What is rate constant of a reaction? Establish the relationbetween the rate constant of a first order reactionwith itshalf-life period. If half-life period of afirst order reaction is T sec, show that after nT sec [1-((1)/(2))^(n)]fraction of initial concentration of reactant has completely reactad.

What is rate constant of a reaction? Establish the relationbetween the

1.	What is rate constant of a reaction? Establish the relationbetween the rate constant of a first order reactionwith itshalf-life period. If half-life period of afirst order reaction is T sec, show that after nT sec [1-((1)/(2))^(n)]fraction of initial concentration of reactant has completely reactad.
Answer» Solution :THIRD part : LET the initial concentration of the reactant A, in first order reaction be `[A]_(0)` . Now , in NTS time , the reaction undergoes n number of half-lives. Therefore, after n NUMBEROF half-lives , concentration of the reactant will be `[A]_(0)//2^(n)` . `therefore` The AMOUNT of reactant completely reacted `=[A]_(0)-([A]_(0))/(2^(n))=[A]_(0){1-(1//2)^(n)}` So , after nT s of time ,`[1-(1//2)^(n)]` fraction of initial concentration of the reactant will completely react.