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Chem 2 - Chemical Equilibrium II: The Reltionship Between Kinetics and the Equilibrium Constant K

Chem 2 - Chemical Equilibrium II: The Reltionship Between Kinetics and the Equilibrium Constant K

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Chem 2 - Chemical Equilibrium II: The Reltionship Between Kinetics and the Equilibrium Constant K

  1. 1. Chemical Equilibrium (Pt. 2) The Relationship Between Kinetics and the Equilibrium Constant K By Shawn P. Shields, Ph.D. This work is licensed by Dr. Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
  2. 2. Recall: Fast Equilibrium Step in a Kinetic Mechanism What is a fast equilibrium step? For the reversible reaction A B The forward reaction is A B The backward reaction is A B (or alternatively B A) k1 k1 k1 k1 k1
  3. 3. Our Example: Gas Phase Equilibrium For the reversible reaction 2 NO2 N2O4 The forward reaction is 2 NO2 N2O4 The backward reaction is N2O4 2 NO2
  4. 4. Write the Reaction as a Fast Equilibrium 2 NO2 N2O4 The rate law for the forward reaction is Rate = k1[NO2]2 The rate law for the backward reaction is Rate = k1[N2O4] k1 k1
  5. 5. Reaction Rates and Equilibrium 2 NO2 (g) N2O4 (g) At the beginning of the reaction, the forward reaction rate is much faster than the back reaction rate! Reactant is converted to product faster than product is converted to reactant.
  6. 6. Time (s) P (atm) 0.75 0.50 0.25 1.0 NO2 is converted to N2O4 at a much faster rate than the reverse at the beginning of the reaction. 𝐏 𝐍𝐎 𝟐 𝐏 𝐍 𝟐 𝐎 𝟒 Recall Experiment 1: Start with 1.0 atm NO2 (g)
  7. 7. 𝐏 𝐍𝐎 𝟐 𝐏 𝐍 𝟐 𝐎 𝟒 The “kinetics ” part of the experiment Kinetics versus Equilibrium The “equilibrium” part of the experiment Time (s) P (atm) 0.75 0.50 0.25 1.0
  8. 8. What is going on at Equilibrium? 2 NO2 N2O4 (g) Once the reaction is at equilibrium, the forward reaction rate is equal to the back reaction rate!
  9. 9. What is going on at Equilibrium? 2 NO2 N2O4 (g) At equilibrium, both of these processes are occurring microscopically at the same rate! 2 NO2 N2O4 N2O4 2 NO2
  10. 10. Deriving the Equilibrium Constant K 2 NO2 N2O4 The forward reaction rate is equal to the backward rate at equilibrium, so set them equal to each other. k1[NO2]2 = k1[N2O4] rate of fwd rxn = rate of back rxn k1 k1
  11. 11. Deriving the Equilibrium Constant K 2 NO2 N2O4 Rearrange to solve for 𝑘1 𝑘−1 𝒌 𝟏 𝐍𝐎 𝟐 𝟐 = 𝒌−𝟏 𝐍 𝟐 𝐎 𝟒 Divide both sides by NO2 2 𝒌 𝟏 𝐍𝐎 𝟐 𝟐 𝐍𝐎 𝟐 𝟐 = 𝒌−𝟏 𝐍 𝟐 𝐎 𝟒 𝐍𝐎 𝟐 𝟐 k1 k1
  12. 12. Deriving the Equilibrium Constant K 2 NO2 N2O4 𝒌 𝟏 𝐍𝐎 𝟐 𝟐 𝐍𝐎 𝟐 𝟐 = 𝒌−𝟏 𝐍 𝟐 𝐎 𝟒 𝐍𝐎 𝟐 𝟐 Divide both sides by k1 𝒌 𝟏 𝒌−𝟏 = 𝒌−𝟏 𝐍 𝟐 𝐎 𝟒 𝒌−𝟏 𝐍𝐎 𝟐 𝟐 k1 k1 Next ...
  13. 13. Deriving the Equilibrium Constant K 2 NO2 N2O4 𝐊 = 𝐤 𝟏 𝐤−𝟏 = 𝐍 𝟐 𝐎 𝟒 𝐍𝐎 𝟐 𝟐 The equilibrium constant K gives the fundamental relationship between kinetics and equilibrium. k1 k1
  14. 14. Deriving the Equilibrium Constant K 2 NO2 N2O4 𝐊 = 𝐍 𝟐 𝐎 𝟒 𝐍𝐎 𝟐 𝟐 The equilibrium constant K is the ratio of the rate constants for a reversible reaction. k1 k1
  15. 15. Summary of the Characteristics of Equilibrium I. At equilibrium, macroscopic observables have stopped changing. II. There is a balance between the forward reaction rate and the backward (reverse) reaction rate.
  16. 16. Summary of the Characteristics of Equilibrium III. The equilibrium state is completely independent of the initial concentrations or partial pressures of reactants and products.
  17. 17. Summary of the Characteristics of Equilibrium IV. The equilibrium state does not depend on reaction rates! The reaction can go to equilibrium either quickly or slowly.
  18. 18. Next up, The Law of Mass Action (LOMA) (Pt 3)

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