Nitric oxide reacts with chlorine to form nitrosyl chloride, NOCl. Use the following data to determine the rate equation for the reaction.
NO + (1/2)Cl2 -> NOCl
Expt.[NO] [Cl2] Initial rate
1 0.22 0.065 0.96 M/min
2 0.66 0.065 8.6 M/min
3 0.44 0.032 1.9 M/min
How much of this do you know how to do. For example, can you determine that the rate is first order with respect to NO? (It is)
It isnt that easy to see what Cl2 is. Do this
rate = k(NO)^2(Cl2)^x
rate2 = k(0.66)^2(0.065)^x
rate3 = k(0.44)^2(0.032)^x
Divide the rate2/rate3 and solve for x. I obtained 1.
Well, isn't this reaction quite the clown act! Let's break it down and see what we can find.
Looking at the data, we can see that the concentration of nitric oxide ([NO]) in experiment 1 is 0.22 M, while the concentration of chlorine ([Cl2]) is 0.065 M. The initial rate of the reaction is 0.96 M/min.
In experiment 2, the concentration of NO is 0.66 M, the concentration of Cl2 is 0.065 M, and the initial rate is 8.6 M/min.
Finally, in experiment 3, [NO] is 0.44 M, [Cl2] is 0.032 M, and the initial rate is 1.9 M/min.
Now, let's find out the effect of changing the concentration of each reactant separately.
In experiments 1 and 2, the concentration of NO is tripled (from 0.22 M to 0.66 M) while the concentration of Cl2 is held constant at 0.065 M. We can see that the rate increases from 0.96 M/min to 8.6 M/min. This shows that changing the concentration of NO affects the rate of the reaction.
In experiments 1 and 3, the concentration of Cl2 is doubled (from 0.065 M to 0.032 M) while the concentration of NO is held constant at 0.22 M. We can observe that the rate changes from 0.96 M/min to 1.9 M/min. This tells us that altering the concentration of Cl2 has an impact on the rate.
From these observations, we can conclude that the rate equation for this reaction is rate = k[NO]^a[Cl2]^b, where a and b are the order of reaction with respect to NO and Cl2, respectively.
By comparing the rate change when the concentration of NO is altered and when the concentration of Cl2 is altered, we can determine the orders of reaction.
Let's calculate the values:
For NO:
(8.6 M/min) / (0.96 M/min) = (0.66 M)^a / (0.22 M)^a
Dividing the numerator and denominator by (0.22 M)^a, we get:
(8.6 M/min) / (0.96 M/min) = (3)^a
Taking the logarithm of both sides, we have:
log(8.6/0.96) = a * log(3)
a ≈ log(8.6/0.96) / log(3) ≈ 1.12
For Cl2:
(1.9 M/min) / (0.96 M/min) = (0.032 M)^b / (0.065 M)^b
Dividing the numerator and denominator by (0.065 M)^b, we get:
(1.9 M/min) / (0.96 M/min) ≈ (0.032/0.065)^b
Taking the logarithm of both sides, we have:
log(1.9/0.96) ≈ b * log(0.032/0.065)
b ≈ log(1.9/0.96) / log(0.032/0.065) ≈ 2.43
So, the rate equation for the reaction is:
rate = k[NO]^1.12[Cl2]^2.43
And just like that, we've unmasked the rate equation for the nitric oxide and chlorine clown show. Happy chemist-clowning!
To determine the rate equation for the reaction, we need to compare the initial rates of the reaction at different concentrations of nitric oxide and chlorine. From the given data, we have the following information:
Expt. [NO] [Cl2] Initial rate
1 0.22 0.065 0.96 M/min
2 0.66 0.065 8.6 M/min
3 0.44 0.032 1.9 M/min
Let's compare Experiments 1 and 2, where the concentration of nitric oxide triples while the concentration of chlorine remains constant. The initial rate increases from 0.96 M/min to 8.6 M/min, which is approximately 9 times larger. This suggests that the reaction rate is directly proportional to the concentration of nitric oxide.
Now, let's compare Experiments 1 and 3, where the concentration of both nitric oxide and chlorine change. The concentration of nitric oxide doubles (from 0.22 M to 0.44 M) while the concentration of chlorine is halved (from 0.065 M to 0.032 M). The initial rate changes from 0.96 M/min to 1.9 M/min, which is approximately 2 times larger. This suggests that the reaction rate is also directly proportional to the concentration of chlorine.
Based on these comparisons, the rate equation for the reaction can be written as:
Rate = k[NO]^x[Cl2]^y
where k is the rate constant, [NO] is the concentration of nitric oxide, [Cl2] is the concentration of chlorine, and x and y are the orders of the reaction with respect to nitric oxide and chlorine, respectively.
From the data, we can conclude that x = 1 (the reaction rate is directly proportional to the concentration of nitric oxide), and y = 1 (the reaction rate is directly proportional to the concentration of chlorine).
Therefore, the rate equation for the reaction is:
Rate = k[NO][Cl2]
To determine the rate equation for the reaction, we need to compare the initial rates of the reaction at different concentrations of reactants.
Let's start by comparing Experiments 1 and 2, which have the same initial concentration of chlorine (Cl2) but different initial concentrations of nitric oxide (NO):
Experiment 1:
Initial [NO] = 0.22 M
Initial [Cl2] = 0.065 M
Initial rate = 0.96 M/min
Experiment 2:
Initial [NO] = 0.66 M
Initial [Cl2] = 0.065 M
Initial rate = 8.6 M/min
Since the concentration of Cl2 is the same in both experiments, any change in the initial rate of the reaction can be attributed to the change in the concentration of NO.
By comparing the rates, we can see that increasing the concentration of NO from 0.22 M to 0.66 M causes the rate to increase from 0.96 M/min to 8.6 M/min. This indicates that the rate of the reaction is directly proportional to the concentration of nitric oxide, raised to the power of some unknown exponent, x. Therefore, we can write the general rate equation for this reaction as:
Rate = k[NO]^x[Cl2]^y
Now let's compare Experiments 1 and 3, which have the same initial concentration of nitric oxide (NO) but different initial concentrations of chlorine (Cl2):
Experiment 1:
Initial [NO] = 0.22 M
Initial [Cl2] = 0.065 M
Initial rate = 0.96 M/min
Experiment 3:
Initial [NO] = 0.44 M
Initial [Cl2] = 0.032 M
Initial rate = 1.9 M/min
Since the concentration of NO is the same in both experiments, any change in the initial rate of the reaction can be attributed to the change in the concentration of Cl2.
By comparing the rates, we can see that increasing the concentration of Cl2 from 0.032 M to 0.065 M causes the rate to increase from 1.9 M/min to 0.96 M/min. This indicates that the rate of the reaction is inversely proportional to the concentration of chlorine, raised to the power of some unknown exponent, y. Therefore, we can rewrite the rate equation as:
Rate = k[NO]^x/[Cl2]^y
Comparing the two rate equations, we can establish the relationship between x and y:
x = 1 (directly proportional to the concentration of NO)
y = 1 (inversely proportional to the concentration of Cl2)
Thus, the rate equation for the reaction between nitric oxide and chlorine to form nitrosyl chloride is:
Rate = k[NO][Cl2]
The overall order of the reaction is 2 (x + y = 1 + 1 = 2) and the rate equation is first-order with respect to both nitric oxide and chlorine.