For the chemical reaction `A + 2B rarr C`, the rate of reaction is increased by `2.82` times when the concentration of `A` is doubled and increased by `9` times when the concentration of `B` was tripled. What is the order with respect to `B` and `A` and total order ?

Explanation

`A + 2B rarr C`
`r_(1) = k[A]^(x)[B]^(y)` …(i)
`r_(2) = 2.82r_(1) = k[2A]^(x)[B]^(y)` …(ii)
`r_(3) = 9r_(1) = [A]^(x)[3B]^(y)` …(iii)
Divide Eq. (ii) by Eq. (i),
`(2.82 r_(1))/(r_(1)) = (k[2A]^(x)[B]^(y))/(k[A]^(x)[B]^(y))`
`2.82 = (2)^(x) rArr (2)^(3//2) = (2)^(x) rArr x = 3//2`
Divide Eq. (iii) by Eq. (i),
`(9r_(1))/(r_(1)) = (k[A]^(x)[3B]^(y))/(k[A]^(x)[B]^(y))`
`9 = (3)^(y) rArr (3)^(2) = (3)^(y) rArr y = 2`
Order w.r.t. `B = 2` , order w.r.t. `A = 3//2`
Total order `= 2 + (3)/(2) = (7)/(2)`
Note: 1/ If rate increases by `2.82` times, order is `3//2`.
2. If rate increases by `5.6` times, order is `5//2`.