Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I just started a physical chemistry class and we are working on probability theory. The questions I am having a hard time with are as follow:

we are given that E is proportional to exp[-E/RT]. It is stated that this is a simple system having only four energy states numbered 1 through 4.

The values for each energy state are E1=0 J/mol, E2= 1000 J/mol, E3= 2000 J/mol, and E4= 3000 J/mol.

The first question asks us to obtain the normalized probability distribution for the system in state i, and evaluate the normalization constant C at T=298K.

So I did it like this P(Ei) = C exp [-Ei/RT], and C= the sum of [(-E1/RT)-(E2/RT)-(E3/RT)-(E4/RT)]^-1

this once you crunch the numbers equals 1/2.4119835807817

So P(Ei)= (exp [-E/RT])/2.4119835807817

So my first question is did I do this correctly? The normalized probability distribution for the system in state i would simply be the formula above correct?

The second question asks us to calculate the average energy per system that a large number of such systems would have at 298K.

My question is should I do an integral from 0 to infinity?

so <P(E)>= (integral [E exp(-E/RT)])/(integral [-E/RT]) from 0 to infinity?

This might all be completely wrong. I don't have the solution manual and therefore cannot check my answers. If it is wrong if someone could explain how it is wrong I would really appreciate it.

Thanks,

Rachael

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# Homework Help: Probability Distribution and Constants

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