The half- life of a first order reaction is ' p ' and its 3 / 4^ th life period is ' q '. p and q are related to each other by: [Given: 3=0.4771, 4=0.6040 ]

Step-by-step solution

For a first order reaction, the rate constant k is given by k = 2 p , where p is the half-life. The 3/4^ th life period q is the time taken for the concentration to reduce to 1/4 of its initial value. The integrated rate equation is k = 1 q ( [A]₀ [A]_t ) . Substituting [A]_t = 1 4 [A]₀ , we get k = 1 q (4) = 2 2 q . Equating the two expressions for k : 2 p = 2 2 q . Simplifying this, we get 1 p = 2 q , which implies q = 2p or 2p = q . Answer: 2 p=q