Equilibrium Constant Expressions

Introduction to Chemical Equilibrium

  • Topic Overview: Chapter 14 of the Chang book on chemical equilibrium and writing equilibrium constant expressions.

Reversible Reactions

  • Definition: A reversible reaction is one where products can revert to reactants depending on concentration.
  • Forward and Reverse Direction:
    • Forward: Reading from left to right (reactants to products).
    • Reverse: Reading from right to left (products to reactants).

Equilibrium Concept

  • Equilibrium State: Occurs when the rate of the forward reaction equals the rate of the reverse reaction.
  • Common Misconception: Just because a reaction is reversible does not mean it is at equilibrium.
  • Dynamic Nature of Equilibrium: It's a dynamic system where both forward and reverse reactions occur at constant rates, making concentrations appear unchanged.

Equilibrium Reaction Dynamics

  • Concentration Variations:
    • Different starting concentrations can lead to different equilibrium states (Graphs A, B, and C).
  • Influencing Factors:
    • Container Size: Affects pressure and concentration of gas reactions.
    • Temperature: Can favor either the endothermic or exothermic direction of the reaction depending on $\Delta H$.

Reaction Rates and Constant Expressions

  • Equality of Rates: Rate of forward ($Rf$) equals that of the reverse ($Rr$) at equilibrium.
  • Rate Constant Definitions:
    • Forward rate constant: $K_f$
    • Reverse rate constant: $K_r$
  • General Equilibrium Expression:
    • $K_c = \frac{[Products]^{coefficients}}{[Reactants]^{coefficients}}$
  • Concentration Units: Square brackets indicate molarity (moles per liter).

Understanding Equilibrium Constants

  • Equilibrium Constant ($K_c$):
    • Temperature Dependency: Must be determined experimentally; not from theory.
    • Coefficient Impact: The coefficients in the balanced equation appear as exponents in the equilibrium expression.
  • Mathematical Relationships: If reactions are reversed or coefficients altered, corresponding changes in K-values can be calculated (e.g., $Kf = \frac{1}{Kr}$).

Heterogeneous Equilibrium

  • Definition: In reactions involving solids and gases, only gases and aqueous solutions appear in the expressions because solids and liquids have constant concentrations.
  • Equilibrium Expression Example: Solid carbon with carbon dioxide producing carbon monoxide.

Multiple Equilibria

  • Linked Reactions: For linked reactions, the overall equilibrium constant can be obtained by multiplying their individual constants (e.g., K overall = K₁ * K₂).

Summary of Equilibrium Constants Guidelines

  • Square Brackets: Mean concentration for aqueous solutions and gases.
  • K Values: Are dimensionless; no units.
  • Balanced Equations: Are necessary to derive K.
  • Temperature Specification: Important for equilibria.

Calculation of Equilibrium Constants

  • Sample Calculations:
    • For given concentrations in a reaction at equilibrium, calculate $K_c$ using the formula for products and reactants.
    • Example: $K = \frac{[Products]}{[Reactants]}$.

Extent of Reaction

  • Interpreting K Values:
    • $K >> 1$: Reaction nearly complete, products favored.
    • $K << 1$: Reactants favored, little product formation.
    • $K \approx 1$: Significant amounts of both reactants and products.

Reaction Quotient (Q)

  • Definition: Similar to K but using initial concentrations. Helps determine if the system is at equilibrium.
  • Comparative Analysis:
    • If $Q < K$: Formation of products favored (shifts forward).
    • If $Q > K$: Formation of reactants favored (shifts reverse).
    • If $Q = K$: System is at equilibrium.

Conclusion

  • Next Steps: Further exploration of equilibrium concepts and calculations in the following sessions.