# Worksheet: Multi-Step Reaction Kinetics

In this worksheet, we will practice using preequilibrium and steady-state approximations to calculate overall rate constants of multi-step reactions.

**Q1: **

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

- Reaction 1: , rate constant =
- Reaction 2: , rate constant =
- Reaction 3: , rate constant =
- Reaction 4: , rate constant =

The rate law for this reaction is given by

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

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 in terms of the elementary reaction rate constants.

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

**Q2: **

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

- Reaction 1: , rate constant =
- Reaction 2: , rate constant =
- Reaction 3: , rate constant =

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?

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

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.

- A
- B
- C
- D
- E

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.

- A
- B
- C
- D
- E

**Q3: **

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

- Reaction 1: , rate constant =
- Reaction 2: , rate constant =
- Reaction 3: , rate constant =
- Reaction 4: , rate constant =

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

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.

- ANo single step is rate determining.
- BReaction 4
- CReaction 2
- DReaction 3
- EReaction 1

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

- A
- B
- C
- D
- E

**Q4: **

The decomposition of compound proceeds via the following three elementary reactions.

Which condition must be satisfied for the preequilibrium approximation to be valid?

- A
- B
- C
- D
- E

Under which of the following conditions would the steady-state approximation be valid but not the preequilibrium approximation?

- A
- B
- C
- D
- E

In the steady-state approximation, the rate of change of is zero. What is the rate of change of in the preequilibrium approximation, in terms of and the elementary reaction rate constants?

- A
- B
- C
- D
- E

**Q5: **

A reaction proceeds via the following three elementary reactions.

In the steady-state approximation, the rate of change in is equal to zero.

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

Find an expression for in terms of and and the elementary reaction rate constants.

- A
- B
- C
- D
- E

Which condition must be satisfied for the reaction to follow Michaelis–Menten kinetics?

- A
- B
- C
- D
- E

**Q6: **

Compound is produced with an overall rate constant . The reaction involves three elementary reactions:

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

Which species act as catalysts in this reaction?

- A only
- B only
- C and
- D and
- E only

Use the preequilibrium approximation to find an expression for in terms of the elementary reaction rate constants.

- A
- B
- C
- D
- E

In the preequilibrium approximation, what is the rate law for the overall reaction?

- ARate =
- BRate =
- CRate =
- DRate =
- ERate =

**Q7: **

Nitryl chloride decomposes with an overall rate constant . The decomposition involves five elementary reactions: Reaction 5 is the rate-determining step. The reaction may be modeled using two preequilibrium approximations:

- rate of reaction 1 = rate of reaction 2,
- rate of reaction 3 = rate of reaction 4.

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

Use the preequilibrium approximation to find an expression for in terms of the elementary reaction rate constants.

- A
- B
- C
- D
- E

In the preequilibrium approximation, what is the rate law for the overall reaction?

- ARate =
- BRate =
- CRate =
- DRate =
- ERate =

**Q8: **

Compounds and react to form compound with an overall rate constant . The reaction involves three elementary reactions:

Write a balanced chemical equation for the overall reaction.

- A
- B
- C
- D
- E

Which condition must be satisfied for the preequilibrium approximation to be valid?

- A
- B
- C
- D
- E

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

- A
- B
- C
- D
- E

In the preequilibrium approximation, what is the order of reaction with respect to ?

- A1
- B0
- C
- D2
- E