Immobilized Enzyme Kinetics — During reaction, how does the rate of substrate transfer to the immobilized catalyst compare to the rate of substrate consumption?
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AThey are equal at steady state (flux into the particle matches consumption by reaction).
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BTransfer rate is always greater than consumption rate regardless of conditions.
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CTransfer rate is always less than consumption rate regardless of conditions.
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DTransfer rate is unrelated to consumption rate.
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EThey are equal only for free enzymes in homogeneous solution.
Answer
Correct Answer: They are equal at steady state (flux into the particle matches consumption by reaction).
Explanation
Introduction:For immobilized enzymes, mass transfer and reaction occur simultaneously. At steady state, the substrate flux entering the catalyst region must balance the rate at which reaction consumes substrate; otherwise, concentrations would change with time. Understanding this balance is essential for modeling and diagnosing diffusion limitations.
Given Data / Assumptions:
- System has reached steady state (no accumulation within the control volume).
- External conditions (bulk concentration, temperature, flow) are constant.
- Reaction occurs throughout the accessible catalytic region.
Concept / Approach:
A steady-state material balance on the immobilized phase sets accumulation to zero, so input by diffusion (and possibly convection within pores) equals consumption by reaction. This equality holds globally for the particle and locally in differential form within the diffusion–reaction model. Deviations occur during transients but not at steady state, which is the typical operating assumption in reactor analysis.
Step-by-Step Solution:
Define a particle control volume; set accumulation term to zero at steady state.Write balance: rate of substrate transfer in − rate of substrate transfer out − rate of consumption = 0.For a reacting particle without product back-diffusion of substrate, this reduces to transfer in = consumption.Conclude that at steady state, the two rates are equal.Verification / Alternative check:
Effectiveness-factor models show that overall reaction rate equals the diffusive flux at the particle surface; measured fluxes match conversion rates when the system is steady.
Why Other Options Are Wrong:
B and C assert one rate always dominates, which violates the steady-state balance. D denies the conservation principle. E incorrectly restricts the equality to homogeneous systems.
Common Pitfalls:
Confusing transient start-up (when accumulation exists) with steady operation; always verify time invariance before applying steady-state equalities.
Final Answer:
They are equal at steady state (flux into the particle matches consumption by reaction).