Nitrosyl chloride, NOCL, decomposes to NO and C1 in accordance with the following equation: 2NOC1(g)--> 2NO(g)+ C1 2(g) Determine the rate equation and the rate constant for the reaction for the following data:
[NOC] 0.10 0.20
Rate, M/s 0.8 x 10(-3) 3.20 x 10(-3)
0.30
7.20 x 10(-3)
To determine the rate equation and rate constant for the given reaction, we need to use the method of initial rates. The rate equation is an expression that relates the rate of the reaction to the concentrations of the reactants. Let's analyze the given data:
[NOC] | 0.10 0.20 0.30
Rate | 0.8 x 10(-3) 3.20 x 10(-3) 7.20 x 10(-3)
We can observe that the rate of the reaction doubles when the concentration of NOCl doubles (from 0.10 to 0.20). Similarly, when the concentration of NOCl is again doubled (from 0.20 to 0.30), the rate of the reaction doubles again. This suggests that the rate of the reaction is directly proportional to the concentration of NOCl, raised to some power.
Let's calculate the ratio between the rates when the concentration of NOCl is doubled:
(3.20 x 10(-3) M/s) / (0.8 x 10(-3) M/s)
This ratio is 4, indicating that the rate of the reaction increases by a factor of 4 when the concentration of NOCl is doubled. Therefore, the rate equation can be written as:
Rate = k [NOC]^n
By comparing the rates for the given concentrations, we can determine the value of 'n'.
(3.20 x 10(-3) M/s) / (0.8 x 10(-3) M/s) = (0.20 M) ^ n / (0.10 M) ^ n
After cancelling out the common terms, we get:
4 = 2^n
Solving for 'n', we find 'n' to be 2.
Therefore, the rate equation for the reaction is:
Rate = k [NOC]^2
Now, to find the rate constant 'k', we can use any one of the data points. Let's use the first data point, where [NOC] = 0.10 M and Rate = 0.8 x 10(-3) M/s.
0.8 x 10(-3) M/s = k (0.10 M)^2
k = (0.8 x 10(-3) M/s) / (0.10 M)^2
Calculating this expression, we get:
k ≈ 8 x 10(-4) / (0.10)^2 ≈ 8 x 10(-4) M^(-1) s^(-1)
Therefore, the rate equation for the reaction is Rate = k [NOC]^2, with a rate constant 'k' approximately equal to 8 x 10(-4) M^(-1) s^(-1).