15. The Rates of Chemical Reactions   Previous PageNext Page
       Exponential First Order Decay
The first-order rate law for the decay of carbon-14 nuclei,
 

is a differential equation. It tells us how the change in with time depends on . It would be desirable to have another expression that simply told how the varies with time in a first-order decay process:
  [C-14] = some function of t

Elementary calculus shows us how we can derive an expression for concentration versus time from a rate equation, using the process of integration. The general method is beyond the scope of this chapter, but we can give the result for a first-order decay:
  [C-14] = [C-14]oe-kt

Starting from an initial concentration at time t = O of [C-14]o the concentration of carbon-14 at some later time, t, decreases exponentially, as shown above. One property of exponential decay is that, if after a certain time interval the has fallen by half, then after another interval of equal length the concentration will have fallen by half again, or to one quarter its original value.

 

  Page 12 of 36 HomeGlossary