For a reaction `A+B rarr C+D` if the concentration of A is doubled without altering the concentration of B, the rate gets doubled. If the concentration of B is increased by nine times without altering the concentration of A, the rate gets tripled. The order of the reaction is

Options

A. 2
B. 1
C. `3//2`
D. `4//3`

Answer

C

Explanation

`A+B rarr C+D`
`r=K[A]^(alpha)[B]^(beta) " "` ….(i)
`2r=K[2A]^(alpha)[B]^(beta) " "` ….(ii)
`3r=K[A]^(alpha)[9B]^(beta) " "` …..(iii)
Dividing eqn. (ii) by eqn. (i)
`2=2^(alpha)` or, `alpha =1`
Dividing eqn. (iii) by eqn. (i)
`3=9^(beta)` or, `3=3^(2beta)` or, `2beta =1` or, `beta = 1//2`
`therefore` Order of the reaction `=1+(1)/(2)=(3)/(2)`.