Catalytic Sequences - Steady State Hypothesis - PowerPoint PPT Presentation

1 / 9
About This Presentation
Title:

Catalytic Sequences - Steady State Hypothesis

Description:

Catalytic Sequences - Steady State Hypothesis Gates considers a catalytic reaction sequence in which an intermediate product, R1C, is highly reactive. – PowerPoint PPT presentation

Number of Views:90
Avg rating:3.0/5.0
Slides: 10
Provided by: pare97
Category:

less

Transcript and Presenter's Notes

Title: Catalytic Sequences - Steady State Hypothesis


1
Catalytic Sequences - Steady State Hypothesis
  • Gates considers a catalytic reaction sequence in
    which an intermediate product, R1C, is highly
    reactive.

C catalyst R reactant P product
k12
k13
fast
k14
2
Catalytic Sequences - Steady State Hypothesis
  • The elementary reactions that make up this
    closed, catalytic sequence are
  • 1.
  • 2.
  • 3.
  • Of interest is the rate of product
  • formation, as dictated by
  • reaction 3.

C catalyst R reactant P product
k12
k13
fast
k14
3
Catalytic Sequences - SSH
  • Application of the SSH to R1C in the simple
    catalytic cycle yields
  • (A)
  • from which the rate of product formation is,
  • (B)
  • and the rate of R1 consumption is
  • These rates are, by nature of the SSH, equal.

4
Catalytic Sequences - SSH
  • Our rate expression is a function of variables
    that are rarely known, R1C or C. A rate
    expression based on the total catalyst
    concentration, CT, is more useful from a design
    perspective
  • According to this mechanism, the active agent
    exists in just two states. The resulting
    material balance is
  • Substituting for C using equation (A) and
    solving for R1C gives
  • Substituting this into equation (B) provides the
    more useful relation

5
Catalytic Sequences - Rate Determining Step
  • Even with a small number of steps, the rate
    expression of a sequence is rather complicated in
    spite of the SSH.
  • Frequently it can be assumed with considerable
    success that a given step in the sequence is
    rate-determining.

6
Catalytic Sequences - Rate Determining Step
  • If one step of a sequence is rate determining,
    all other steps will be in quasi-equilibrium.
  • the problem is reduced to the kinetics of a
    single step and the equilibrium position of all
    others.
  • In our generic example, the two reactions are
  • Reaction 1 Near equilibrium
  • Reaction 2 Rate determining
  • The overall rate of reaction (r) equals that of
    reaction 2
  • If one step of a sequence is rate determining,
    all other steps will be in quasi-equilibrium.
  • the problem is reduced to the kinetics of a
    single step and the equilibrium position of all
    others.
  • In our generic example, the two reactions are
  • Reaction 1 Near equilibrium
  • Reaction 2 Rate determining
  • The overall rate of reaction (r) equals that of
    reaction 2

7
Catalytic Sequences - Rate Determining Step
  • With reaction 1 achieving a near-equilibrium
    state, we can write
  • where K1 represents the equilibrium constant.
  • In order to express r as a function of measurable
    quantities, we need a mass balance on the total
    amount of catalyst CT.
  • We can now express the concentration of the
    intermediate R1C as

8
Catalytic Sequences - Rate Determining Step
  • The overall rate of reaction in terms of useful
    quantities becomes
  • Rate-determining
  • step approach
  • If we reexamine our SSH solution, deriving the
    reaction rate as a function of total catalyst
    concentration, we find
  • SSH approach

9
Catalytic Sequences - Rate Determining Step
  • The water-gas shift reaction catalyzed by a
    supported metal with an active site (S) may be
    treated with the rate determining step approach.
  • Simplified Reaction Sequence
  • r1
  • r2
  • If CO and H2O are passed continuously over the
    catalyst, the system will come to a steady state
    condition where all concentrations are constant.
  • Exercise Assuming that reaction 2 is rate
    limiting, derive an expression for the overall
    reaction rate as a function of measurable
    quantities.
Write a Comment
User Comments (0)
About PowerShow.com