An enzyme is immobilized on the surface of a non-porous

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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 (m mol.L^–1.s^–1) at the surface is equal to mass transfer rate (m mol.L^–1.s^–1). The substrate concentration at the surface of the immobilized particle will be ________ mM.

1. 8.5 : 8.5
2. 7.5 : 7.5
3. 5.5 : 5.5
4. 2.5 : 2.5

Correct Option: B

V₁ =	V_maxA[s]	, V₂ = K_LA([s₀] - [s])
	K_m + [S] +

Reaction rate Mass transfer rate
The given condition is
V₁ = V₂ at steady state.
Further V_max = K_Ls_o = 1 × 10 = 10.
∴ 10|s| = [10 – s] ⇒ s² + 10s – 100 = 0
Solving for s

Using	- b ± √b² - 4ac
	2a

s = 6.180 or – 16.180
∴ s = 6.180