The reaction `Aoverset(k)rarr` Product, is zero order while the reaction `Boverset(k)rarr` Product, is first order reaction. For what intial concentration of A are the half lives of the two reacions equal?

Options

A. `(log_(2)4) M`
B. 2M
C. 2 log 2 M
D. ln 2 M

Answer

A

Explanation

For zero order reaction,
x=kt
`:. (a)/(2)=kxxt_(1//2),i.e.,t_(1//2)=(a)/(2k)" ".....(i)`
For frist order reaction,
`t_(1//2)=(log_(e)2)/(k)" ".....(ii)`
From eqs. (i) and (ii), `(a)/(2k)=(log_(e)2)/(k)`
`a=log_(e)4M`