In an enzyme-catalyzed reaction with stoichiometry A ! B, A is consumed at a rate given

Chapter 10, Problem 10.22

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In an enzyme-catalyzed reaction with stoichiometry A ! B, A is consumed at a rate given by an expression of the MichaelisMenten form: rA mol/Ls k1CA 1 k2CA where CAmol/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 CA0. Derive an expression for dCA=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 CA0 5:00 mol/L. ts 60.0 120.0 180.0 240.0 480.0 CAmol/L 4.484 4.005 3.561 3.154 1.866