In first order reactions, the rate of reaction will be proportional to the concentration of the reactant. Thus the concentration will decrease exponentially.
as time progresses until it reaches zero, and the half-life will be constant, independent of concentration.
The time  for  to decrease from  to  in a first-order reaction is given by the following equation:It can be solved forFor a first-order reaction, the half-life of a reactant is independent of its initial concentration. Therefore, if the concentration of  at some arbitrary stage of the reaction is , then it will have fallen to  after a further interval of  Hence, the half-life of a first order reaction is given as the following:The half-life of a first order reaction is independent of its initial concentration and depends solely on the reaction rate constant, .