Calculate k.
k = 0.693/t1/2
k = 0.693/0.34 = ?
Then ln(No/N) = kt.
Use No = 100
and N = 12.5 (that's 100%-87.5% = 12.5%)
k from above.
Substitute and solve for t(in hours).
How long does it takes for 87.5% of Aspirin to be removed from the body?
k = 0.693/t1/2
k = 0.693/0.34 = ?
Then ln(No/N) = kt.
Use No = 100
and N = 12.5 (that's 100%-87.5% = 12.5%)
k from above.
Substitute and solve for t(in hours).
The half-life of a first-order reaction can be calculated using the following formula:
t1/2 = (0.693 / k)
Here, k is the rate constant for the reaction. In this case, the value of k is given as 0.34/h. Plugging in this value, we can calculate the half-life (t1/2):
t1/2 = (0.693 / 0.34) ≈ 2.04 h
Now that we know the half-life of the reaction, we can determine the time it takes for 87.5% of the Aspirin to be removed. We'll use the concept that each half-life removes half of the remaining Aspirin.
To find the number of half-lives required to remove 87.5%:
Number of half-lives = log(0.875) / log(0.5)
Using a calculator:
Number of half-lives ≈ 1.643
Now, we multiply the number of half-lives by the half-life time:
Time = Number of half-lives × t1/2
Time = 1.643 × 2.04 ≈ 3.34 hours
Therefore, it takes approximately 3.34 hours for 87.5% of Aspirin to be removed from the body.