The rate of reaction for an enzyme-catalyzed substrate in a batch reactor can be

Question

The rate of reaction for an enzyme-catalyzed substrate in a batch reactor can be described by the following relationship (Michealis-Menten equation).

KM [S] where maximum reaction rate, molL min Km Michealis Menten rate constant a. Using this rate expression, derive an equation that can be used to predict the reduction of substrate concentration with time in a batch reactor. b. If k equals 40 molL min and Km 100 molL, determine the time required to decrease the substrate concentration from 1000 to 100 molL.

Explanation / Answer

For batch reactor ,

dS/dt = k(S)/(km + S)

Initial concentration of S = S0 at time t=0

k(S)/(km + S) dS = dt

t= k((S-S0) - km* log((km+S0)/(km+S)))

Given km = 100; k = 40 and S0 = 1000 and S = 100

t= 35925

Units are not given in question

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