A reaction `P rarr Q` is completed 25 % in 25 min, 50 % completed in 25 min if [P] is halved, 25 % completed in 50 min if [P] is doubled. The order of reaction is

Options

A. 1
B. 2
C. 0
D. 3

Answer

C

Explanation

By hit and trial method, if reaction is of zero order,
`k = (1)/(t){[A]_(0)-[A]}`
Case I. `k = (1)/(25) xx (25)/(100) = 10^(-2)`
Case II. `k = (1)/(25) xx (1)/(2) {[A]_(0)-[A]}` (as [P] is halved)
`= (1)/(25) xx (1)/(2) xx (50)/(100) = 10^(-2)`
Case III. `k = (1)/(50) xx 2{[A]_(0)-[A]}`
`" "` (as [P] is doubled )
` = (1)/(50)k xx 2 xx (25)/(100) = 10^(-2)`
As k comes out to be constant, hence the given reaction is of zero order.