Answer:
15.3 s
Explanation:
Let's consider the first-order decomposition of a generic compound A. We can find the concentration at a certain time using the following expression.
[tex][A]_{t}=[A]_{0}.e^{-k\times t }[/tex]
where,
[tex][A]_{t}[/tex]: concentration of A at a time t
[tex][A]_{0}[/tex]: initial concentration of A
k: rate constant
When 75% of A decomposes, the remaining concentration is 25% ([tex][A]_{t}[/tex] = 0.25 [tex][A]_{0}[/tex]). The required time is:
[tex][A]_{t}/[A]_{0}=e^{-0.0909s^{-1} \times t }\\[/tex]
[tex]0.25[A]_{0}/[A]_{0}=e^{-0.0909s^{-1} \times t }\\[/tex]
t = 15.3 s
