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

Options

A. `1(1)/(2)`
B. `1(1)/(3)`
C. 2
D. 1

Answer

A

Explanation

rate, `r=k[A]^(m)[B]^(n)` (say)
Let initial `[A]=aM and [B] = bM`
`:. r_(1) = k a^(m)b^(n)`
`r_(2)=k(2a)^(m)b^(n)`
`r_(3) = k a^(m)(9b)^(n)`
`(r_(2))/(r_(1))=2,(r_(3))/(r_(1))=3`
`:. M = 1,n=1//2`
`:.` Order of reaction `= m+n`
`= 1 + (1)/(2)=1(1)/(2)`.