For the non-stoichiometric reaction `2A +B rarr C+D`, The following data were obtained in three separate experiments, all at 298 K.

The rate law for the formation of C is:

Options

A. `(dc)/(dt)=k[A][B]`
B. `(dc)/(dt)=k[A]^(2)[B]`
C. `(dc)/(dt)=k[A][B]^(2)`
D. `(dc)/(dt)=k[A]`

Answer

D

Explanation

Let rate of reaction `=(d[C])/(t) = k[A]^(x) [B]^(y)`
Now from the given data
`1.2 xx 10^(-3)=k[0.1]^(x)[0.1]^(y)` ...(i)
`1.2 xx 10^(-3)=[0.1]^(x)[0.2]^(y)` ...(ii)
`2.4 xx 10^(-3)=[0.2]^(x)[0.1]^(y)` ...(iii)
Dividing equation (i) by (ii)
`implies (1.2 xx 10^(-3))/(1.2 xx 10^(-3))=(k[0.1]^(x)[0.1]^(y))/(k[0.1]^(x)[0.2]^(y))`
We find, y = 0
Now dividing equation (i) by (iii) `implies (1.2 xx 10^(-3))/(2.4 xx 10^(-3))=(k[0.1]^(x)[0.1]^(y))/(k[0.2]^(x)[0.1]^(y))`
We find, x = 1
Hence `(d[C])/(dt)=k[A]^(1)[B]^(0)`