33) A first-order reaction has a rate constant of 0.33 min-1. It takes __________ min for the reactant
concentration to decrease from 0.13 M to 0.088 M.
A) 1.4 B) 0.13 C) 1.2 D) 0.85 E) 0.51
how can i set this up?
To solve this problem, we can use the integrated rate law for first-order reactions:
ln([A]t/[A]0) = -kt
where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration, k is the rate constant, and t is the time.
In this case, we are given the rate constant (k = 0.33 min^(-1)), and we are asked to find the time it takes for the reactant concentration to decrease from 0.13 M to 0.088 M.
We can use the given information to set up the equation:
ln(0.088 M / 0.13 M) = -0.33 min^(-1) * t
Simplifying:
ln(0.088 / 0.13) = -0.33 t
-0.4599 = -0.33 t
t = -0.4599 / -0.33
t ≈ 1.395 ≈ 1.4 min
Therefore, it takes approximately 1.4 minutes for the reactant concentration to decrease from 0.13 M to 0.088 M. Hence, the correct answer is A) 1.4.
To solve this problem, we can use the integrated rate law for a first-order reaction, which is given by:
ln([A]t/[A]0) = -kt
Where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, k is the rate constant, and t is the time.
We are given the rate constant k as 0.33 min^-1. The initial concentration [A]0 is 0.13 M, and the final concentration [A]t is 0.088 M. We are asked to find the time it takes for the reactant concentration to decrease from 0.13 M to 0.088 M, which we can represent as t.
Substituting the given values into the integrated rate law, we can solve for t:
ln(0.088/0.13) = -0.33t
Now we can solve for t:
ln(0.088/0.13) = -0.33t
t = ln(0.088/0.13) / -0.33
Using a calculator, we find:
t ≈ 1.4 minutes
Therefore, the answer is A) 1.4 min.