Question

How many half-lives are required for the concentration of reactant to decrease to 1.56% of its original value?4247.56.56

Answer 1

6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.

Step-by-step explanation:

Using integrated rate law for first order kinetics as:

`[A_t]=[A_0]e^(-kt)`

Where,

`[A_t]` is the concentration at time t

`[A_0]` is the initial concentration

Given:

Concentration is decreased to 1.56 % which means that 0.0156 of
`[A_0]` is decomposed. So,

`\frac {[A_t]}{[A_0]}` = 0.0156

Thus,

`\frac {[A_t]}{[A_0]}=e^(-k* t)`

`0.0156=e^(-k* t)`

kt = 4.1604

The expression for the half life is:-

Half life = 15.0 hours

`t_(1/2)=\frac {ln\ 2}{k}`

Where, k is rate constant

So,

`k=\frac {ln\ 2}{t_(1/2)}`

`(4.1604)/(t)=\frac {ln\ 2}{t_(1/2)}`

`t = 6* t_(1/2)`

6 half-lives are required for the concentration of reactant to decrease to 1.56% of its original value.