Lecture Notes: Chemical Equilibrium

Introduction to Equilibrium

• Equilibrium in Chemistry: Occurs when the rate of the forward reaction equals the rate of the reverse reaction.
• Dynamic Equilibrium: The reactions continue to occur, but the concentrations of reactants and products remain constant.

Conceptual Illustration

• Example: Two cities (A and B) with cars moving between them.
  • Cars moving at equal rates from A to B and B to A result in no net change in the number of cars in each city.
• Concentration Profile: Graph with concentration vs. time
  • Concentration of reactants and products become constant over time at equilibrium.

Reaction Rates

• Rate of Forward and Reverse Reactions:
  • Forward reaction rate: (k_1[A])
  • Reverse reaction rate: (k_{-1}[B])
  • At equilibrium, these rates are equal._

Equilibrium Constant (K)

• Definition: Ratio of the concentration of products to reactants at equilibrium.
  • (K = \frac{k_1}{k_{-1}})
• Expressions:
  • For concentration: (K_c)
  • For partial pressure: (K_p)_

Calculating Equilibrium Constants

• General Reaction: (aA + bB \rightleftharpoons cC + dD)
• Equilibrium Expression:
  • (K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b})
  • (K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b})

Example Problems

1. Writing Equilibrium Expressions:

   • Use stoichiometric coefficients as exponents.
   • (K_c): concentration of products/reactants.
   • (K_p): pressure of products/reactants.

2. Calculating Equilibrium Constants:

   • For given chemical reactions, balance the equation, determine concentrations or pressures at equilibrium, and solve for (K_c) or (K_p).

3. Converting Between (K_c) and (K_p):

   • Use the equation (K_p = K_c(RT)^\Delta n)
   • (\Delta n) is the change in moles of gas.

4. Adjusting Equilibrium Constants:

   • Doubling a Reaction: (K' = K^2)
   • Halving a Reaction: (K' = K^{1/2})
   • Reversing a Reaction: (K' = \frac{1}{K})

5. ICE Tables:

   • Initial, Change, Equilibrium tables to solve for unknown concentrations or pressures.

Advanced Calculations

• Complex Reactions:
  • Balance equations and solve using given data and ICE tables to find equilibrium concentrations and constants.
• Partial Pressure Calculations:
  • Convert between concentration and pressure using the ideal gas law.

Key Points

• Remember the distinction between (K_c) and (K_p).
• Consider changes in reaction stoichiometry and how it affects equilibrium constants.
• Use ICE tables for systematic solving of equilibrium problems.
• Understand the relationship between forward and reverse rate constants and equilibrium constants.