Lesson: Multi-Step Reaction Kinetics Modern Chemistry

Chemistry

In this lesson, we will learn how to use preequilibrium and steady-state approximations to calculate overall rate constants of multi-step reactions.

Worksheet

Q1:

The decomposition of compound A into compounds B and E is a first-order reaction with overall rate constant 𝑘. The decomposition involves the following four elementary reactions.

  • Reaction:AB+Crateconstant1,=𝑘
  • Reaction:B+CArateconstant2,=𝑘
  • Reaction:B+CB+D+Erateconstant3,=𝑘
  • Reaction:C+D2Brateconstant4,=𝑘

The rate law for this reaction is given by RatedEdABC=[]𝑡=𝑘[]=𝑘[][].

Write a balanced chemical equation for the overall reaction.

In the preequilibrium approximation, the rates of reactions 1 and 2 are equal. Use the preequilibrium approximation to find an expression for 𝑘 in terms of the elementary reaction rate constants.

In the steady-state approximation, the rates of change of [C] and [D] are zero. No assumptions are made regarding [B] or the rates of reactions 1 and 2. Use the steady-state approximation to find an expression for 𝑘 in terms of the elementary reaction rate constants.

Which condition must be satisfied for the preequilibrium and steady-state approximations to produce the same expression for 𝑘?

Q2:

Compound A decomposes into compounds C, D, and E. The decomposition involves the following three elementary reactions.

  • Reaction 1: AB, rate constant = 𝑘
  • Reaction 2: A+BB+C+D, rate constant = 𝑘
  • Reaction 3: 2BE, rate constant = 𝑘

The rates of reaction may be estimated by using a steady-state approximation. In this approximation, the rate of change of [B] is zero.

The stoichiometry of the reaction depends on the relative rates of reactions 2 and 3. Based on the mechanism described, which of the following is not a balanced reaction equation?

Which condition must be satisfied for the steady-state approximation to be valid?

Use the steady-state approximation to find an expression for the rate of formation of C in terms of [A] and the elementary reaction rate constants.

Use the steady-state approximation to find an expression for the rate of formation of E in terms of [A] and the elementary reaction rate constants.

Q3:

A reaction proceeds via four elementary reactions with an overall rate constant 𝑘.

  • Reaction 1: 2AB, rate constant = 𝑘
  • Reaction 2: B2A, rate constant = 𝑘
  • Reaction 3: B+CD+E, rate constant = 𝑘
  • Reaction 4: C+ED+F, rate constant = 𝑘

Write a balanced chemical equation for the overall reaction.

The reaction is found to be of the second order with respect to A and the first order with respect to C. Identify the rate-determining step for the reaction.

Use the preequilibrium approximation to find an expression for 𝑘 in terms of [A] and [C] and the elementary reaction rate constants.

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