The initial rate of a reaction `A+B to` Products is doubled when the concentration of A is doubled and increases eight fold when the initial concentration of both A and B are doubled. State the order of the reaction with respect to A and with respect to B. Write the rate equation.

Explanation

Let for the given reaction,
Rate ` =k [A]^x [Y]^y`
Let the concentration of A and B be a and b respectively.
Now,`r=k [a]^x [b]^y `
` 2r =kr [2a]^x [b]^y`
` 8r =k [2a]^x [2b]^y`
Dividing eq (2) by (1), we get
` (2r)/(r ) = ( k[2a]^x [b]^y)/( k[a]^x [b]^y ) or 2=2^x or x=1`
hence order w.r.t A is 1
Again dividing eqatuion (3) by (2)
` (8r)/(2r) = 4= ((2a)^x (2b)^y)/((2a)^x (b)^y )=2^y`
` or 2^2 = 2^y or y=2`
hence order w.r.t B is 2
rate equation is r-k `[A]^1 [B]^2`