For a reaction `A+B to C +2D`, experimental results were collected for three trials and the data obtained are given below:

The correct rate law of the reaction is

Options

A. Rate = `k[A]^(0)[B]^(2)`
B. Rate = `k[A][B]^(2)`
C. Rate = k[A][B]
D. Rate = `k[A][B]^(0)`

Answer

A

Explanation

Let the rate according to the law = `k[A]^(x)[B]^(y)`
Then from the experiments
`5.5xx10^(-4)=k[0.4]^(x)[0.2]^(y)` … (i)
`5.5xx10^(-4)=k[0.8]^(x)[0.2]^(y)` ….. (ii)
`2.2xx10^(-3)=k[0.4]^(x)[0.4]^(y)` ….. (iii)
From equation (i) and (ii)
`(5.5xx10^(-4))/(5.5xx10^(-4))=(k[0.4]^(x)[0.2]^(y))/(k[0.8]^(x)[0.2]^(y))`
`1=((0.4)/(0.8))^(x)=((1)/(2))^(x)impliesx=0`
From equations (i) and (iii), we have
`(5.5xx10^(-4))/(5.5xx10^(-3))=(k[0.4]^(x)[0.2]^(y))/(k[0.4]^(x)[0.4]^(y))`
`(1)/(4)=((0.2)/(0.4))^(y)=((1)/(2))^(y)impliesy=2`
Thus rate law
Rate = `k[A]^(0)[B]^(2)` .