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 CA (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 CA0. Write a balance on A and integrate it to obtain an expression for the time required to achieve a specified concentration Ck.

(b) Use the expression of part (a) to devise a graphical method of determining k, and k. 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.