Answer: The half-life of the compound is 93 minutes
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
t = age of sample
a = let initial amount of the reactant =100
a - x = amount left after decay process = (100-36) = 64
a) for completion of 36 % of reaction
[tex]60=\frac{2.303}{k}\log\frac{100}{100-36}[/tex]
[tex]k=\frac{2.303}{60}\log\frac{100}{64}[/tex]
[tex]k=0.0074min^{-1}[/tex]
b) for completion of half life:
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]t_{\frac{1}{2}}=\frac{0.693}{0.0074min^{-1}}=93min[/tex]
The half-life of the compound is 93 minutes
