For a reactions `A + B rarr` product, it was found that rate of reaction increases four times if concentration of `'A'` is doubled, but the rate of reaction remains unaffected. If concentration of `'B'` is doubled. Hence, the rate law for the reaction is

Options

A. rate `= k[A] [B]`
B. rate `= k[A]^(2)`
C. rate `= k[A]^(2) [B]^(1)`
D. rate `= k[A]^(2) [B]^(2)`

Answer

B

Explanation

Let the rate of reaction depends on `x^(th)` power of `[A]`. Then
`r_(1) = k[A]^(x)` and `r_(2) = k[2A]^(x)`
`:. (r_(1))/(r_(2)) = ([A]^(x)]/([2A]^(x)] = (1)/(4) = ((1)/(2))^(2)` `(because r_(2) = 4r_(1))`
`:. x = 2`. As the reaction rate does not depend upon the concentration of `B`. Hence, the correct rate law will be rate
`= K[A]^(2) [B]^(@)` or `= K [A]^(2)`