The half-life of a first order reaction is determined to be 79.0 years. How long will it take for the concentration of the reactant to reach 2% of its initial value?
.02 = (1/2)^(t/79)
t = 445.865 years
This is a question from the second midterm of 3.091x by edx. Stop cheating, it's silly and pointless.
482.5
To determine how long it will take for the concentration of the reactant to reach 2% of its initial value, we need to use the concept of half-life in a first-order reaction.
First, let's define the half-life of a reaction. The half-life of a reaction is the time it takes for half of the reactant to be consumed or for the concentration of the reactant to decrease by half.
In this case, the half-life of the first-order reaction is given as 79.0 years. This means that after 79.0 years, the concentration of the reactant will be halved.
Now, we want to find how long it will take for the concentration to reach 2% of its initial value. Since the half-life is given, we can use the following formula:
t = (ln(0.02) * t1/2) / ln(0.5)
where:
t = time for concentration to reach 2% of initial value
ln = natural logarithm
t1/2 = half-life of the reaction
Plugging in the values, we get:
t = (ln(0.02) * 79.0) / ln(0.5)
Using a scientific calculator, we can compute the value of t.
Therefore, to determine how long it will take for the concentration of the reactant to reach 2% of its initial value, we calculate t using the formula above.