Respuesta :
Answer: The time taken by the reaction is 84.5 seconds
Explanation:
The equation used to calculate half life for first order kinetics:
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
where,
[tex]t_{1/2}[/tex] = half-life of the reaction = 9.0 s
k = rate constant = ?
Putting values in above equation, we get:
[tex]k=\frac{0.693}{9}=0.077s^{-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] ......(1)
where,
k = rate constant = [tex]0.077s^{-1}[/tex]
t = time taken for decay process = 50.7 sec
[tex][A_o][/tex] = initial amount of the reactant = ?
[A] = amount left after decay process = 0.0741 M
Putting values in equation 1, we get:
[tex]0.077=\frac{2.303}{50.7}\log\frac{[A_o]}{0.0741}[/tex]
[tex][A_o]=3.67M[/tex]
Now, calculating the time taken by using equation 1:
[tex][A]=0.0055M[/tex]
[tex]k=0.077s^{-1}[/tex]
[tex][A_o]=3.67M[/tex]
Putting values in equation 1, we get:
[tex]0.077=\frac{2.303}{t}\log\frac{3.67}{0.0055}\\\\t=84.5s[/tex]
Hence, the time taken by the reaction is 84.5 seconds
