For the reaction A to products}, the following data were obtained: t=0 s, A}]=0.715 M; 22 s, 0.605 M; 74 s, 0.345 M; 132 s, 0.055 M.
What is the half-life of the reaction?
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To determine the half-life of the reaction, we will use the given data and the integrated rate law for a first-order reaction.
The integrated rate law for a first-order reaction is given by:
ln([A]t/[A]0) = -kt
Where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is the time.
We can rearrange the equation to solve for t:
t = (ln([A]t/[A]0)) / -k
To find the rate constant, we can use any set of data points and solve for k. Let's choose the first and second data points:
t1 = 22 s
[A]1 = 0.605 M
t2 = 0 s
[A]2 = 0.715 M
We can plug these values into the equation to solve for k:
k = (ln(0.605/0.715)) / (22 - 0)
k ≈ -0.027 s^-1
Now that we have the rate constant, we can use it to find the half-life.
To find the half-life (t1/2), we can use the equation:
t1/2 = (ln(2)) / k
Plugging in the value of k, we get:
t1/2 = (ln(2)) / -0.027 s^-1
t1/2 ≈ 25.7 s
Therefore, the half-life of the reaction is approximately 25.7 seconds.
To determine the half-life of the reaction, we need to find the time at which the concentration of A decreases to half of its initial value.
Given the data:
t = 0 s, [A] = 0.715 M
t = 22 s, [A] = 0.605 M
t = 74 s, [A] = 0.345 M
t = 132 s, [A] = 0.055 M
Since the concentration decreases over time, we can see that it takes time for the concentration to decrease from 0.715 M to 0.605 M. Similarly, it takes time for the concentration to decrease from 0.605 M to 0.345 M, and so on.
To find the half-life, we need to find the time it takes for the concentration to decrease from 0.715 M to 0.3575 M, which is half of the initial concentration of 0.715 M.
Let's calculate the times it takes for the concentration to reach half of its initial value:
From t = 22 s to t = 74 s, the concentration decreases from 0.605 M to 0.345 M. This is a decrease of 0.260 M.
Now, let's find the time it takes for the concentration to decrease by half of this amount:
0.260 M / 2 = 0.130 M
Therefore, the half-life of the reaction is the time it takes for the concentration to decrease by 0.130 M, which is from t = 22 s to t = 74 s.
Thus, the half-life of the reaction is 74 s - 22 s = 52 s.