Question

In a first order decomposition, how long does it take (in seconds) for 75% of the compound to decompose given that k is 0.0909 sec-1 (give answer to 1 decimal place)?

Answer 1

15.3 s

Step-by-step 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.

`[A]_(t)=[A]_(0).e^(-k* t )`

where,

`[A]_(t)`: concentration of A at a time t

`[A]_(0)`: initial concentration of A

k: rate constant

When 75% of A decomposes, the remaining concentration is 25% (
`[A]_(t)` = 0.25
`[A]_(0)`). The required time is:

`[A]_(t)/[A]_(0)=e^{-0.0909s^(-1) * t }\\`

`0.25[A]_(0)/[A]_(0)=e^{-0.0909s^(-1) * t }\\`

t = 15.3 s