Given the following data, determine the rate constant of the reaction
2NO(g) + Cl2(g) 2NOCl(g)
Experiment [NO] (M) [Cl2] (M) Rate (M/s)
1 0.0300 0.0100 3.4 x 10–4
2 0.0150 0.0100 8.5 x 10–5
3 0.0150 0.0400 3.4 x 10–4
a. 1.13 M –2s–1
b. 9.44 M –2s–1
c. 37.8 M –2s–1
d. 0.0265 M –2s–1
e. 59.6 M –2s–1
These are difficult to do on this forum but here is how you go about it.
rate = k(NO)x(Cl2)y
You want to determine x and y, the exponents, first. Use experiments that have the same concn for each; i.e., if you use 2 and 3 (NO) will cancel and you can determine y. Then use experiments 1 and 2 so (Cl2) cancels and you can determine x. Knowing x and y, then choose any of the 3 experiments, substitute the concns and rate and solve for k. Post your work if you get stuck.
I am getting stuck on this problem. I got x=1 and y=1 when I used experiment 2/1 and then experiment 3/2. However I am unsure what to do next. The formula I'm using is Rate=K(NO)^x(Cl2)^y is this correct? I am getting 37.77 as an answer when I plug in values into experiment 2:
8.5*10^-5=k(.015)^2(.01)
Help would be greatly appreciated!
To determine the rate constant of the reaction, we can use the rate equation for the reaction:
Rate = k[NO]^a[Cl2]^b
Where k is the rate constant and a and b are the stoichiometric coefficients of NO and Cl2 in the balanced equation, respectively.
Comparing experiments 1 and 2, we can determine the order of the reaction with respect to NO by keeping the concentration of Cl2 constant:
Rate1 / Rate2 = ([NO]1 / [NO]2)^a
(3.4 x 10^-4 M/s) / (8.5 x 10^-5 M/s) = (0.0300 M / 0.0150 M)^a
4 = 2^a
2^2 = 2^a
Therefore, a = 2.
Now, comparing experiments 2 and 3, we can determine the order of the reaction with respect to Cl2 by keeping the concentration of NO constant:
Rate2 / Rate3 = ([Cl2]2 / [Cl2]3)^b
(8.5 x 10^-5 M/s) / (3.4 x 10^-4 M/s) = (0.0100 M / 0.0400 M)^b
0.25 = 0.25^b
1 = b
Now that we have the orders of the reaction with respect to NO and Cl2, we can calculate the rate constant by using any of the given experiments and solving for k:
Rate = k[NO]^2[Cl2]
Using experiment 1:
k = Rate / ([NO]^2[Cl2])
k = (3.4 x 10^-4 M/s) / ((0.0300 M)^2(0.0100 M))
k = 3.4 x 10^-4 M/s / (9 x 10^-5 M^3)
k = 3.8 M^-2 s^-1
So, the rate constant for the reaction is approximately 3.8 M^-2 s^-1.
None of the given answer choices match our calculated rate constant, so none of the provided options are correct.
To determine the rate constant of the reaction, we can use the rate equation:
rate = k[NO]^x[Cl2]^y
Where k is the rate constant, [NO] and [Cl2] are the concentrations of the reactants, and x and y are the order of the reaction with respect to each reactant.
To find the values of x and y, we can compare the rates of the reaction for different experiments and determine how they relate to the changes in concentration.
Let's compare experiments 1 and 2:
Experiment 1: rate = 3.4 x 10^(-4) M/s
Experiment 2: rate = 8.5 x 10^(-5) M/s
The concentration of NO ([NO]) changed from 0.0300 M to 0.0150 M, so we can see that it was divided by 2. Therefore, the order of the reaction with respect to [NO] is 1 (1^x = 2, x = 1).
The concentration of Cl2 ([Cl2]) remained constant at 0.0100 M, so it doesn't affect the rate. Therefore, the order of the reaction with respect to [Cl2] is 0.
Now let's compare experiments 1 and 3:
Experiment 1: rate = 3.4 x 10^(-4) M/s
Experiment 3: rate = 3.4 x 10^(-4) M/s
The concentration of NO ([NO]) remained constant at 0.0150 M, so it doesn't affect the rate. Therefore, the order of the reaction with respect to [NO] is 0.
The concentration of Cl2 ([Cl2]) changed from 0.0100 M to 0.0400 M, so we can see that it was multiplied by 4. Therefore, the order of the reaction with respect to [Cl2] is 1 (1^y = 4, y = 1).
Now that we have determined the values for x and y, we can substitute them into the rate equation to calculate the rate constant (k).
Using Experiment 1:
rate = k[NO]^x[Cl2]^y
3.4 x 10^(-4) M/s = k(0.0300 M)^1(0.0100 M)^0
3.4 x 10^(-4) = k(0.0300)
k = (3.4 x 10^(-4)) / (0.0300)
k = 1.13 x 10^(-2) M^(-1) s^(-1)
Therefore, the rate constant of the reaction is 1.13 x 10^(-2) M^(-1) s^(-1).
The answer is (a) 1.13 M^(-2) s^(-1).