, only the time to reach equilibrium.

Solubility Product K_sp

For a sparingly soluble salt: M_xA_y(s) ⇌ xM^(y+)(aq) + yA^(x−)(aq)

K_sp = [M^(y+)]^x [A^(x−)]^y

K_sp is an equilibrium constant for dissolution — the solid is omitted. Smaller K_sp = less soluble (for salts with the same stoichiometry).

Molar solubility (s): Concentration of salt that dissolves to form a saturated solution (mol/L).

Worked Example: K_sp of AgCl = 1.8 × 10⁻¹⁰. What is its molar solubility?

• AgCl(s) ⇌ Ag⁺ + Cl⁻; K_sp = [Ag⁺][Cl⁻] = s²
• s = √(1.8 × 10⁻¹⁰) = 1.3 × 10⁻⁵ M

Worked Example: K_sp of CaF₂ = 3.9 × 10⁻¹¹. What is molar solubility?

• CaF₂(s) ⇌ Ca²⁺ + 2F⁻; K_sp = [Ca²⁺][F⁻]² = s(2s)² = 4s³
• s = ³√(3.9 × 10⁻¹¹ / 4) = ³√(9.75 × 10⁻¹²) = 2.1 × 10⁻⁴ M

Common Ion Effect

Adding a common ion (an ion already present in the equilibrium) shifts the solubility equilibrium left, decreasing solubility. This is a direct application of Le Chatelier's Principle.

Example: AgCl is less soluble in 0.10 M NaCl than in pure water because the added Cl⁻ shifts AgCl(s) ⇌ Ag⁺ + Cl⁻ to the left.

Precipitation Prediction

Compare Q_sp (the ion product at current concentrations) to K_sp:

• Q_sp < K_sp: no precipitate; solution is unsaturated.
• Q_sp = K_sp: saturated solution at equilibrium.
• Q_sp > K_sp: precipitate forms until Q_sp = K_sp.

Key Equations

Common Traps

• Including solids/liquids in K expressions.
• Thinking pressure changes alter K (they don't — only temperature does).
• Forgetting to square the concentration in K_sp for 1:2 salts (CaF₂: s × (2s)² = 4s³).
• Applying Le Chatelier to a catalyst addition (catalysts don't shift equilibrium).
• Confusing Q and K — Q uses initial/current values; K is the equilibrium benchmark.