Question

`t_(1/4)` can be taken as the time taken for the concentration of a reactant to drop to `3/4` of its initial value. If the rate constant for a first order reaction is k, the `t_(1/4)` can be written as ______.

पर्याय

• 0.75/k

• 0.69/k

• 0.29/k

• 0.10/k

Answer 1

`t_(1/4)` can be taken as the time taken for the concentration of a reactant to drop to `3/4` of its initial value. If the rate constant for a first order reaction is k, the `t_(1/4)` can be written as 0.29/k.

Explanation:

[A]₀ is the initial concentration.

[A]_t is the concentration at time t.

`k = 2.303/t log ([A]_0/[A]_t)`

`k = 2.303/t_(1/4) log([A]_0/(3/4[A]_0))`

The [A]₀ terms cancel out, leaving:

`k = 2.303/t_(1/4) log (4/3)`

`k = (2.303xx0.1249)/t_(1/4)`

`k = 0.287/t_(1/4)`

`t_(1/4) = 0.29/k`