Top topic this week
Back to FAQs
Related FAQs
Frequently Asked Question
Questions asked by users might not always be phrased in the clearest way.
A certain reaction with a single reactant is found to be fourth-order and to have a half-life of 10.00 s at a certain temperature with an initial concentration of 0.100 ๐๐๐ ยท ๐ฟ โ1 . (a) Determine the value of the rate constant of the reaction with its appropriate units. Show detailed workings.
Accepted Answer
Here's how to determine the rate constant for a fourth-order reaction:
1. Understand the Relationship between Half-Life and Rate Constant for a Fourth-Order Reaction:
For a fourth-order reaction with a single reactant (A โ products), the integrated rate law is:
1/[A]t - 1/[A]0 = 3kt
Where:
[A]t is the concentration of A at time t
[A]0 is the initial concentration of A
k is the rate constant
The half-life (t1/2) is the time it takes for the concentration of the reactant to decrease to half its initial value. For a fourth-order reaction:
t1/2 = 1 / (3k[A]0^3)
2. Solve for the Rate Constant (k):
We are given t1/2 = 10.00 s and [A]0 = 0.100 mol/L.
Substitute these values into the half-life equation and solve for k:
10.00 s = 1 / (3k (0.100 mol/L)^3)
3k = 1 / (10.00 s
(0.100 mol/L)^3)
k = 1 / (3
10.00 s
(0.100 mol/L)^3)
k โ 333.33 L^3 mol^-3 s^-1
Therefore, the rate constant (k) for this reaction is approximately 333.33 L^3 mol^-3 s^-1.
Articles you might like