Answer :
Answer : The original mass of the sample was 0.581 grams.
Explanation :
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]0.131\text{ years}^{-1}[/tex]
t = time passed by the sample = 5.00 years
a = original or initial amount of the reactant = ?
a - x = amount left after decay process = 0.302 g
Now put all the given values in above equation, we get
[tex]5.00\text{ years}=\frac{2.303}{0.131\text{ years}^{-1}}\log\frac{a}{0.302g}[/tex]
[tex]a=0.581g[/tex]
Therefore, the original mass of the sample was 0.581 grams.