Answer:
![[A]_0=0.400M](https://tex.z-dn.net/?f=%5BA%5D_0%3D0.400M)
Explanation:
Hello.
In this case, since the first-order reaction is said to be linearly related to the rate of reaction:
![r=-k[A]](https://tex.z-dn.net/?f=r%3D-k%5BA%5D)
Whereas [A] is the concentration of hydrogen peroxide, when writing it as a differential equation we have:
![\frac{d[A]}{dt} =-k[A]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5BA%5D%7D%7Bdt%7D%20%3D-k%5BA%5D)
Which integrated is:
![ln(\frac{[A]}{[A]_0} )=-kt](https://tex.z-dn.net/?f=ln%28%5Cfrac%7B%5BA%5D%7D%7B%5BA%5D_0%7D%20%29%3D-kt)
And we can calculate the initial concentration of the hydrogen peroxide as follows:
![[A]_0=\frac{[A]}{exp(-kt)}](https://tex.z-dn.net/?f=%5BA%5D_0%3D%5Cfrac%7B%5BA%5D%7D%7Bexp%28-kt%29%7D)
Thus, for the given data, we obtain:
![[A]_0=\frac{0.321M}{exp(-2.54x10^{-4}s^{-1}*855s)}](https://tex.z-dn.net/?f=%5BA%5D_0%3D%5Cfrac%7B0.321M%7D%7Bexp%28-2.54x10%5E%7B-4%7Ds%5E%7B-1%7D%2A855s%29%7D)
![[A]_0=0.400M](https://tex.z-dn.net/?f=%5BA%5D_0%3D0.400M)
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