A first-order reaction has a rate law in which the sum of the exponents is equal to 1. In a first–order reaction, the reaction rate is directly proportional to the concentration of one of the reactants. A first–order reaction depends on the concentration of one reactant, and the rate law is:
r=−dAdt=k[A] r = − dA dt = k [ A ] .
For a first–order reaction, a plot of the natural logarithm of the concentration of a reactant versus time is a straight line with a slope of −k.