Respuesta :
Answer:
16 years is the age of a sample.
Explanation:
The equation used to calculate half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
[tex]k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}[/tex]
where,
k = rate constant
[tex]t_{1/2}[/tex]= half life of the sample
t = time taken for decay process
[tex][A_o][/tex] = initial amount of the sample
[A] = amount left after decay process
We are given:
[tex][A_o][/tex] = 24 grams
[A] = 6 grams
[tex]t_{1/2}= 8 years[/tex]
Putting values in above equation, we get:
[tex]k=\frac{0.693}{8 years}=0.086625 year^{-1}[/tex]
Rate law expression for first order kinetics is given by the equation:
[tex]t=\frac{2.303}{k}\log\frac{[A_o]}{[A]}[/tex]
On substituting the values we get value of t:
t = 16.00 years
16 years is the age of a sample.
