Half-lives of a first order and a zero order reaction are same. Then the ratio of the initial rates of the first order reaction to that of zero order reaction is

Options

A. `(1)/(0.693)`
B. `2xx0.693`
C. `0.693`
D. `(2)/(0.693)`

Answer

B

Explanation

`t_(1//2)` for 1 st order reaction `= (0.693)/(k)`
`t_(1//2)` for zero order reaction `=([A]_(0))/(2k)`
Initial rate for 1st order reaction `(r_(1)) = k[A]_(0)`
Initial rate for zero order reaction `(r_(0)) = k'`
`therefore (r_(1))/(r_(0)) = (k[A]_(0))/(k')`
But `(0.693)/(k) = ([A]_(0))/(2k')`
`therefore (k[A]_(0))/(k') = 2 xxx 0.693, i.e., (r_(1))/(r_(0)) = 2 xx 0.693`