## Qualitative Entropy of Diatomic Gases

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Payton Kammerer 2B
Posts: 49
Joined: Tue May 01, 2018 3:00 am

### Qualitative Entropy of Diatomic Gases

"Which would you expect have a higher standard molar entropy at 298K? a) Iodine vapor or bromine vapor"

Both of these elements are diatomic, and since they're both in the same state and it is asking about standard molar entropy, the only difference between them is their molar mass. What effect does molar mass have on entropy?

I know that the lighter molecule, bromine, will move more quickly, but iodine has more electrons, which I think may increase its entropy since electrons are pretty chaotic particles.

Mulin_Li_2J
Posts: 105
Joined: Sat Aug 17, 2019 12:16 am

### Re: Qualitative Entropy of Diatomic Gases

In this problem, you want to consider the residual entropy of each gas molecule by applying Boltzmann Formula instead. For one, the two gases look pretty much the same macroscopically because they all follow ideal gas law. But they differ quiet a lot in microscopic state because of different atomic size and number of particles each of the gas molecules contains.

Since Iodine has a larger atomic size, more protons, more neutrons, and more electrons than Bromine does, it can occupy so much more microstates, or arrangement of molecules, while achieving the overall energy level. Thus, Iodine gas has a higher degeneracy W than Bromine gas does. And based on the equation S = k*ln(W), Iodine gas has a higher entropy than Bromine gas does.

Hope this can help! -_+

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