A first-order reaction is 35.5% complete in 4.90 minutes. The rate constant of the reaction is _____
I would use the integrated rate equation for a first order reaction. Check my thinking.
To determine the rate constant (k) of a first-order reaction, we can use the integrated rate equation:
ln([A]t/[A]0) = -kt
Where:
[A]t is the concentration of reactant at time t
[A]0 is the initial concentration of reactant
k is the rate constant
t is the time
We are given:
[A]t/[A]0 = 35.5%
t = 4.90 minutes
First, convert the given percentage to a decimal:
35.5% = 0.355
Substituting these values into the integrated rate equation, we get:
ln(0.355) = -k * 4.90
Now, we can solve for the rate constant (k):
-ln(0.355) = k * 4.90
k = -ln(0.355) / 4.90
Now, let's calculate the rate constant using this information.
To determine the rate constant of a first-order reaction, you can use the formula:
ln(A/Ao) = -kt
Where:
A represents the concentration of the reactant at a given time.
Ao represents the initial concentration of the reactant.
k represents the rate constant of the reaction.
t represents the time.
In this case, the reaction is reported as 35.5% complete, which means that A/Ao is 0.355. The time is given as 4.90 minutes.
We can rearrange the formula to solve for the rate constant, k:
k = -ln(A/Ao) / t
Let's plug in the values:
k = -ln(0.355) / 4.90
Now, we can calculate the rate constant using a scientific calculator or an online calculator that supports natural logarithms.
Calculating -ln(0.355) gives approximately -1.032.
Plugging this value into the equation:
k = -1.032 / 4.90
The rate constant, k, is approximately -0.211 min^-1 (or -0.211 min to the power of -1).