In a kinetic study of the reaction
2NO(g) + O2 --> 2NO2(g)
the following data were obtained fro the initial rates if disapperance of NO:
Initial concentraition
NO O2 Inital Rate NO
exp 1. 0.0125M 0.0253M 0.0281 M/s
exp 2. 0.0250M 0.0253M 0.0112 M/s
exp 3. 0.0125M 0.0506M 0.0561 M/s
Obtain the rate law. What is the value of the rate constant?
I got 88.9 L/(mol*s)
To obtain the rate law for the given reaction, you need to determine the order with respect to each reactant and the overall reaction order.
First, compare the initial rates for experiments 1 and 2 while keeping the O2 concentration constant.
exp 1: Initial Rate = k [NO]^x [O2]^y = 0.0281 M/s
exp 2: Initial Rate = k [NO]^x [O2]^y = 0.0112 M/s
Since [O2] is constant, the change in the initial rate is solely due to the change in [NO].
Therefore, by comparing exp 1 and exp 2, you can see that doubling the [NO] concentration (from 0.0125 M to 0.0250 M) causes the initial rate to decrease by a factor of 2.
Hence, the reaction is first order with respect to NO. (x = 1)
Next, compare the initial rates for experiments 1 and 3 while keeping the NO concentration constant.
exp 1: Initial Rate = k [NO]^x [O2]^y = 0.0281 M/s
exp 3: Initial Rate = k [NO]^x [O2]^y = 0.0561 M/s
Since [NO] is constant, the change in the initial rate is solely due to the change in [O2].
Therefore, by comparing exp 1 and exp 3, you can see that doubling the [O2] concentration (from 0.0253 M to 0.0506 M) causes the initial rate to double as well.
Hence, the reaction is also first order with respect to O2. (y = 1)
Now that you have determined the order with respect to each reactant, you can write the rate law for the reaction:
Rate = k [NO]^1 [O2]^1
Simplifying this, you get:
Rate = k [NO] [O2]
The value of the rate constant (k) can be determined by selecting any one of the given experiments and substituting the relevant concentrations and rate into the rate law equation.
Let's use exp 1:
Rate = k [NO] [O2] = 0.0281 M/s
0.0281 M/s = k (0.0125 M) (0.0253 M)
Solving for k:
k = 0.0281 M/s / (0.0125 M) (0.0253 M)
Calculating this, you should obtain the value of the rate constant (k) as 88.9 L/(mol*s).
Therefore, the rate law for the given reaction is Rate = k [NO] [O2], and the value of the rate constant is 88.9 L/(mol*s).