Calculating Molar Energy Change in Molecular System Conversion?

[Chemist@]

Homework Statement

Consider a molecular system containing X type molecules and Y type molecules. X and Y can interconvert, and each has two energy levels (given below). The population in moles (n), of each energy state for X and Y, are given at equilibrium of T=300K.

For X n₀=0.8 and E₀=0
and n₁=0.2 and E₁=?

For Y n₀=0.6 and E₀=0
and n₁=0.4 and E₁=?

What is the molar change in energy for total conversion from a completely populated X state to a completely populated Y state?

Homework Equations

Don't know which equation to use. I just think that the population amount is proportional to the energy.

The Attempt at a Solution

The change is X→Y .Seems as at T=300K the second energy level of X has a four times bigger energy than the first level. For Y, the energy of the second level is 1.5 times bigger than of the first one, but as the first one has E=0, I am clueless.

 

[hilbert2]

I think you're supposed to use the Boltzmann distribution here... There are four different states where the molecule can be, and the relative probability of it being in a state with energy $E$ is $\exp\left(-\frac{E}{k_{B}T}\right)$. Remember to normalize the probabilities with the partition function $Z$.

This should work, as far as I know, but honestly I'm not sure whether the fact that identical molecules in the same state are indistinguishable would affect the form of the probability distribution here.