The following rearrangement reaction is first order:
C3H6 �¨ CH3CH=CH2
The rate constant for this reaction is 6.7 �~ 10−4. How many minutes will it take for the concentration of C3H6 to drop to 11.75% of its initial value?
How do I calculate this step by step.
My answer was 3.1 minutes and it was wrong.
You don't have any units on k. Also, I'm not sure I've translated the mumbo jumbo symbols you have correctly so check the below carefully.
ln(No/N) = kt
No = 100
N = 11.75
k = 6.7E-4 (min^-1 or sec^-1 or whatever)
t = time and the time will be minutes, seconds, hours, days, or whatever the unit of k. Then time will need to be convert to minutes if k is in some unit other than minutes.
To calculate the time required for the concentration of C3H6 to drop to 11.75% of its initial value, we can use the first-order reaction rate equation:
ln(Ct/C0) = -kt
where Ct is the concentration at time t, C0 is the initial concentration, k is the rate constant, and t is the time. In this case, we want to find the time at which the concentration is 11.75% of the initial value, so Ct = 0.1175C0.
Let's go through the calculation step by step:
Step 1: Write down the given values:
- Rate constant (k) = 6.7 × 10^(-4) min^(-1)
- Final concentration is 11.75% of the initial concentration.
Step 2: Substitute the values into the equation:
ln(0.1175C0/C0) = -6.7 × 10^(-4) min^(-1) × t
Simplifying, we get:
ln(0.1175) = -6.7 × 10^(-4) min^(-1) × t
Step 3: Solve for t:
t = ln(0.1175)/(-6.7 × 10^(-4) min^(-1))
Using a calculator, we find:
t ≈ -2.1442/(-6.7 × 10^(-4)) ≈ 3192.2 min
Therefore, it will take approximately 3192.2 minutes for the concentration of C3H6 to drop to 11.75% of its initial value.
It seems there was an error in your calculation. Make sure to recheck your steps and calculations to find out where the mistake occurred.