The Swedish physicist/chemist Svante Arrhenius derived the equation which relates the rate of a chemical reaction, r, to the temperature, T, (with units K), the gas constant, R (with units J mol−1 K

−1

), and the reaction’s activation energy, Ea (with units J mol−1

). The Arrhenius equation is r(T) = Ae

−Ea RT , where A and Ea are positive constants (they will be different for different reactions, of course).

a. What is the scientific domain?

b. What is the scientific range for the Arrhenius equation?

(Use any appropriate software to help you. You will probably find it very helpful to draw a graph of the function. To do this, just pick arbitrary positive values for A and Ea.)

c. Rewrite this equation three times; (i) making A the subject, (ii) making Ea the subject, and (iii) making T the subject.

d. If T is increasing, what happens to the value of (i) 1 T , (ii) −
1 T , (iii) −
Ea RT , (iv) e −
Ea RT ?