For the reaction ` A + 2B to ` C, the reaction rate is doubled if the concentration of A is doubled , the rate is increased by four times when concentrations of both A and B are increased by four times . The order of the reaction is _______.

Options

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

Answer

C

Explanation

Rate, `r = k [A]^(a)[B]^(b)" "…(i)`
`2r = [2 A]^(a) [B]^(b)" "…(ii)`
`4r = [ 4 A ]^(a) [ 4 B]^(b) " "…(iii)`
Divding eqn. (ii) by eqn. (i), `2 = 2^(a) therefore a = 1`
Divding eqn. (ii) by eqn. (i)
`4 = 4^(a) 4^(b) = 4 xx 4^(b) = 4^(b+1)`
`therefore b + 1 = 1 or b = 0`
Hence, overall order = 1.