A particular reactant decomposes with a half-life of 103 s when its initial concentration is 0.397 M. The same reactant decomposes with a half-life of 213 s when its initial concentration is 0.192 M.
what is the reaction order and rate constant
To determine the reaction order and rate constant, we need to use the half-life equation for a first-order reaction:
t1/2 = (0.693 / k)
where t1/2 is the half-life and k is the rate constant.
First, let's calculate the rate constant (k) using the given values for the first half-life:
t1/2 = 103 s
[Reactant] = 0.397 M
Rearranging the half-life equation, we have:
k = 0.693 / t1/2
k = 0.693 / 103 s
k ≈ 0.0067 s^(-1) (rounded to four significant figures)
Now, let's calculate the rate constant (k) using the second set of values:
t1/2 = 213 s
[Reactant] = 0.192 M
Using the same equation:
k = 0.693 / t1/2
k = 0.693 / 213 s
k ≈ 0.0032 s^(-1) (rounded to four significant figures)
If the reaction order is the same for both concentrations, the rate constant should remain constant. However, if it changes, it suggests that the reaction order is different.
Comparing the rate constants:
k₁ = 0.0067 s^(-1)
k₂ = 0.0032 s^(-1)
Since the rate constants are different, it indicates that the reaction order changes depending on the initial concentration.
To determine the reaction order, we need to compare the rate constants at different concentrations. Let's calculate the reaction order for the given values.
Let's consider the ratio of the rate constants (k₂ / k₁):
(k₂ / k₁) = (0.0032 s^(-1) / 0.0067 s^(-1)) ≈ 0.48 (rounded to two significant figures)
Since the ratio is less than 1, it indicates that the reaction is a second-order reaction.
Therefore, the reaction order is second-order, and the rate constant is dependent on the initial concentration.