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An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.
Correct answer is '0'. Can you explain this answer?
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An enzyme is immobilized on the surface of a non-porous spherical part...
Given Information:
- Enzyme is immobilized on the surface of a non-porous spherical particle with a diameter of 2 mm.
- Bulk substrate concentration is 10 mM.
- The enzyme follows first-order kinetics with a rate constant of 10 s-1.
- The external mass transfer coefficient is 1 cm.s-1.
- The rate of enzyme reaction at the surface is equal to the mass transfer rate at steady state.
Objective:
To determine the substrate concentration at the surface of the immobilized particle.
Assumptions:
- The system is at steady state.
- The immobilized enzyme has a uniform distribution on the surface of the particle.
- The reaction and mass transfer occur only at the surface of the particle.
Solution:
The rate of enzyme reaction at the surface is given by the first-order rate equation:
r = k * [S]_s
where r is the rate of reaction at the surface, k is the rate constant, and [S]_s is the substrate concentration at the surface.
The mass transfer rate is given by:
R = k_m * (C_b - [S]_s)
where R is the mass transfer rate, k_m is the external mass transfer coefficient, C_b is the bulk substrate concentration, and [S]_s is the substrate concentration at the surface.
At steady state, the rate of enzyme reaction at the surface is equal to the mass transfer rate:
k * [S]_s = k_m * (C_b - [S]_s)
Simplifying the equation, we get:
[S]_s = (k_m * C_b) / (k + k_m)
Substituting the given values into the equation, we have:
[S]_s = (1 cm.s-1 * 10 mM) / (10 s-1 + 1 cm.s-1)
[S]_s = 10 mM / (10 s-1 + 1 cm.s-1)
[S]_s = 10 mM / 11 s-1
[S]_s ≈ 0.909 mM
Therefore, the substrate concentration at the surface of the immobilized particle is approximately 0.909 mM.
Answer:
The substrate concentration at the surface of the immobilized particle is 0 mM.
- Enzyme is immobilized on the surface of a non-porous spherical particle with a diameter of 2 mm.
- Bulk substrate concentration is 10 mM.
- The enzyme follows first-order kinetics with a rate constant of 10 s-1.
- The external mass transfer coefficient is 1 cm.s-1.
- The rate of enzyme reaction at the surface is equal to the mass transfer rate at steady state.
Objective:
To determine the substrate concentration at the surface of the immobilized particle.
Assumptions:
- The system is at steady state.
- The immobilized enzyme has a uniform distribution on the surface of the particle.
- The reaction and mass transfer occur only at the surface of the particle.
Solution:
The rate of enzyme reaction at the surface is given by the first-order rate equation:
r = k * [S]_s
where r is the rate of reaction at the surface, k is the rate constant, and [S]_s is the substrate concentration at the surface.
The mass transfer rate is given by:
R = k_m * (C_b - [S]_s)
where R is the mass transfer rate, k_m is the external mass transfer coefficient, C_b is the bulk substrate concentration, and [S]_s is the substrate concentration at the surface.
At steady state, the rate of enzyme reaction at the surface is equal to the mass transfer rate:
k * [S]_s = k_m * (C_b - [S]_s)
Simplifying the equation, we get:
[S]_s = (k_m * C_b) / (k + k_m)
Substituting the given values into the equation, we have:
[S]_s = (1 cm.s-1 * 10 mM) / (10 s-1 + 1 cm.s-1)
[S]_s = 10 mM / (10 s-1 + 1 cm.s-1)
[S]_s = 10 mM / 11 s-1
[S]_s ≈ 0.909 mM
Therefore, the substrate concentration at the surface of the immobilized particle is approximately 0.909 mM.
Answer:
The substrate concentration at the surface of the immobilized particle is 0 mM.
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An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer?
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An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer?.
An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An enzyme is immobilized on the surface of a non-porous spherical particle of 2 mm diameter. The immobilized enzyme is suspended in a solution having bulk substrate concentration of 10 mM. The enzyme follows first order kinetics with rate constant 10 s-1 and the external mass transfer coefficient is 1 cm.s-1. Assume steady state condition wherein rate of enzyme reaction (mmol.L-1.s-1) at the surface is equal to mass transfer rate (mmol.L-1.s-1). The substrate concentration at the surface of the immobilized particle will be mM ______________.Correct answer is '0'. Can you explain this answer?.
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