In an enzyme-catalyzed reaction with stoichiometry A → B, A is consumed at a rate given by an expression of the Michaelis–Menten form:

where C_A(mol/L) is the reactant concentration, and k₁ and k₂ depend only on temperature.

(a) The reaction is carried out in an isothermal batch reactor with constant reaction mixture volume V (liters), beginning with pure A at a concentration C_A0. Derive an expression for dC_A/dt, and provide an initial condition. Sketch a plot of CA versus t, labeling the value of CA at t = 0 and the asymptotic value as t → 1.

(b) Solve the differential equation of Part (a) to obtain an expression for the time required to achieve a specified concentration CA.

(c) Use the expression of Part (b) to devise a graphical method of determining k₁ and k₂ from data for CA versus t. Your plot should involve fitting a straight line and determining the two parameters from the slope and intercept of the line. (There are several possible solutions.) Then apply your method to determine k1 and k2 for the following data taken in a 2.00-liter reactor, beginning with A at a concentration C_A0 = 5:00 mol/L.

Transcribed Image Text:

kịCA ralmol/(L-s)] : 1+ K2CA