Question

"A reaction is second order respect to the reactant A. If the reaction is 85% complete in 12 minutes, how long would it take for the reaction to be 15% complete?"

Answer 1

0.3738 min

Step-by-step explanation:

Integrated rate law for second order kinetics is:

`(1)/([A_t]) = (1)/([A]_0)+kt`

Where,
`[A_t]` is the final initial concentration

`[A_0]` is the initial concentration

k is the rate constant

t is the time

Given that:-

85% is complete which means that 0.85 of
`[A_0]` is decomposed. So,

`{[A_t]}` = 1 - 0.85
`[A_0]` =
`0.15[A_0]`

t = 12 minutes

`(1)/(0.15[A_0]) = (1)/([A]_0)+k* 12`

`(5.6666)/([A_0]) =12k`

`[A_0]=(5.6666)/(12k)` - 1

Also,

15 % is complete which means that 0.15 of
`[A_0]` is decomposed. So,

`{[A_t]}` = 1 - 0.15
`[A_0]` =
`0.85[A_0]`

t = ?

`(1)/(0.85[A_0]) = (1)/([A]_0)+kt`

`(0.1765)/([A_0]) =tk`

Applying value from 1

`(0.1765)/((5.6666)/(12k)) =tk`

`t=(2.118)/(5.6666)\ min=0.3738\ min`