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. `1(1)/(2)`
D. `1(1)/(3)`

Answer

C

Explanation

Reaction `A+B to C+D`
According to question,
`r=k[A]^(x)[B]^(y)` . . . (1) `2r=k[2A]^(x)[B]^(y)` . . (2)
`3r=k[A]^(x)[9B]^(y)` . . (3)
Dividing equation (2) by (1)
`2=2x` or x=1
Similarly, dividing equation (3) by (1)
`3=[9]^(y) or 3=3^(2y) or 2y=1`
`y=(1)/(2)`
Hence order of reaction `1+(1)/(2)=1(1)/(2)`