For a reaction , X+Y rarr Product , quadrupling [x] . Increases the rate by afactor of 8 . Quadrupling both [x] and [y] , increases the rate by a factor of 16. Find the order of the reaction with respect to x and y . What is the overall order of the reaction.

For a reaction , X+Y rarr Product , quadrupling [x] . Increases the ra

1.	For a reaction , X+Y rarr Product , quadrupling [x] . Increases the rate by afactor of 8 . Quadrupling both [x] and [y] , increases the rate by a factor of 16. Find the order of the reaction with respect to x and y . What is the overall order of the reaction.
Answer» Solution :`{:(,X+yrarr,"Product(Z)"),(,x+yrarr,z),("condition"-1implies,4x+y,8),("condition"-2implies,4x+4yrarr,16):}` `z=k[x]^m[y]^n""(1)` `8Z=k[4x]^m[y]^n""(2)` `16z=k[4x]^m[4y]^n""...(3)` Dividing Eq (2) by Eq (1) we get `(8z)/z=(k[4x]^m[y]^n)/(k[x]^m[y]^n)` `8=4^mrArr2^3=(2^2)^mimplies2^3=2^(2m),2m=3,m=3//2` 1.5 ORDER with respect to x . Dividing Eq (3) by Eq (1) we get , `(16z)/z = (k[4x]^m[4y]^n)/(k[x]^m[y]^n)` `16=4^m.4^n` `16=4^2.4^n` `16/16=4^n` `1 = 4n ` `:. n = 0 ` [Zero order with respect to y ] OVERALL order of the reaction , `k[x]^m[y]^n` `k[x]^(1.5)[y]^0` Order `=(1.5+0)=1.5`