Chemical Equilibrium

3.A - Concept of Equilibrium

• Definition of Equilibrium:

  • Equilibrium applies to the extent of a chemical reaction – it determines how far the reaction proceeds to produce products.

  • Equilibrium Concentrations: The concentrations of reactants and products at a point when the reaction no longer changes, i.e., after infinite time.

• Example Reaction:

  • 2 HCO3− (aq) + Ca2+ (aq) ⇌ CaCO3 (s) + CO2 (g) + H2O (l)

3.B - Equilibrium Calculations

Dynamic Equilibrium

• A system is in dynamic chemical equilibrium if:

  1. The forward and reverse reactions are both occurring.

  2. They occur at equal rates, resulting in no net change in the concentration of reactants and products.

• Example with N2O4:

  • Reaction: N2O4 (g) ⇌ 2 NO2 (g) at T = 100°C

  • Concentration data at intervals shows how concentrations reach equilibrium.

Equilibrium Expressions

• Rate Equations:

  • For the reaction N2O4 (g) ⇌ 2 NO2 (g), at equilibrium:

  • Rate of the forward reaction, ratef = kf[N2O4]

  • Rate of the reverse reaction, rater = kr[NO2]²

• Equilibrium Constant:

  • K = kf / kr = [NO2]² / [N2O4]

  • General equilibrium expression for a reaction:

    • Kc Expression: Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ for aA + bB ⇌ cC + dD

    • Kp Expression: Kp = (P_C)ᶜ(P_D)ᵈ / (P_A)ᵃ(P_B)ᵇ

Comparison of K Values

• K Values indicate the direction of the equilibrium:

  • K << 1 → Reactant-favored, very little product present.

  • K ≈ 1 → Neither reactants nor products predominates significantly.

  • K >> 1 → Product-favored, significant amount of products present.

Special Cases in Equilibrium Calculations

1. Reactions Involving Solids:

   • Concentrations of solids are excluded from equilibrium expressions.

2. Dilute Solutions:

   • Concentrations of liquid water are not included.

3. Gaseous Reactions:

   • Use of Kc and Kp relationships, with Kp = Kc(RT)∆n.

Calculation of K from Known Reactions

• Reactions involving known equilibrium constants can be manipulated:

  • Adding, reversing, or multiplying reactions influences the K value accordingly.

Reaction Quotient, Q

• At any point in time, Q can be calculated to determine the state of the reaction:

  • Q < K → proceeds to the right (towards products)

  • Q > K → proceeds to the left (towards reactants)

  • Q = K → system is at equilibrium.

Examples of Equilibrium Calculations

1. N2 + O2 ⇌ 2 NO at high temperatures: K = 1.7 x 10⁻³

   • Calculate changes in concentration over time.

2. Dissolution of AgCl in Water:

   • Equilibrium expressions for solid AgCl’s dissociation into ions.

3. Finding concentrations from K values:

   • Given initial conditions, calculate concentrations at equilibrium using ICE tables.

Steps for Performing Equilibrium Calculations

1. Write a balanced equation.

2. Calculate Q and compare to K.

3. Construct ICE tables to solve for unknowns.

4. Make sure units are consistent (mol/L or atm).

5. Derive the equilibrium constant expression and solve for the desired concentration or pressure.

6. Use approximations where applicable, applying the 5% rule or quadratic formulas where necessary.