Answer
75s
Work Step by Step
The given reaction is a first order reaction and as it take 25 sec for it to become half of its concentration thus the half life of this reaction.
$t_{1/2}$ = 25
for the initial concentration to become 1/8th it requires 1/2 to be mutiplied by 1/2 another 2 times that means we are reducing the initial concentration to 1/8th.
thus $\frac{1}{2}$ * $\frac{1}{2}$ * $\frac{1}{2}$ = $\frac{1}{8}$
thus the time = 3*25sec = 75 sec
the time for $\frac{1}{4}$ to become $\frac{1}{8}$ is just halving the concentration thus it will be just the half life. that is 25 sec.
