Consider the kinetic data given in the following table for the reaction `A+B+C rarr` Product.

The rate of the reaction for `[A] =0.15" mol dm"^(-3), [B]=0.25" mol dm"^(-3) and [C] =0.15" mol dm"^(-3)`, is found to be `Y xx 10^(-5)" mol dm"^(-3) s^(-1)`. The value of Y is ____.

Explanation

`r=k[A]^(x)[B]^(y) [C]^(z)`
`6xx10^(-5)=k (0.2)^(x) (0.1)^(y) (0.1)^(z)" ……(i)"`
`6xx10^(-5)=k (0.2)^(x) (0.2)^(y) (0.1)^(z)" ……..(ii)"`
`1.2xx10^(-4)=k (0.2)^(x) (0.1)^(y) (0.2)^(z)" …….(iii)"`
`9xx10^(-5) =k (0.3)^(x) (0.1)^(y) (0.1)^(z)" .....(iv)"`
From (i) & (ii) `rArr y=0`
From (i) & (iii) `rArr z=1`
From (i) & (iv) `rArr x=1`
`therefore" "r=k[A] [C]`
From equation (i)
`6xx10^(-5)=k(0.2) (0.1)`
`k=(6xx10^(-5))/(2xx10^(-2))=3xx10^(-3)" "therefore r=3xx10^(-3) [A] [C]`
For `[A] =0.15" mol dm"^(-3), [B] =0.25" mol dm"^(-3) & [C] =0.15" mol dm"^(-3)`
`r=3xx10^(-3)xx0.15xx0.15`
`r=6.75xx10^(-5)" "therefore y=6.75`