To determine the order of the reaction with respect to
Cl2 and NO , we can use the method of initial rates. The general rate law for the reaction can be written as:
‌ Rate ‌=k[Cl2]m[NO]n where:
k is the rate constant
m is the order of the reaction with respect to
Cl2n is the order of the reaction with respect to NO
Next, we'll use the data from the experiments to find the values of
m and
n.
First, we compare Experiments I and II to determine the order with respect to
Cl2. The initial concentration of NO remains constant while the concentration of
Cl2 is doubled:
From Experiment I:
‌ Rate ‌1=k[Cl2]1m[NO]1n=0.60 From Experiment II:
‌ Rate ‌2=k[Cl2]2m[NO]2n=1.20 Taking the ratio of Rate
‌2 and Rate
‌1 :
‌| ‌ Rate ‌2 |
| ‌ Rate ‌ |
=‌| k[Cl2]2m[NO]2n |
| k[Cl2]1n[NO]1n |
=‌=2 ‌‌=2‌(‌)m=2‌2m=2‌m=1 This indicates that the reaction is first order with respect to
Cl2.
Next, we compare Experiments I and III to determine the order with respect to NO. The initial concentration of
Cl2 remains constant while the concentration of NO is doubled:
From Experiment I:
‌ Rate ‌1=k[Cl2]1m[NO]1n=0.60From Experiment III:
‌ Rate ‌3=k[Cl2]3m[NO]3n=2.40Taking the ratio of Rate
‌3 and Rate
‌1 :
‌‌| ‌ Rate ‌3 |
| ‌ Rate ‌ |
=‌| k[Cl2]3m[NO]3n |
| k[Cl]1m[NO]1n |
=‌=4‌‌=4‌(‌)n=4‌2n=4‌n=2 This indicates that the reaction is second order with respect to NO.
Therefore, the rate law is:
‌ Rate ‌=k[Cl2]1[NO]2To find the rate constant
k, we can use the data from any of the experiments. Let's use Experiment I :
‌0.60=k(0.15)1(0.15)2‌0.60=k×0.15×0.0225‌0.60=k×0.003375k=‌≈177.7mol−2L2min−1Hence, the correct option is:
Option C
Order with respect to
Cl2=1‌‌ Order with respect to
NO=2‌‌k=177.7mol−2L2min−1