Butadiene, C4H6, in the gas phase undergoes a reaction to produce C8H12. The following data were obtained for the reaction.
[C4H6] Time (min)
1 0
0.98 20
0.91 100
0.66 500
0.49 1000
0.32 2000
0.25 3000
Determine the order of the reaction.
Order with respect to [C4H6] = 2
Calculate the rate constant for the reaction.
k = .00102 M-1min-1
How long does it take for the initial concentration to decrease by one-half?
t1/2 = 980 min
How long does it take for half of the initial concentration to decrease by one-half?
Second t1/2 = _____ min
I do not understand how to get the second t1/2. Please help. Thanks.
Your question is not complete. If it is about the rate law and/or the rate law constant, k, look ate 2nd example here:
http://www.science.uwaterloo.ca/~cchieh/cact/c123/intratel.html
To find the second t1/2, we first need to understand what it means and how it is related to the reaction order and rate constant.
The half-life (t1/2) is the time it takes for the concentration of a reactant to decrease by half. In a first-order reaction, the half-life is a constant value and does not depend on the initial concentration of the reactant. However, in higher-order reactions like the one stated in the question, the half-life will vary depending on the extent of reaction.
To find the second t1/2, we need to consider that we have already determined the order of the reaction as 2. This indicates that the reaction is second-order with respect to [C4H6].
Now, let's define the equation for the second-order reaction:
Rate = k[C4H6]^2
To find the second t1/2, we need to determine the time it takes for the concentration of [C4H6] to decrease by half, starting from a specific concentration. Let's take the initial concentration of [C4H6] as [C4H6]0.
At t = 0, [C4H6] = [C4H6]0
At t = t1/2, [C4H6] = 0.5[C4H6]0
We can write this relationship as follows:
[C4H6]0 / [C4H6] = 2
Now, we know that the reaction is second-order, so we substitute the rate equation into the above equation:
k[C4H6]0^2 / k[C4H6]^2 = 2
Simplifying the equation:
[C4H6]^2 / [C4H6]0^2 = 0.5
Taking the square root of both sides:
[C4H6] / [C4H6]0 = sqrt(0.5)
Now, we know that [C4H6] decreases by half in the second half-life, so we can say:
t1/2 = 2nd t1/2
Therefore, we have:
[C4H6] / [C4H6]0 = sqrt(0.5) = 0.7071
Plugging this value into the equation:
0.7071 = [C4H6] / [C4H6]0
Now, solving for the second t1/2, we get:
2nd t1/2 = t1/2 / 0.7071
Substituting the value of the first t1/2 as 980 min, we have:
2nd t1/2 = 980 min / 0.7071
Calculating the value, we find:
2nd t1/2 ≈ 1386 min
Therefore, the second t1/2 is approximately 1386 minutes.