The concentration, r, of reactants over the course of a simple chemical reaction is defined by Since r is decreasing along an exponential curve, this is called exponential decay. r(t) = Re−kt

, where k is the rate constant, t is time and R is the initial concentration of the reactant. Let k be 100 s−1

.

b. Plot r(t) for R = 1 and R = 5.

c. With the aid of your table and plots deduce i. For what value of t is r(t) approximately half of r(0)?
ii. For what value is r(t) equal to r(0)/e (roughly 36% of r(0))?

d. Two of the most common ways to describe an exponential decay process are to use lifetime (τ) and half-life (t1/2).
The former is defined as the time it takes for the amount remaining to reach 1/e of the original, and the latter, for the amount to reach half of the original material. What are τ and t1/2 as functions of R and k? Are they functions of R?