GATE2016-52

Question

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.