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 π‘˜. The decomposition involves the following four elementary reactions.

  • Reaction:AB+Crateconstant1,=π‘˜οŠ§
  • Reaction:B+CArateconstant2,=π‘˜οŠ±οŠ§
  • Reaction:B+CB+D+Erateconstant3,=π‘˜οŠ¨
  • Reaction:C+D2Brateconstant4,=π‘˜οŠ©

The rate law for this reaction is given by RatedEdABC=[]𝑑=π‘˜[]=π‘˜[][].

Write a balanced chemical equation for the overall reaction.

  • AA2B+E
  • B2AB+E
  • C2A2B+E
  • D2A4B+E
  • EA4B+E

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

  • Aπ‘˜π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§
  • Bπ‘˜π‘˜π‘˜οŠ±οŠ§οŠ¨οŠ§
  • C(π‘˜+π‘˜)π‘˜οŠ¨οŠ©οŠ±οŠ§
  • Dπ‘˜(π‘˜+π‘˜)π‘˜οŠ±οŠ§οŠ¨οŠ©οŠ§
  • Eπ‘˜(π‘˜+π‘˜)π‘˜οŠ§οŠ¨οŠ©οŠ±οŠ§

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 π‘˜ in terms of the elementary reaction rate constants.

  • Aπ‘˜π‘˜π‘˜+2π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨
  • Bπ‘˜π‘˜π‘˜+π‘˜+π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨οŠ©
  • Cπ‘˜π‘˜π‘˜βˆ’π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨
  • Dπ‘˜π‘˜π‘˜+π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨
  • Eπ‘˜π‘˜π‘˜βˆ’π‘˜βˆ’π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨οŠ©

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

  • Aπ‘˜π‘˜β‰ͺπ‘˜+π‘˜+π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨οŠ©
  • Bπ‘˜β‰«π‘˜+π‘˜οŠ±οŠ§οŠ¨οŠ©
  • Cπ‘˜β‰ͺπ‘˜οŠ±οŠ§οŠ¨
  • Dπ‘˜π‘˜β‰«π‘˜βˆ’π‘˜βˆ’π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ¨οŠ©
  • Eπ‘˜β‰«π‘˜οŠ±οŠ§οŠ¨

Q2:

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

  • Reaction 1: AB, rate constant = π‘˜οŠ§
  • Reaction 2: A+BB+C+D, rate constant = π‘˜οŠ¨
  • Reaction 3: 2BE, rate constant = π‘˜οŠ©

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?

  • A7AC+D+3E
  • B10A4C+4D+3E
  • C13A5C+5D+4E
  • D8A3C+3D+4E
  • E4A2C+2D+E

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

  • Aπ‘˜β‰ͺπ‘˜οŠ©οŠ§
  • Bπ‘˜β‰«π‘˜οŠ¨οŠ§
  • Cπ‘˜β‰«π‘˜οŠ©οŠ¨
  • Dπ‘˜β‰ͺπ‘˜οŠ¨οŠ§
  • Eπ‘˜β‰«π‘˜οŠ©οŠ§

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.

  • AdCdA[]𝑑=π‘˜ο„Ÿπ‘˜π‘˜[]
  • BdCdA[]𝑑=π‘˜ο„Ÿπ‘˜π‘˜[]
  • CdCdA[]𝑑=π‘˜ο„Ÿπ‘˜π‘˜[]
  • DdCdA[]𝑑=π‘˜ο„Ÿπ‘˜π‘˜[]
  • EdCdA[]𝑑=π‘˜ο„Ÿπ‘˜π‘˜[]

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.

  • AdEdA[]𝑑=π‘˜[]
  • BdEdA[]𝑑=π‘˜π‘˜π‘˜[]
  • CdEdA[]𝑑=π‘˜π‘˜π‘˜[]
  • DdEdA[]𝑑=π‘˜[]
  • EdEdA[]𝑑=π‘˜[]

Q3:

A reaction proceeds via four elementary reactions with an overall rate constant π‘˜.

  • Reaction 1: 2AB, rate constant = π‘˜οŠ§
  • Reaction 2: B2A, rate constant = π‘˜οŠ±οŠ§
  • Reaction 3: B+CD+E, rate constant = π‘˜οŠ¨
  • Reaction 4: C+ED+F, rate constant = π‘˜οŠ©

Write a balanced chemical equation for the overall reaction.

  • A2A+CD+2F
  • BA+2C2D+2F
  • C2A+C2D+F
  • D2A+2C2D+F
  • EA+CD+F

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 π‘˜ in terms of [A] and [C] and the elementary reaction rate constants.

  • A2π‘˜π‘˜οŠ¨οŠ±οŠ§
  • Bπ‘˜π‘˜οŠ¨οŠ±οŠ§
  • Cπ‘˜π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§
  • D2π‘˜π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§
  • Eπ‘˜π‘˜2π‘˜οŠ§οŠ¨οŠ±οŠ§

Q4:

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

  • Reaction1:ABrateconstant=π‘˜οŠ§
  • Reaction2:BArateconstant=π‘˜οŠ±οŠ§
  • Reaction3:BC+Drateconstant=π‘˜οŠ¨

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

  • Aπ‘˜β‰ˆπ‘˜οŠ±οŠ§οŠ§
  • Bπ‘˜β‰ͺπ‘˜οŠ§οŠ¨
  • Cπ‘˜β‰«π‘˜οŠ§οŠ±οŠ§
  • Dπ‘˜β‰«π‘˜οŠ±οŠ§οŠ¨
  • Eπ‘˜β‰ˆπ‘˜οŠ±οŠ§οŠ¨

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

  • Aπ‘˜>π‘˜β‰«π‘˜οŠ¨οŠ±οŠ§οŠ§
  • Bπ‘˜>π‘˜β‰«π‘˜οŠ§οŠ¨οŠ±οŠ§
  • Cπ‘˜β‰ˆπ‘˜β‰«π‘˜οŠ¨οŠ§οŠ±οŠ§
  • Dπ‘˜β‰«π‘˜β‰«π‘˜οŠ±οŠ§οŠ§οŠ¨
  • Eπ‘˜β‰«π‘˜β‰ˆπ‘˜οŠ§οŠ±οŠ§οŠ¨

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

  • Aβˆ’π‘˜π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§[A]
  • Bβˆ’(π‘˜+π‘˜)[A]
  • Cβˆ’π‘˜οŠ¨[A]
  • Dβˆ’π‘˜π‘˜π‘˜οŠ±οŠ§οŠ¨οŠ§[A]
  • E(π‘˜βˆ’π‘˜βˆ’π‘˜)[A]

Q5:

A reaction proceeds via the following three elementary reactions.

  • Reaction1:A+BC,rateconstant=π‘˜οŠ§
  • Reaction2:CA+B,rateconstant=π‘˜οŠ±οŠ§
  • Reaction3:CD+E,rateconstant=π‘˜οŠ¨

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

Write a balanced chemical equation for the overall reaction.

  • ABD+E
  • BA+BD+E
  • CAD+E
  • DA+CD+E
  • ECD+E

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

  • Aπ‘˜π‘˜βˆ’π‘˜οŠ§οŠ±οŠ§οŠ¨[A][B]
  • Bπ‘˜π‘˜+π‘˜οŠ¨οŠ±οŠ§οŠ¨([A]+[B])
  • Cπ‘˜π‘˜+π‘˜οŠ§οŠ±οŠ§οŠ¨[A][B]
  • Dπ‘˜π‘˜οŠ§οŠ±οŠ§[A][B]
  • Eπ‘˜π‘˜οŠ¨οŠ±οŠ§([A]+[B])

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

  • AB=D
  • BA=B=D=E
  • CB=D=E
  • DD=E
  • EA=B

Q6:

Compound D is produced with an overall rate constant π‘˜. The reaction involves three elementary reactions: reaction1:A+BC+Drateconstantreaction2:C+DA+Brateconstantreaction3:C+EA+Drateconstant;=π‘˜;=π‘˜;=π‘˜οŠ§οŠ±οŠ§οŠ¨

Write a balanced chemical equation for the overall reaction.

  • AB+E2D
  • BA+B+E2D
  • CA+BD
  • DE2D
  • EA+ED

Which species act as catalysts in this reaction?

  • AB only
  • BA only
  • CA and C
  • DA and B
  • EC only

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

  • Aπ‘˜(π‘˜βˆ’π‘˜)
  • Bπ‘˜π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§
  • Cπ‘˜(π‘˜βˆ’π‘˜)
  • Dπ‘˜π‘˜π‘˜οŠ±οŠ§οŠ¨οŠ§
  • Eπ‘˜βˆ’π‘˜π‘˜οŠ¨οŠ±οŠ§οŠ§

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

  • ARate = π‘˜[A][E]
  • BRate = π‘˜[B][E]
  • CRate = π‘˜[][][][]ADEB
  • DRate = π‘˜[][][][]ABDE
  • ERate = π‘˜[][][][]ABED

Q7:

Nitryl chloride (NOCl)2 decomposes with an overall rate constant π‘˜. The decomposition involves five elementary reactions: reaction1:2NOClClO+NO+ClOrateconstantreaction2:ClO+NO+ClO2NOClrateconstantreaction3:NO+ClONO+NOClrateconstantreaction4:NO+NOClNO+ClOrateconstantreaction5:NOCl+ClONO+Clrateconstant22222222222222;=π‘˜;=π‘˜;=π‘˜;=π‘˜;=π‘˜οŠ§οŠ±οŠ§οŠ¨οŠ±οŠ¨οŠ© 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.

  • A16NOCl8NO+8NO+6ClO+5Cl22222
  • B8NOCl4NO+6ClO+Cl2222
  • C2NOCl2NO+Cl222
  • D3NOClNO+NO+ClO+Cl22222
  • E6NOClNO+2NO+4ClO+Cl22222

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

  • Aπ‘˜π‘˜π‘˜π‘˜π‘˜οŠ§οŠ¨οŠ©οŠ±οŠ§οŠ±οŠ¨
  • Bπ‘˜(π‘˜βˆ’π‘˜)(π‘˜βˆ’π‘˜)
  • Cπ‘˜+π‘˜+π‘˜π‘˜+π‘˜οŠ§οŠ¨οŠ©οŠ±οŠ§οŠ±οŠ¨
  • Dπ‘˜+π‘˜π‘˜+π‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§οŠ±οŠ¨οŠ©
  • Eπ‘˜βˆ’π‘˜π‘˜βˆ’π‘˜π‘˜οŠ§οŠ±οŠ§οŠ¨οŠ±οŠ¨οŠ©

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

  • ARate = π‘˜[][]NOClNO22
  • BRate = π‘˜[][][]NOClNOCl222
  • CRate = π‘˜[][]NOClNO22
  • DRate = π‘˜[][]NOClCl22
  • ERate = π‘˜[][]NOClCl22

Q8:

Compounds A and C react to form compound D with an overall rate constant π‘˜. The reaction involves three elementary reactions: reaction1:A2B;rateconstantreaction2:2BA;rateconstantreaction3:B+CD;rateconstant=π‘˜=π‘˜=π‘˜οŠ§οŠ±οŠ§οŠ¨

Write a balanced chemical equation for the overall reaction.

  • AA+2C2D
  • B2A+2CD
  • CA+CD
  • D2A+C2D
  • EA+2CD

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

  • Aπ‘˜β‰ˆπ‘˜+π‘˜οŠ§οŠ±οŠ§οŠ¨
  • Bπ‘˜β‰«π‘˜οŠ±οŠ§οŠ§
  • Cπ‘˜β‰ͺπ‘˜οŠ±οŠ§οŠ¨
  • Dπ‘˜β‰ˆπ‘˜οŠ§οŠ±οŠ§
  • Eπ‘˜β‰«π‘˜οŠ±οŠ§οŠ¨

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

  • Aο„Ÿπ‘˜π‘˜οŠ±οŠ§οŠ§
  • Bπ‘˜ο„Ÿπ‘˜π‘˜οŠ§οŠ±οŠ§οŠ¨
  • Cπ‘˜ο„Ÿπ‘˜π‘˜οŠ§οŠ¨οŠ±οŠ§
  • Dπ‘˜ο„Ÿπ‘˜π‘˜οŠ¨οŠ±οŠ§οŠ§
  • Eπ‘˜ο„Ÿπ‘˜π‘˜οŠ¨οŠ§οŠ±οŠ§

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

  • A1
  • B0
  • C12
  • D2
  • E32

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