Answer : The time taken for the reaction is, 28 s.
Explanation :
Expression for rate law for first order kinetics is given by :
[tex]k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}[/tex]
where,
k = rate constant = 0.0632
t = time taken for the process = ?
[tex][A_o][/tex] = initial amount or concentration of the reactant = 1.28 M
[tex][A][/tex] = amount or concentration left time 't' = [tex]1.28\times \frac{17}{100}=0.2176M[/tex]
Now put all the given values in above equation, we get:
[tex]0.0632=\frac{2.303}{t}\log\frac{1.28}{0.2176}[/tex]
[tex]t=28s[/tex]
Therefore, the time taken for the reaction is, 28 s.
