Respuesta :
This problem is not about chemistry it is about math. the half-life of a certain thing is the time that it needs to decay 50% of what it had before. so if there is 4g, after 1 half there will be only 2g. so to become 1g it is passed 2 half-lives. 4,0g, 2,0g, 1,0g so it is the time divided by 2( numbers of half-lives). So the half-life of Francium 210 is 2,6 min.
Answer: The half life of the reaction is 2.6 minutes.
Explanation:
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 = ?
t = time taken for decay process = 5.2 minutes
[tex][A_o][/tex] = initial amount of the reactant = 4.0 g
[A] = amount left after decay process = 1.0 g
Putting values in above equation, we get:
[tex]k=\frac{2.303}{5.2min}\log\frac{4.0}{1.0}\\\\k=0.267min^{-1}[/tex]
The equation used to calculate half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
We are given:
[tex]k=0.267min^{-1}[/tex]
Putting values in above equation, we get:
[tex]t_{1/2}=\frac{0.693}{0.267min^{-1}}=2.6min[/tex]
Hence, the half life of the reaction is 2.6 minutes.
