The dimerization of butadiene is a second order reaction process. In an experiment a sample of 0.0087 mol of butadiene was heated in a liter flask. After 600 seconds 21% of the butadiene has dimerized. Calculate the rate constant.
To calculate the rate constant for the dimerization of butadiene, we can use the equation for a second order reaction:
rate = k * [A]^2
Here, [A] represents the concentration of butadiene, and k is the rate constant we want to determine.
From the information given, we know that after 600 seconds, 21% of the butadiene has dimerized. This means that 79% of the butadiene remains unreacted.
First, let's calculate the initial concentration of butadiene [A]₀:
[A]₀ = (0.0087 mol) / (1 L) = 0.0087 M
Next, let's calculate the concentration of butadiene [A] at 600 seconds:
[A] = (79% * 0.0087 M) = 0.0069 M
Now, we can use these values to calculate the rate constant k. Rearranging the equation for a second order reaction:
k = rate / [A]^2
Since the rate is not provided, we need to find it using the change in concentration of butadiene:
rate = (change in [A]) / (change in t)
The change in [A] is ([A] - [A]₀) = (0.0069 M - 0.0087 M) = -0.0018 M
The change in t is 600 seconds.
Now we can calculate the rate:
rate = (-0.0018 M) / (600 seconds) = -3 × 10^(-6) M/s
Finally, we can substitute the rate and the concentration into the rate constant equation:
k = (-3 × 10^(-6) M/s) / (0.0069 M)^2
k ≈ 0.1 M^(-2) s^(-1)
Thus, the approximate rate constant for the dimerization of butadiene is 0.1 M^(-2) s^(-1).