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 𝑘 . The decomposition involves four elementary reactions:

  • Reaction 1: A B + C , rate constant = 𝑘 .
  • Reaction 2: B + C A , rate constant = 𝑘 .
  • Reaction 3: B + C B + D + E , rate constant = 𝑘 .
  • Reaction 4: C + D 2 B , rate constant = 𝑘 .

The rate law for this reaction is given by: R a t e d E d A B C = [ ] 𝑡 = 𝑘 [ ] = 𝑘 [ ] [ ] .

Write a balanced chemical equation for the overall reaction.

  • A 2 A 2 B + E
  • B A 2 B + E
  • C 2 A B + E
  • D 2 A 4 B + E
  • E A 4 B + E

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

  • A 𝑘 𝑘 𝑘
  • B 𝑘 𝑘 𝑘
  • C ( 𝑘 + 𝑘 ) 𝑘
  • D 𝑘 ( 𝑘 + 𝑘 ) 𝑘
  • E 𝑘 ( 𝑘 + 𝑘 ) 𝑘

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.

  • A 𝑘 𝑘 𝑘 𝑘 𝑘
  • B 𝑘 𝑘 𝑘 𝑘
  • C 𝑘 𝑘 𝑘 + 2 𝑘
  • D 𝑘 𝑘 𝑘 + 𝑘
  • E 𝑘 𝑘 𝑘 + 𝑘 + 𝑘

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

  • A 𝑘 𝑘
  • B 𝑘 𝑘 𝑘 + 𝑘 + 𝑘
  • C 𝑘 𝑘
  • D 𝑘 𝑘 + 𝑘
  • E 𝑘 𝑘 𝑘 𝑘 𝑘

Q2:

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

  • Reaction 1: A B , rate constant = 𝑘 .
  • Reaction 2: A + B B + C + D , rate constant = 𝑘 .
  • Reaction 3: 2 B E , 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?

  • A 1 0 A 4 C + 4 D + 3 E
  • B 4 A 2 C + 2 D + E
  • C 1 3 A 5 C + 5 D + 4 E
  • D 8 A 3 C + 3 D + 4 E
  • E 7 A C + D + 3 E

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

  • A 𝑘 𝑘
  • B 𝑘 𝑘
  • C 𝑘 𝑘
  • D 𝑘 𝑘
  • E 𝑘 𝑘

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 d C d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]
  • B d C d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]
  • C d C d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]
  • D d C d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]
  • E d C d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]

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 d E d A [ ] 𝑡 = 𝑘 [ ]
  • B d E d A [ ] 𝑡 = 𝑘 [ ]
  • C d E d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]
  • D d E d A [ ] 𝑡 = 𝑘 [ ]
  • E d E d A [ ] 𝑡 = 𝑘 𝑘 𝑘 [ ]

Q3:

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

  • Reaction 1: 2 A B , rate constant = 𝑘 .
  • Reaction 2: B 2 A , rate constant = 𝑘 .
  • Reaction 3: B + C D + E , rate constant = 𝑘 .
  • Reaction 4: C + E D + F , rate constant = 𝑘 .

Write a balanced chemical equation for the overall reaction.

  • A 2 A + C 2 D + F
  • B A + C D + F
  • C 2 A + C D + 2 F
  • D 2 A + 2 C 2 D + F
  • E A + 2 C 2 D + 2 F

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

  • AReaction 3
  • BReaction 4
  • CReaction 2
  • DReaction 1
  • ENo single step is rate-determining.

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

  • A 𝑘 𝑘
  • B 𝑘 𝑘 𝑘
  • C 2 𝑘 𝑘 𝑘
  • D 𝑘 𝑘 2 𝑘
  • E 2 𝑘 𝑘

Q4:

The decomposition of compound A proceeds via three elementary reactions:

  • Reaction 1: A B , rate constant = 𝑘 .
  • Reaction 2: B A , rate constant = 𝑘 .
  • Reaction 3: B C + D , rate constant = 𝑘 .

Which condition must be satisfied for the pre-equilibrium approximation to be valid?

  • A 𝑘 𝑘
  • B 𝑘 𝑘
  • C 𝑘 𝑘
  • D 𝑘 𝑘
  • E 𝑘 𝑘

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

  • A 𝑘 > 𝑘 𝑘
  • B 𝑘 𝑘 𝑘
  • C 𝑘 𝑘 𝑘
  • D 𝑘 > 𝑘 𝑘
  • E 𝑘 𝑘 𝑘

In the steady-state approximation, the rate of change of [B] is zero. What is the rate of change of [B] in the pre-equilibrium approximation, in terms of [A] and the elementary reaction rate constants?

  • A ( 𝑘 + 𝑘 ) [ ] A
  • B ( 𝑘 𝑘 𝑘 ) [ ] A
  • C 𝑘 𝑘 𝑘 [ ] A
  • D 𝑘 [ ] A
  • E 𝑘 𝑘 𝑘 [ ] A

Q5:

A reaction proceeds via three elementary reactions:

  • Reaction 1: A + B C , rate constant = 𝑘 .
  • Reaction 2: C A + B , rate constant = 𝑘 .
  • Reaction 3: C D + E , rate constant = 𝑘 .

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

Write a balanced chemical equation for the overall reaction.

  • A C D + E
  • B A D + E
  • C A + C D + E
  • D A + B D + E
  • E B D + E

Find an expression for [C] in terms of [A], [B] and the elementary reaction rate constants.

  • A 𝑘 𝑘 + 𝑘 [ ] [ ] A B
  • B 𝑘 𝑘 𝑘 [ ] [ ] A B
  • C 𝑘 𝑘 ( [ ] + [ ] ) A B
  • D 𝑘 𝑘 [ ] [ ] A B
  • E 𝑘 𝑘 + 𝑘 ( [ ] + [ ] ) A B

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

  • A A B D E = = =
  • B B D E = =
  • C B D =
  • D D E =
  • E A B =

Q6:

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

Write a balanced chemical equation for the overall reaction.

  • A E 2 D
  • B A + E D
  • C A + B D
  • D B + E 2 D
  • E A + B + E 2 D

Which species act as catalysts in this reaction?

  • A A only
  • B A and C
  • C A and B
  • D B only
  • E C only

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

  • A 𝑘 𝑘 𝑘
  • B 𝑘 𝑘 𝑘
  • C 𝑘 𝑘 𝑘
  • D 𝑘 ( 𝑘 𝑘 )
  • E 𝑘 ( 𝑘 𝑘 )

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

  • ARate = 𝑘 [ ] [ ] [ ] [ ] A B E D
  • BRate = 𝑘 [ ] [ ] [ ] [ ] A D E B
  • CRate = 𝑘 [ A ] [ E ]
  • DRate = 𝑘 [ ] [ ] [ ] [ ] A B D E
  • ERate = 𝑘 [ B ] [ E ]

Q7:

Nitryl chloride ( N O C l ) 2 decomposes with an overall rate constant 𝑘 . 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 3 N O C l N O + N O + C l O + C l 2 2 2 2 2
  • B 1 6 N O C l 8 N O + 8 N O + 6 C l O + 5 C l 2 2 2 2 2
  • C 8 N O C l 4 N O + 6 C l O + C l 2 2 2 2
  • D 2 N O C l 2 N O + C l 2 2 2
  • E 6 N O C l N O + 2 N O + 4 C l O + C l 2 2 2 2 2

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

  • A 𝑘 𝑘 𝑘 𝑘 𝑘 1 2 3 1 2
  • B 𝑘 𝑘 𝑘 𝑘 𝑘 1 1 2 2 3
  • C 𝑘 + 𝑘 + 𝑘 𝑘 + 𝑘 1 2 3 1 2
  • D 𝑘 ( 𝑘 𝑘 ) ( 𝑘 𝑘 ) 3 1 1 2 2
  • E 𝑘 + 𝑘 𝑘 + 𝑘 𝑘 1 2 1 2 3

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

  • ARate = 𝑘 [ ] [ ] N O C l C l 2 2
  • BRate = 𝑘 [ ] [ ] N O C l N O 2 2
  • CRate = 𝑘 [ ] [ ] N O C l N O 2 2 2
  • DRate = 𝑘 [ ] [ ] N O C l C l 2 2 2
  • ERate = 𝑘 [ ] [ ] [ ] N O C l N O C l 2 2 2 2

Q8:

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

Write a balanced chemical equation for the overall reaction.

  • A 2 A + 2 C D
  • B A + C D
  • C 2 A + C 2 D
  • D A + 2 C 2 D
  • E A + 2 C D

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

  • A 𝑘 𝑘 1 2
  • B 𝑘 𝑘 1 1
  • C 𝑘 𝑘 + 𝑘 1 1 2
  • D 𝑘 𝑘 1 2
  • E 𝑘 𝑘 1 1

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.

  • A 𝑘 𝑘 𝑘 2 1 1
  • B 𝑘 𝑘 1 1
  • C 𝑘 𝑘 𝑘 2 1 1
  • D 𝑘 𝑘 𝑘 1 2 1
  • E 𝑘 𝑘 𝑘 1 1 2

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

  • A 1 2
  • B 0
  • C 2
  • D 1
  • E 3 2

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