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 1: AB+C, rate constant = π‘˜οŠ§
  • Reaction 2: B+CA, rate constant = π‘˜οŠ±οŠ§
  • Reaction 3: B+CB+D+E, rate constant = π‘˜οŠ¨
  • Reaction 4: C+D2B, rate constant = π‘˜οŠ©

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

Write a balanced chemical equation for the overall reaction.

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

  • A π‘˜ π‘˜ π‘˜    
  • B π‘˜ π‘˜ π‘˜    
  • C ( π‘˜ + π‘˜ ) π‘˜    
  • D π‘˜ ( π‘˜ + π‘˜ ) π‘˜     
  • E π‘˜ ( π‘˜ + π‘˜ ) π‘˜     

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.

  • A π‘˜ π‘˜ π‘˜ + 2 π‘˜     
  • B π‘˜ π‘˜ π‘˜ + π‘˜ + π‘˜      
  • C π‘˜ π‘˜ π‘˜ βˆ’ π‘˜     
  • D π‘˜ π‘˜ π‘˜ + π‘˜     
  • E π‘˜ π‘˜ π‘˜ βˆ’ π‘˜ βˆ’ π‘˜      

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

  • A π‘˜ π‘˜ β‰ͺ π‘˜ + π‘˜ + π‘˜      
  • B π‘˜ ≫ π‘˜ + π‘˜    
  • C π‘˜ β‰ͺ π‘˜   
  • D π‘˜ π‘˜ ≫ π‘˜ βˆ’ π‘˜ βˆ’ π‘˜      
  • E π‘˜ ≫ π‘˜   

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?

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

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

  • A π‘˜ β‰ͺ π‘˜  
  • B π‘˜ ≫ π‘˜  
  • C π‘˜ ≫ π‘˜  
  • D π‘˜ β‰ͺ π‘˜  
  • E π‘˜ ≫ π‘˜  

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 [ ] 𝑑 = π‘˜ ο„Ÿ π‘˜ π‘˜ [ ]   
  • B d C d A [ ] 𝑑 = π‘˜ ο„Ÿ π‘˜ π‘˜ [ ]     
  • C d C d A [ ] 𝑑 = π‘˜ ο„Ÿ π‘˜ π‘˜ [ ]   
  • D d C d A [ ] 𝑑 = π‘˜ ο„Ÿ π‘˜ π‘˜ [ ]     
  • E d C d A [ ] 𝑑 = π‘˜ ο„Ÿ π‘˜ 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.

  • A d E d A [ ] 𝑑 = π‘˜ [ ]  
  • B d E d A [ ] 𝑑 = π‘˜ π‘˜ π‘˜ [ ]   
  • C d E d A [ ] 𝑑 = π‘˜ π‘˜ π‘˜ [ ]   
  • D d E d A [ ] 𝑑 = π‘˜ [ ]  
  • E d E d A [ ] 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.

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

  • A 2 π‘˜ π‘˜   
  • B π‘˜ π‘˜   
  • C π‘˜ π‘˜ π‘˜    
  • D 2 π‘˜ π‘˜ π‘˜    
  • E π‘˜ π‘˜ 2 π‘˜    

Q4:

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

  • R e a c t i o n 1 : A B r a t e c o n s t a n t = π‘˜ 
  • R e a c t i o n 2 : B A r a t e c o n s t a n t = π‘˜  
  • R e a c t i o n 3 : B C + D r a t e c o n s t a n t = π‘˜ 

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

  • A π‘˜ β‰ˆ π‘˜   
  • B π‘˜ β‰ͺ π‘˜  
  • C π‘˜ ≫ π‘˜   
  • D π‘˜ ≫ π‘˜   
  • E π‘˜ β‰ˆ π‘˜   

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

  • A π‘˜ > π‘˜ ≫ π‘˜    
  • B π‘˜ > π‘˜ ≫ π‘˜    
  • C π‘˜ β‰ˆ π‘˜ ≫ π‘˜    
  • D π‘˜ ≫ π‘˜ ≫ π‘˜    
  • E π‘˜ ≫ π‘˜ β‰ˆ π‘˜    

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?

  • A βˆ’ π‘˜ π‘˜ π‘˜     [ A ]
  • B βˆ’ ( π‘˜ + π‘˜ )    [ A ]
  • C βˆ’ π‘˜  [ A ]
  • D βˆ’ π‘˜ π‘˜ π‘˜     [ A ]
  • E ( π‘˜ βˆ’ π‘˜ βˆ’ π‘˜ )     [ A ]

Q5:

A reaction proceeds via the following three elementary reactions.

  • R e a c t i o n 1 : A + B C , r a t e c o n s t a n t = π‘˜ 
  • R e a c t i o n 2 : C A + B , r a t e c o n s t a n t = π‘˜  
  • R e a c t i o n 3 : C D + E , r a t e c o n s t a n t = π‘˜ 

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

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

  • A π‘˜ π‘˜ βˆ’ π‘˜     [ A ] [ B ]
  • B π‘˜ π‘˜ + π‘˜     ( [ A ] + [ B ] )
  • C π‘˜ π‘˜ + π‘˜     [ A ] [ B ]
  • D π‘˜ π‘˜    [ A ] [ B ]
  • E π‘˜ π‘˜    ( [ A ] + [ B ] )

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

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

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

Which species act as catalysts in this reaction?

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

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

  • A π‘˜ ( π‘˜ βˆ’ π‘˜ )    
  • B π‘˜ π‘˜ π‘˜    
  • C π‘˜ ( π‘˜ βˆ’ π‘˜ )    
  • D π‘˜ π‘˜ π‘˜    
  • E π‘˜ βˆ’ π‘˜ π‘˜    

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: 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 6 N O C l N O + 2 N O + 4 C l O + C l 2 2 2 2 2
  • D 8 N O C l 4 N O + 6 C l O + C l 2 2 2 2
  • E 2 N O C l 2 N O + C l 2 2 2

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

  • A π‘˜ + π‘˜ π‘˜ + π‘˜ π‘˜ 1 2 βˆ’ 1 βˆ’ 2 3
  • B π‘˜ βˆ’ π‘˜ π‘˜ βˆ’ π‘˜ π‘˜ 1 βˆ’ 1 2 βˆ’ 2 3
  • C π‘˜ + π‘˜ + π‘˜ π‘˜ + π‘˜ 1 2 3 βˆ’ 1 βˆ’ 2
  • D π‘˜ ( π‘˜ βˆ’ π‘˜ ) ( π‘˜ βˆ’ π‘˜ ) 3 1 βˆ’ 1 2 βˆ’ 2
  • E π‘˜ π‘˜ π‘˜ π‘˜ π‘˜ 1 2 3 βˆ’ 1 βˆ’ 2

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

  • ARate = π‘˜[][][]NOClNOCl2222
  • BRate = π‘˜[][]NOClNO22
  • CRate = π‘˜[][]NOClCl22
  • DRate = π‘˜[][]NOClCl222
  • ERate = π‘˜[][]NOClNO222

Q8:

Compounds A and C react to form compound D with an overall rate constant π‘˜. The reaction involves three elementary reactions: reaction1:A2Brateconstantreaction2:2BArateconstantreaction3:B+CDrateconstant;=π‘˜;=π‘˜;=π‘˜οŠ§οŠ±οŠ§οŠ¨

Write a balanced chemical equation for the overall reaction.

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

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

  • A π‘˜ β‰ˆ π‘˜ + π‘˜    
  • B π‘˜ ≫ π‘˜   
  • C π‘˜ β‰ͺ π‘˜   
  • D π‘˜ β‰ˆ π‘˜   
  • E π‘˜ ≫ π‘˜   

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.

  • A ο„Ÿ π‘˜ π‘˜   
  • B π‘˜ ο„Ÿ π‘˜ π‘˜    
  • C π‘˜ ο„Ÿ π‘˜ π‘˜    
  • D π‘˜ ο„Ÿ π‘˜ π‘˜    
  • E π‘˜ ο„Ÿ π‘˜ π‘˜    

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

  • A1
  • B0
  • C 1 2
  • D2
  • E 3 2

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