Answer : The time required would be, 60.0 hours
Explanation :
Half-life = 15 hr
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]k=\frac{0.693}{15\text{ hr}}[/tex]
[tex]k=0.0462\text{ hr}^{-1}[/tex]
Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]0.0462\text{ hr}^{-1}[/tex]
t = time passed by the sample = ?
a = initial amount of the reactant = 0.010 mol
a - x = amount left after decay process = 6.25 × 10⁻⁴ mol
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{0.0462}\log\frac{0.010}{6.25\times 10^{-4}}[/tex]
[tex]t=60.0\text{ hr}[/tex]
Therefore, the time required would be, 60.0 hours
