Consider the reaction, `A + B to C + D`.
The initial rate for different initial concentrations of the reactants are given below :

What is the overall order ?

Explanation

For the given reaction, rate `= k [A]^x [B]^y` . After substituting the values of initial rates and initial concentrations, the value of x and y can be calculated. Then (x + y) will give the order of the reaction. For experiment (i) `2.0 xx10^(-3) = [1.0]^(x) [1.0]^y`
For experiment (ii) `4.0 xx 10^(-3) = [2.0]^x [1.0]^y` ...(2)
For experiment (iii) `8.0 xx 10^(-3) = [4.0]^x [1.0]^y `
For experiment (iv) `2.0 xx 10^(-3) = [1.0]^x [2.0]^y`
For experiment (v) `2.0 xx 10^(-3) =[1.0]^x [4.0]^y`
Determination of x. In order to get the value of x, divide equation (2) by (1)
` ( 4.0 xx 10^(-3))/( 2.0 xx 10^(-3)) = ([2.0 ]^x [1.0 ]^y)/([1.0 ]^x[1.0]^y), (2)^1 =(2)^x or x=1`
Determination of y. In order to get the value of y, divide equation (4) by (1)
`(2.0 xx 10^(-3))/(2.0 xx 10^(-3)) =([1.0 ]^x [2.0 ]^y)/( [1.0]^x [1.0]^y), (1)^1 = [2.0]^y or y=0`
The overall order of reaction = 1+0=1