A reaction `2A + B overset(k)rarr C+ D` is first order with respect to `A` and 2nd order with respect to `B`. Initial conc. `(t = 0)` of `A` is `C_(0)` while `B` is `2C_(0)`. If at `t` as `30` minutes the conc. of `C` is `C_(0)//4`, then rate expression at `t = 30` minutes is:

Options

A. `R = 7 C_(0)^(3) k//16`
B. `R = 27C_(0)^(3) k//32`
C. `R = 247 C_(0)^(3) k//64`
D. `R = 49 k C_(0)^(3)//32`

Answer

D

Explanation

`2 A + B overset (k)rarr C + D`
`r = K[A]^(1) [B]^(2) r_(0) = K(C_(0))^(1) (2C_(0))^(2) = 4 K(C_(0))^(3)` …(i)
`{:(,2A+,Boversetkrarr,C+,D),(t=0,C_0,2C_0,0,0),(,(C_0-2x),(2C_0-x),x,x):}`
`x = ((C_(0))/(4)) [A] = CO - (C_(0))/(2) = (C_(0))/(2)`
`[B] = 2 CO - (C_(0))/(4) = (7C_(0))/(4)`
`r = K((C_(0))/(2))((7C_(0))/(7))^(2) = (49K(C_(0))^(3))/(32)`