Conisder a reaction `X + Y rarr` Products. If the initial concentration of `X` increased to four times of its original value, keeping the concentration of `Y` constant, the rate of reaction increases four-fold. When the concentration of both `X` and `Y` becomes four times their original values the rate of reaction becomes `16` times its original values. The observed rate law is

Options

A. `k[X]^(2)[Y]^(2)`
B. `k[X]^(1)[Y]^(2)`
C. `k[X]^(1)[Y]^(1)`
D. `k[X]^(2)[Y]^(1)`

Answer

C

Explanation

`r_(1) = k[X]^(m)[Y]^(n)` …(i)
`r_(2) = 4r_(1) = k[4X]^(m)[Y]^(n)` …(ii)
`r_(3) = 16r_(1) = k[4X]^(m)[4Y]^(n)` …(iii)
Divide Eq. (ii) by Eq. (i),
`4 = (4)^(m) rArr (4)^(1) = (4)^(m) rArr m = 1`
Divide Eq. (iii) by (ii),
`4 = (4)^(n) rArr (4)^(1) = (4)^(n) rArr n = 1`
The observed rate law `= k[X]^(1)[Y]^(1)`