CBSE Class 12-science Answered

To illustrate this point, consider the reaction

A   ?   B

The rate of reaction, r, is given by

r = -

d [A] d t

Suppose this reaction obeys a first-order rate law:

r = k [A]

This rate law can also be written as

r = -

d [A] d t

= k [A]

This equation is a differential equation that relates the rate of change in a concentration to the concentration itself. Integration of this equation produces the corresponding integrated rate law, which relates the concentration to time. When you viewed concentration-time curves in previous pages, you viewed the integrated rate laws.

d [A] [A]

=

- k d t

At t = 0, the concentration of A is [A]₀. The integrated rate law is thus

[A] = [A]₀ e^{- k t}