Chemical equilibrium is reached in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of all reactants and products remain constant over time. This does not mean the reactions have stopped — both forward and reverse reactions continue at equal rates, making equilibrium a dynamic state.
Key Concepts
Reversible Reactions: Reactions that can proceed in both directions are written with a double arrow (⇌). For example: N2(g) + 3H2(g) ⇌ 2NH3(g).
Equilibrium Constant (Kc): For a reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is:
Kc = [C]c × [D]d / ([A]a × [B]b)
Only gaseous and aqueous species appear in the expression; pure solids and pure liquids are excluded.
Kp: When concentrations are expressed as partial pressures, we use Kp. The relationship between Kp and Kc is:
Kp = Kc × (RT)deltan
where deltan = (moles of gaseous products) - (moles of gaseous reactants) and R = 0.0821 L·atm·mol-1·K-1.
Le Chatelier's Principle: If an equilibrium system is disturbed by changing concentration, pressure, or temperature, the system shifts to counteract that change and re-establish equilibrium.
Degree of Dissociation (alpha): The fraction of the original substance that has dissociated at equilibrium.
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Worked Examples
Write the Kc expression for 2SO2(g) + O2(g) ⇌ 2SO3(g).
Kc = [SO3]2 / ([SO2]2 × [O2])
Note: exponents match stoichiometric coefficients.
For N2(g) + 3H2(g) ⇌ 2NH3(g), if Kc = 0.5 at 400°C and T = 673 K, find Kp.
deltan = 2 - (1 + 3) = -2
Kp = Kc × (RT)deltan = 0.5 × (0.0821 × 673)-2
= 0.5 / (55.25)2 = 0.5 / 3052.6 ≈ 1.64 × 10-4
At equilibrium, [H2] = 0.2 M, [I2] = 0.2 M, [HI] = 1.6 M for H2 + I2 ⇌ 2HI. Calculate Kc.
Kc = [HI]2 / ([H2][I2]) = (1.6)2 / (0.2 × 0.2) = 2.56 / 0.04 = 64
Le Chatelier application — In the reaction N2 + 3H2 ⇌ 2NH3 (exothermic), predict the effect of increasing temperature.
Increasing temperature favours the endothermic (reverse) direction, so NH3 yield decreases and Kc decreases.
For PCl5(g) ⇌ PCl3(g) + Cl2(g), if initial moles of PCl5 = 1 mol and degree of dissociation alpha = 0.5 at total pressure P, find Kp.
Moles at equilibrium: PCl5 = 0.5, PCl3 = 0.5, Cl2 = 0.5. Total = 1.5.
Mole fractions: x(PCl3) = x(Cl2) = 0.5/1.5 = 1/3; x(PCl5) = 0.5/1.5 = 1/3
Kp = (P/3 × P/3) / (P/3) = P/3
Predict direction of reaction if Qc < Kc.
When the reaction quotient Q is less than Kc, the system proceeds in the forward direction to reach equilibrium, producing more products.
A buffer solution contains 0.1 M CH3COOH and 0.1 M CH3COONa. If Ka = 1.8 × 10-5, find pH.
pH = pKa + log([salt]/[acid]) = -log(1.8 × 10-5) + log(0.1/0.1) = 4.74 + 0 = 4.74
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Key Formulas
Key formulas
Common mistakes
- Including solids/liquids in K expressions — pure solids and liquids have activity = 1 and must be omitted.
- Confusing Kc and Kp units — both are dimensionless in modern convention but deltan determines the numerical relationship.
- Assuming equilibrium means equal concentrations — it means constant concentrations, not necessarily equal.
Summary
Equilibrium is dynamic; Kc and Kp quantify the position of equilibrium. Le Chatelier's principle predicts how systems respond to stress. Ionic equilibria involving weak acids, bases, and buffers are governed by Ka, Kb, and Kw.