<u>Answer:</u> The time taken by the reaction is 84.5 seconds
<u>Explanation:</u>
The equation used to calculate half life for first order kinetics:
where,
= half-life of the reaction = 9.0 s
k = rate constant = ?
Putting values in above equation, we get:
Rate law expression for first order kinetics is given by the equation:
......(1)
where,
k = rate constant =
t = time taken for decay process = 50.7 sec
= initial amount of the reactant = ?
[A] = amount left after decay process = 0.0741 M
Putting values in equation 1, we get:
Now, calculating the time taken by using equation 1:
Putting values in equation 1, we get:
Hence, the time taken by the reaction is 84.5 seconds
