Respuesta :
Answer: The concentration of radon after the given time is [tex]3.83\times 10^{-30}mol/L[/tex]
Explanation:
All the radioactive reactions follows first order kinetics.
The equation used to calculate half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
We are given:
[tex]t_{1/2}=3.82days[/tex]
Putting values in above equation, we get:
[tex]k=\frac{0.693}{3.82}=0.181days^{-1}[/tex]
Rate law expression for first order kinetics is given by the equation:
[tex]k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}[/tex]
where,
k = rate constant = [tex]0.181days^{-1}[/tex]
t = time taken for decay process = 3.00 days
[tex][A_o][/tex] = initial amount of the reactant = [tex]1.45\times 10^{-6}mol/L[/tex]
[A] = amount left after decay process = ?
Putting values in above equation, we get:
[tex]0.181days^{-1}=\frac{2.303}{3.00days}\log\frac{1.45\times 10^{-6}}{[A]}[/tex]
[tex][A]=3.83\times 10^{-30}mol/L[/tex]
Hence, the concentration of radon after the given time is [tex]3.83\times 10^{-30}mol/L[/tex]
