Answer: The half-life of a first-order reaction is, [tex]3.3\times 10^2s[/tex]
Explanation:
All the radioactive reactions follows first order kinetics.
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 = 440 s
[tex][A_o][/tex] = initial amount of the reactant = 0.50 M
[A] = left amount = 0.20 M
Putting values in above equation, we get:
[tex]k=\frac{2.303}{440s}\log\frac{0.50}{0.20}[/tex]
[tex]k=2.083\times 10^{-3}s^{-1}[/tex]
The equation used to calculate half life for first order kinetics:
[tex]t_{1/2}=\frac{0.693}{k}[/tex]
Putting values in this equation, we get:
[tex]t_{1/2}=\frac{0.693}{2.083\times 10^{-3}s^{-1}}=332.69s=3.3\times 10^2s[/tex]
Therefore, the half-life of a first-order reaction is, [tex]3.3\times 10^2s[/tex]
