You are performing an experiment in which the

Chapter 3, Problem 3.54

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You are performing an experiment in which the concentration, CA, of a reactive species is measured as a function of time, t, at several temperatures, T. At a fixed temperature, CAvaries with t according to the relation (1) where CA(mol/liter) is the concentration of A at time t(min), CAo(mol/liter) is the inital concentration of A, and k[L/(mol'min)] is the reaction rate constant. The rate constant in turn depends on temperature, according to the formula k == koexp[-E/(8.314T)] (2) where ko is a contant, T (K) is the reactor temperature, and E (l/mol) is the reaction activation energy. Write a computer program that will carry out the following tasks: (a) Read in MA , the molecular weight of A, and NT, the number of temperatures at which measurements were made. (b) For the first temperature, read in the value of T in e, the number of data points, N; and the concentrations and times (t1. CAl), (t2, CAl)... , (tn, CAn), where the times are in minutes and the concentrations are in grams of Alliter. (c) Convert the temperature to kelvin and the concentrations to mol AIL. (d) Use the method of least squares (Appendix A.1) in conjunction with Equation 1 to find the value of k that best fits the data. (Hint: First cast the equation in the form y = kx + b.) Store the values of k and T in arrays. (e) Print out in a neat format the values of T (K), the converted concentrations (mol/L) and times. and k. (f) Repeat steps (b) through (d) for the other temperatures. [For extra credit: Use the method of least squares again in conjunction with Equation 2 to determine the value of E that best fits the calculated (T, k) values. Again, start by casting Equation 2 in the form y = ax +b.] It will be convenient to perform the least-squares slope calculation in a subroutine, since it must be done repeatedly. Test your program on the following data: MA = 65.0 glmol T = 94C T = 110C T = 127C T = 142C t(min) CA(glL) CA(g/L) CA(glL) CA(giL) 10 8.1 3.5 1.5 0.72 20 4.3 1.8 0.76 0.36 30 3.0 1.2 0.50 0.24 40 2.2 0.92 0.38 0.18 50 1.8 0.73 0.30 0.15 60 1.5 0.61 0.25 0.12