Question
The following results have been obtained during the kinetic studies of the reaction:
2A + B → C + D
|
exp.
|
[A]/ |
[B]/M |
Initial rate of formation |
|
I |
0.1 |
0.1 |
|
|
II |
0.3 |
0.2 |
7.2 x 10–2 |
|
III |
0.3 |
0.4 |
2.88 x 10–1 |
|
IV |
0.4 |
0.1 |
2.40 x 10–2 |
Determine the rate law and the rate constant for the reaction.
Solution
Let rate law of reaction be,
where x and y are order of reaction w.r.t. A and B respectively.
From experiments I and IV, we can write
6.0 x 10–3 = k[0.1]y [0.1]y ...(i)
2.4 x 10–2 = k[0.4]y [0.1]y ...(ii)
Dividing (ii) by (i), we can write
or
From experiments I and III, we can write
Dividing (iv) by (iii), we can write
or
or
Order of reaction w.r.t. A = 1
Order of reaction w.r.t. B = 2
Overall order of reaction = 1 + 2 = 3.
Substituting the values of initial rate of formation of experiment (I) (equ. V) we can write 6.0 x 103 mol L–1 min–1.
= k[0.1 mol L–1] [0.1 mol L–1]2
or
where x and y are order of reaction w.r.t. A and B respectively.
From experiments I and IV, we can write
6.0 x 10–3 = k[0.1]y [0.1]y ...(i)
2.4 x 10–2 = k[0.4]y [0.1]y ...(ii)
Dividing (ii) by (i), we can write
or
From experiments I and III, we can write
Dividing (iv) by (iii), we can write
or
or
Order of reaction w.r.t. A = 1
Order of reaction w.r.t. B = 2
Overall order of reaction = 1 + 2 = 3.
Substituting the values of initial rate of formation of experiment (I) (equ. V) we can write 6.0 x 103 mol L–1 min–1.
= k[0.1 mol L–1] [0.1 mol L–1]2
or
