The bromination of acetone that occurs in acid solution is represented by `CH_(3)COCH_(3)(aq)+Br_(2)(aq)rarrCH_(3)COCH_(2)Br(aq)+H^(+)(aq)+Br^(-)(aq)`
These kinetic data were obtained for given reaction concentration

Based on these data rate equation is

Options

A. Rate `k[CH_(3)COCH_(3)][Br_(2)][H^(+)]^(2)`
B. Rate `k[CH_(3)COCH_(3)][Br_(2)][H^(+)]`
C. Rate `k[CH_(3)COCH_(3)][H^(+)]`
D. Rate `k[CH_(3)COCH_(3)][Br_(2)]`

Explanation

Rate = `[k[CH_(3)COCH_(3)]^(alpha)[Br_(2)]^(beta)[H^(+)]^(gamma)`
`5.7 xx 10^(-5) = k[0.30]^(alpha)[0.05]^(beta)[0.05]^(gamma)` …(i) `5.7 xx 10^(-5) = k[0.30]^(alpha) [0.10]^(beta)[0.05]^(gamma)` …(ii)
`1.2 xx 10^(-4) = k [0.30]^(alpha)[0.10]^(beta)[0.10]^(gamma)` ...(iii) `3.1 xx 10^(-4) = k[0.40]^(alpha)[0.05]^(beta)[0.20]^(gamma)` ...(iv)
Dividing eq. (i) by eq. (ii), `1 = [(1)/(2)]^(beta)`, ie., `beta = 0`
Dividing eq. (ii) by eq. (iii), `1 = [(1)/(2)]^(gamma)`, ie., `gamma = 1`
Dividing eq. (i) by eq. (iv), `(5.7 xx 10^(-5))/(3.1 xx 10^(-4)) = [(3)/(4)]^(alpha) xx [(1)/(4)]^(1)`
`alpha = 1`. Thus, rate law will be, rate `= k[CH_(3)COCH_(3)]^(1)[H^(+)]^(1)`