4.Consider the following reaction: NO 2(g) NO (g) + O (g) The concentration of N
ID: 1007398 • Letter: 4
Question
4.Consider the following reaction:
NO2(g) NO(g) + O(g)
The concentration of NO2(g) was measured at 25°C as a function of time.
Time (s)
[NO2], M
0
0.01000
50
0.00887
100
0.00797
150
0.00723
200
0.00662
250
0.00611
300
0.00567
350
0.00528
400
0.00495
450
0.00466
500
0.00440
550
0.00416
600
0.00395
a. What is the specific rate law for this reaction? Show your work and reasoning. No credit for a lucky guess!.
b. Determine the value of the rate constant for this reaction.
Time (s)
[NO2], M
0
0.01000
50
0.00887
100
0.00797
150
0.00723
200
0.00662
250
0.00611
300
0.00567
350
0.00528
400
0.00495
450
0.00466
500
0.00440
550
0.00416
600
0.00395
Explanation / Answer
Consider the first two entries in the table.
The change in concentration of NO2, i.e, [NO2] = (0.00887 – 0.01000) M = -(1.13*10-3 M); the change in time, i.e, t = (50-0) secs = 50 secs
Now rate of the reaction = rate of disappearance of NO2 = -[NO2]/t = - (-1.13*10-3 M)/50 secs = 2.26*10-5 M/sec; this is the specific rate of the reaction when the concentration of the reactants is unity (ans)
Let the rate of the reaction be r = -d[NO2]/dt = k[NO2]x where k is the rate constant and x is the order of the reaction. Construct the following table:
[NO2] (M)
[NO2] (M)
t (sec)
t (sec)
r =- [NO2]/t
0.01000
-
0
-
-
0.00887
- 1.13*10-3
50
50
2.26*10-5
0.00797
-9.0*10-4
100
50
1.8*10-5
0.00723
-7.4*10-4
150
50
1.48*10-5
0.00662
-6.1*10-4
200
50
1.22*10-5
Compare the second and third entries in the final column.
r1/r2 = 2.26*10-5/1.8*10-5 = k(0.00887)x/k (0.00797)x (rate constant remains constant)
====> 1.255 = (0.00887/0.00797)x = (1.113)x
====> log10(1.255) = xlog10(1.113)
====> 0.0986 = x.(0.0465)
====> x = 0.0986/0.0465 = 2.12 2
The order of the reaction with respect to NO2 is 2. Thus the rate law is
2.26*10-5[NO2]2 (ans)
[NO2] (M)
[NO2] (M)
t (sec)
t (sec)
r =- [NO2]/t
0.01000
-
0
-
-
0.00887
- 1.13*10-3
50
50
2.26*10-5
0.00797
-9.0*10-4
100
50
1.8*10-5
0.00723
-7.4*10-4
150
50
1.48*10-5
0.00662
-6.1*10-4
200
50
1.22*10-5
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