Afirst order reaction completed the 90%in 30minute find the time for99.9%,,,,
ln(No/N) = kt
You know No = 100
N = 100-90 = 10
K = ?
t = 30
Solve for k.
Use the same equation above, plug in k from above, the new N and solve for the new t.
Post your work if you get stuck.
https://socratic.org/questions/a-first-order-reaction-is-50-completed-after-30-minutes-this-implies-that-the-ti
ln(.1)=-k (30)
k== 0.0767528364
ln(.1/100)= -0.0767528364 t
t= ln(.001)/0.0767528364=90 min
Now think: it took 30 min to go to 90 percent. In another 30 min, it will go 9 percent (to 99). In another 30 min, it will go another .9 percent (99.9)
To find the time for 99.9% completion, we can use the concept of reaction order and the equation for a first-order reaction.
In a first-order reaction, the rate of the reaction is directly proportional to the concentration of the reactant. Mathematically, it can be expressed as:
Rate = k[A]
Where, Rate is the rate of the reaction, k is the rate constant, and [A] is the concentration of the reactant.
For a first-order reaction, the expression for calculating the time taken for a certain percentage of completion is:
t = (2.303/k) * (log(initial concentration/final concentration))
Here, t is the time taken for completion, k is the rate constant, and the logarithm is in base 10.
Given that the reaction is 90% complete in 30 minutes, we can use this information to find the rate constant (k).
0.90 = 1 - (final concentration/initial concentration)
0.90 = 1 - (0.90/initial concentration)
0.90 = (initial concentration - 0.90)/initial concentration
0.90 * initial concentration = initial concentration - 0.90
0.10 * initial concentration = 0.90
initial concentration = 0.90/0.10
initial concentration = 9
Using this information, we can calculate the rate constant (k):
t = (2.303/k) * (log(initial concentration/final concentration))
30 = (2.303/k) * (log(9/1))
30 = (2.303/k) * 2.1972
Now, we can solve this equation to obtain the value of k:
k = (2.303 * 2.1972) / 30
k ≈ 0.168 min^-1
Now, substituting the value of k into the equation, we can find the time for 99.9% completion:
t = (2.303/k) * (log(initial concentration/final concentration))
t = (2.303/0.168) * (log(9/0.001))
t ≈ 161.67 minutes
Therefore, it would take approximately 161.67 minutes for the reaction to achieve 99.9% completion.