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Deriving the equation for S* for competitive product inhibition

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Problem Statement:
Derive the equation for S* for competitive product inhibiton.

Definition of variables:
S* = the surface substrate concentration at steady state. (For plug flow reactor);

Sb = bulk substrate conc;
Ks = mass transfer coeff;
Ki = competitive inhibition rate constant;
Km = substrate conc that give 1/2 max enzyme reaction rate;
Vmax = max specific growth rate;
V= specific growth rate;

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Solution Summary

The derivation of the equation for S* for competitive product inhibition is outlined. The competitive inhibition rate constants are given.

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Ns=Ks(Sb-S*)=(V'maxS*)/(Km+S*+P(Km/Ki)) ...

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