The initial concentration of the a substance was 1.95 M. After 27.72 hours the concentration was 0.9750 M. After anothers 55.44 hours the concentration was 0.4875 M (total time = 83.16 hours).
If another experiment were conducted in which the initial concentration was 0.427 M, how long would it take for the substance to reach a concentration 0.0213 M?
You use 1st order equation of
ln(No/N) = kt and solve for k.
Use the second time period to calculate k again. If k is the same, then this is a first order reaction and you can use that equation on the other experiment. If k is not the same; you assume it is a second order equation and try that for both sets to see if k really is k. If it is then you can use second order equation for the other experiment.
Second order equation is
(1/A) - (1/Ao) = akt.
Post your work if you get stuck.
To solve this problem, we can use the concept of the rate of reaction and the general rate law equation. The rate law equation for a first-order reaction is given by:
ln(Ct/Co) = -kt
Where:
Ct = Final concentration
Co = Initial concentration
k = Rate constant
t = Time
In this case, we need to find the time (t) it would take for the substance to reach a concentration of 0.0213 M, given an initial concentration of 0.427 M.
Let's first calculate the rate constant (k) using the given data points:
ln(0.9750 M / 1.95 M) = -k * 27.72 hours
ln(0.4875 M / 1.95 M) = -k * 55.44 hours
We can solve these two equations simultaneously to find the value of k:
(-0.6931) = -k * 27.72 hours
(-0.7213) = -k * 55.44 hours
Dividing the second equation by the first equation:
(-0.7213) / (-0.6931) = (-k * 55.44 hours) / (-k * 27.72 hours)
1.039 = 2
Therefore, we can conclude that k is a constant value of approximately 2.
Now we can use this value of k in the rate law equation to find the time required for the substance to reach a concentration of 0.0213 M:
ln(0.0213 M / 0.427 M) = -2 * t
Simplifying the equation:
ln(0.0213 / 0.427) = -2t
ln(0.0497) = -2t
Now, solving for t, we can rearrange the equation as:
t = (-ln(0.0497)) / 2
Using a scientific calculator or online calculator, we can evaluate the right-hand side to find the value of t. Let's compute it:
t ≈ (-ln(0.0497)) / 2 ≈ 22.39 hours
Therefore, it would take approximately 22.39 hours for the substance to reach a concentration of 0.0213 M with an initial concentration of 0.427 M.