The following experimental data were obtained for the reaction;
2 NO + 2 H2 ¡æ N2+ 2 H2O
Rate/10-5M/s [NO]/10-2M [H2]/10-2M
0.50 0.50 0.20
2.00 1.00 0.20
0.25 0.25 0.40
Write a rate law in agreement with the data.
Rate =
What is the value and units of the rate constant?
To determine the rate law, we need to analyze the relationship between the rate of the reaction and the concentrations of the reactants. The rate law generally follows the format:
Rate = k [A]^m [B]^n
Where:
- Rate is the rate of the reaction
- k is the rate constant
- [A] and [B] are the concentrations of the reactants involved in the reaction
- m and n are the reaction orders with respect to reactants A and B, respectively.
To find the rate law, we can compare the data provided and see how changing the concentration of each reactant affects the rate.
Let's examine the first set of data:
Rate/10^-5 M/s [NO]/10^-2 M [H2]/10^-2 M
0.50 0.50 0.20
We can see that when the concentration of NO is halved (from 0.50 to 0.25), the rate is also halved (from 0.50 to 0.25).
This indicates that the rate is directly proportional to the concentration of NO, so we can assign m = 1 for NO.
Now, let's examine the second set of data:
Rate/10^-5 M/s [NO]/10^-2 M [H2]/10^-2 M
2.00 1.00 0.20
We can see that when the concentration of H2 is doubled (from 0.20 to 0.40), the rate stays the same (2.00). This suggests that the concentration of H2 does not affect the rate, so we can assign n = 0 for H2.
Therefore, the rate law can be written as:
Rate = k [NO]^1 [H2]^0
Rate = k [NO]
To determine the value and units of the rate constant, we can use any set of data provided since k should remain constant. Let's use the first set of data:
Rate = k [NO]
0.50 = k (0.50)
Simplifying the equation, we can solve for k:
k = 0.5 / 0.50 = 1
The rate constant (k) in this case has a value of 1 and no units since it was canceled out during the simplification process.
Therefore, the rate law is: Rate = [NO], and the value of the rate constant is 1 with no units.
To determine the rate law, we can use the method of initial rate. The rate law can be written in the form:
Rate = k[NO]^a[H2]^b
Using the given data, we can determine the values of a and b.
For the first set of data:
Rate/10^-5 M/s = 0.50
[NO]/10^-2 M = 0.50
[H2]/10^-2 M = 0.20
Since the concentrations of both NO and H2 are varied while the rate remains constant, we can determine that a = 1 and b = 1.
Therefore, the rate law is:
Rate = k[NO][H2]
To find the value and units of the rate constant, we can use any of the given data sets. Let's use the second set of data to calculate the rate constant.
Rate/10^-5 M/s = 2.00
[NO]/10^-2 M = 1.00
[H2]/10^-2 M = 0.20
Plugging these values into the rate law equation, we can solve for k:
2.00 = k(1.00)(0.20)
k = 2.00 / (1.00)(0.20)
k = 10.00
Therefore, the value of the rate constant (k) is 10.00, and the units depend on the overall order of the reaction, which is the sum of a and b. In this case, since a = 1 and b = 1, the overall order is 1 + 1 = 2.
So, the units of the rate constant (k) would be M^-1 s^-1.