Question

The decomposition of hydrogen peroxide follows first order kinetics and has a rate constant of 2.54 x 10-4 s-1 at a certain temperature. If the concentration of hydrogen peroxide is 0.321 M after 855 s , what was the initial concentration of hydrogen peroxide at this temperature

Answer 1

`[A]_0=0.400M`

Step-by-step explanation:

Hello.

In this case, since the first-order reaction is said to be linearly related to the rate of reaction:

`r=-k[A]`

Whereas [A] is the concentration of hydrogen peroxide, when writing it as a differential equation we have:

`(d[A])/(dt) =-k[A]`

Which integrated is:

`ln(([A])/([A]_0) )=-kt`

And we can calculate the initial concentration of the hydrogen peroxide as follows:

`[A]_0=([A])/(exp(-kt))`

Thus, for the given data, we obtain:

`[A]_0=(0.321M)/(exp(-2.54x10^(-4)s^(-1)*855s))`

`[A]_0=0.400M`

Best regards!