A particular reactant decomposes with a half-life of 139 seconds when its initial concentration is 0.342 M. The same reactant decomposes with a half-life of 237 seconds when its initial concentration is 0.201. What is the value and unit for this rate constant?
To find the rate constant, we can use the equation for the half-life of a first-order reaction:
t1/2 = 0.693 / k
where t1/2 is the half-life and k is the rate constant.
Let's first calculate the rate constant for the first case when the initial concentration is 0.342 M and the half-life is 139 seconds.
0.693 / k1 = 139 seconds
Simplifying the equation, we have:
k1 = 0.693 / 139 seconds
k1 ≈ 0.004990 M^(-1) s^(-1)
Now, let's calculate the rate constant for the second case when the initial concentration is 0.201 M and the half-life is 237 seconds.
0.693 / k2 = 237 seconds
Simplifying the equation, we have:
k2 = 0.693 / 237 seconds
k2 ≈ 0.002922 M^(-1) s^(-1)
Since both cases involve the same reactant, the rate constant should be the same. Therefore, we can take the average of k1 and k2 to find the value of the rate constant.
(k1 + k2) / 2 = (0.004990 M^(-1) s^(-1) + 0.002922 M^(-1) s^(-1)) / 2
≈ 0.003956 M^(-1) s^(-1)
So, the value and unit for the rate constant is approximately 0.003956 M^(-1) s^(-1).