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.
Determine rate order and rate constant.
To determine the rate order and rate constant, we can use the relationship between the half-life and rate constant for first-order reactions.
For a first-order reaction, the half-life is given by the equation:
t1/2 = (0.693 / k)
where t1/2 is the half-life and k is the rate constant.
Let's calculate the rate constant using the given information for the first set of conditions:
t1/2 = 103 s
initial concentration = 0.397 M
Using the half-life equation, we have:
103 s = (0.693 / k)
To solve for k, we rearrange the equation:
k = 0.693 / 103 s
We can calculate k as:
k = 0.00673 s^-1 (approximately)
Next, let's calculate the rate constant using the second set of conditions:
t1/2 = 213 s
initial concentration = 0.192 M
Using the half-life equation, we have:
213 s = (0.693 / k)
To solve for k, we rearrange the equation:
k = 0.693 / 213 s
We can calculate k as:
k = 0.003252 s^-1 (approximately)
As the rate constants obtained for the two sets of conditions are not equal, this indicates that the reaction is not a first-order reaction.
To determine the rate order, we can compare the rate constants for the two sets of conditions. If we observe that changing the initial concentration has an effect on the rate constant, it implies that the reaction is not first-order.
Comparing the rate constants:
0.00673 s^-1 (for 0.397 M)
0.003252 s^-1 (for 0.192 M)
Since the rate constants are different for the two different initial concentrations, we can conclude that the reaction is not a first-order reaction.
Therefore, we cannot determine the rate order and rate constant without further information or data of the reactant decomposition.