Answer : The half-life of the compound is, 145 years.
Explanation :
First we have to calculate the rate constant.
Expression for rate law for first order kinetics is given by:
[tex]k=\frac{2.303}{t}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = ?
t = time passed by the sample = 60.0 min
a = let initial amount of the reactant = 100 g
a - x = amount left after decay process = 100 - 25 = 75 g
Now put all the given values in above equation, we get
[tex]k=\frac{2.303}{60.0}\log\frac{100g}{75g}[/tex]
[tex]k=4.79\times 10^{-3}\text{ years}^{-1}[/tex]
Now we have to calculate the half-life of the compound.
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]4.79\times 10^{-3}\text{ years}^{-1}=\frac{0.693}{t_{1/2}}[/tex]
[tex]t_{1/2}=144.676\text{ years}\approx 145\text{ years}[/tex]
Therefore, the half-life of the compound is, 145 years.
