1997 #4 Kinetics

2 A + B ---> C + D

The following results were obtained when the reaction represented above was studied at 25 °C

Experiment

Initial
[A]

Initial
[B]

Initial Rate
of Formation
of C (mol L¯1 min¯1)

1

0.25

0.75

4.3 x 10¯4

2

0.75

0.75

1.3 x 10¯3

3

1.50

1.50

5.3 x 10¯3

4

1.75

??

8.0 x 10¯3

a)  Determine the order of the reaction with respect to A and B. Justify your answer.

 

b) Write the rate law for the reaction. Calculate the value of the rate constant, specifying units.

 

c) Determine the initial rate of change of [A] in Experiment 3.

 

d) Determine the initial value of [B] in Experiment 4.

 

e) Identify which of the reaction mechanisms represented below is consistent with the rate law developed in part (b). Justify your choice.

1

A + B ---> C + M

Fast

 

M + A ---> D

Slow

 

 

 

2

B <===> M

Fast equilibrium

 

M + A ---> C + X

Slow

 

A + X ---> D

Fast

 

 

 

3

A + B<===> M

Fast equilibrium

 

M + A ---> C + X

Slow

 

X ---> D

Fast

1997 #4 Kinetics Answers

(a) three points

1.3 x 10¯3 / 4.3 x 10¯4 = k (0.75)x (0.75)y / k (0.25)x (0.75)y leads to 3 = (3)x leads to x = 1, first order in A

5.3 x 10¯3 / 1.3 x 10¯4 = k(1.50)(1.50)y/ k(0.75)(0.75)y => 4= 2(2)y => y=1 => First order in B

Notes; Verbal descriptions accepted, but no point earned for just "if A doubles, the rate doubles". If A given as second order, 2 points can be earned for showing that B must be zero order.

(b) two points

rate = k[A][B] (equation must be consistent with part (a))

k= 4.3 x 10¯4M min¯1 / (0.25M) (0.75M) = 2.3 x 10¯3 M¯ 1 min¯1

Note; Units must be correct to earn second point. If no part (a) shown, 1 point can be earned for a reasonable (first or second order) rate law.

(c) one point

D[A] / Dt = -2 (5.3 x 10¯3 M¯1 min¯1) = - 1.06 x 10¯2 M¯1 min¯ 1

Note; Units ignored; no penalty for ( ¯ ) sign.

(d) one point

8.0 x 10 ¯3 M¯1 min¯1 = (2.3 x 10¯2 M¯1 min¯1) (1.75 M) [B]

[B] = 2.0 M

Note; No penalty if answer is consistent with wrong part (b).

(e) two points

Mechanism 2 is consistent

rate proportional to [M][A] and [M] proportional to [B] => rate proportional to [A][B]

Notes; Verbal discussion accepted for second point. Mechanism must be consistent with rate law in part (b). Showing that mechanisms 1 and 3 are inconsistent is not required.