# 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