SectionC9_BB - Tagged

Page 1: Introduction to Equilibrium Constant

• Subject: Chemistry for Bioscientists I (CHEM10021) from the University of Manchester

• Section: C9 - Equilibrium constant

• Focus: Understanding the concept of the equilibrium constant in chemical reactions.

Page 2: Definition of Equilibrium Constant

• Equilibrium Condition:

  • ArG: Maximum useful work, relates to chemical equilibrium.

  • Equilibrium Expression: At equilibrium, Q (reaction quotient) equals K (equilibrium constant).

Page 3: Relationship between Q and K

• Reaction Direction:

  • If Q > K: The reaction shifts to the left (favoring reactants).

  • If Q < K: The reaction shifts to the right (favoring products).

  • If Q = K: The system is at equilibrium (ArG = 0).

Page 4: Calculating Equilibrium Constant

• Equilibrium Dynamics:

  • At equilibrium, the reaction quotient equals the equilibrium constant, K.

• Gibbs Free Energy Relation:

  • ArG = G° + RT ln(Q)

  • At equilibrium, ArG = 0, so: 0 = G° + RT ln(K).

  • Rearranging results in: ArG° = -RT ln(K).

Page 5: Significance of K Values

• Interpreting K:

  • If K > 1: Products dominate at equilibrium.

  • If K >> 1: Reaction essentially favors products.

  • If K < 1: Reactants dominate at equilibrium.

  • If K = 0: Reaction is not thermodynamically feasible.

Page 6: Temperature Effects on Equilibrium

• Gibbs Energy Relation with Temperature:

  • G° = -RT ln(K) and G° = H° - T S°.

  • Resulting equation: ln(K) = H°/R - S°/R T.

• Key Formula: ln(K1) - ln(K2) = R(T2 - T1).

Page 7: Temperature's Influence on K

• Effect of Temperature:

  • Increase in T affects 1/T.

  • Exothermic Reactions:

    • Effect: ln(K) change is negative; shifts to left/reactants.

  • Endothermic Reactions:

    • Effect: ln(K) change is positive; shifts to right/products.

Page 8: Kinetic Interpretation of K

• Forward and Backward Rates:

  • Forward Rate: R -> P with rate constant kf.

  • Backward Rate: P -> R with rate constant kb.

• Rate Definitions:

  • Rate of formation of P: Rate = kf[R].

  • Rate of decomposition of P: Rate = kb[P].

Page 9: Rate Equation

• Reaction Representation:

  • Coiled DNA (R) vs. Uncoiled DNA (P).

  • Net rate of formation of P: d[P]/dt = kf[R] - kb[P].

Page 10: Equilibrium Condition in Kinetics

• At Equilibrium:

  • [R] and [P] concentrations at equilibrium are [R]eq and [P]eq.

  • Hence, at equilibrium: d[P]/dt = 0.

  • This leads to: kf[R]eq = kb[P]eq.

  • Definition of K: K = [P]eq / [R]eq = kf / kb.

Page 11: Complex Equilibrium Example

• General Reaction: A + B ↔ C + D

• Equilibrium Constant: K = [C][D]/[A][B].

• Forward and Backward Rates:

  • Forward rate = kf[A][B]; Backward rate = kb[C][D].

  • At equilibrium, kf[A][B] = kb[C][D].

Page 12: Role of Catalysts

• Effect of Catalysts:

  • They alter the activation energy for forward and backward reactions.

  • Catalysts do not affect the position of equilibrium or the equilibrium constant, but they accelerate attaining equilibrium.

Page 13: Conclusion

• Summary of Equilibrium Constants and their importance in understanding chemical reactions in biosciences.