Many physical processes can be modeled by an exponential equation. For example, chemical reaction rates depend on a reaction-rate constant that is a function of temperature and activation energy:

                                                             

In this equation,

R = universal gas constant, 8.314 kJ/kmol K ,

Q = activation energy, in kJ/kmol,

T = temperature, in K, and

k₀ = constant whose units depend on characteristics of the reaction. One possibility is s^-1.

One approach to fi nding the values of k₀ and Q from experimental data is to plot the natural logarithm of k on the y-axis and 1/ T on the x-axis. This should result in a straight line with slope -Q /R and intercept ln(k₀)—that is,

                                           

since the equation now has the form

                                        y = ax + b

with . Now consider the following data: T,

                                            

(a) Plot the data with 1/ T on the x-axis and ln( k) on the y-axis.

(b) Use the polyfit function to find the slope of your graph, -Q /R,and the intercept, ln(k₀).

(c) Calculate the value of Q. (d) Calculate the value of k₀.