Respuesta :
Answer: 8.1 days
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 = x
a - x = amount left after decay process= [tex]\frac{x}{4}[/tex]
a) to find rate constant
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]k=\frac{0.693}{2.7days}=0.257days^{-1}[/tex]
b) for completion of one fourth of reaction
[tex]t=\frac{2.303}{k}\log\frac{x}{\frac{x}{4}}[/tex]
[tex]t=\frac{2.303}{0.257}\log{4}[/tex]
[tex]t=8.1days[/tex]
Thus after 8.1 days , one fourth of original amount will remain.
