The rate constants of two first order reactions at a specific temperature are `k_(1) and k_(2)` , respectively . If `k_(1)gtk_(2)` , then which reaction has a longer half-life ?

Explanation

For the first order reaction , `t_(1/2)=(0.693)/(k) " i.e.,"t_(1/2)prop(1)/(k)` . Thus the reaction having higher rate constant will have shorter half-life and vice- versa . As the value of `k_(2)` is lower than `k_(1)` , hence the reaction having rate constant `k_(2)` will have longer half -life.