When i was reading text from a book i came to read a fact
" the collison are not so effective in heterogeneous system as in homogenous systems "
I tried to proof it mathematically
I assumed i have container who have 10 molecules of x and 10 molecules of y ...
Let the volume of container be 10 units..
Now i seperated the container into two equal parts (say A and B) by a imaginary line...
X and Y following first order of kinetics.
Case 1 : Homogeneous system
5 molecules of each x and y are in A as in B
So the average rate = k/2 ( [X]A[Y]A + [X]B[Y]B )
(I divided the whole equation by 2 because i am measuring the average reaction.....reactions in two different containers are going on independently..)
Rate = k/2 ( (5/5)(5/5) + (5/5)(5/5) )
= k
Case 2 - heterogenous system
Say in A , 6 X and 4 Y and
In B, 6 Y and 4 X
Rate = k/2 ( (6/5)(4/5) + (4/5)(6/5) )
= 0.96k
Case 3 : heterogeneous system
In A , 6 X , 6 Y
In B , 4 X , 4 Y
Average rate = k/2 ( (6/5)(6/5) + (4/5)(4/5) )
= 1.04k
So what is the problem with case 3 .?
It is opposing the fact..!!!