## Ideal Monatomic Gas Entropy

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

Rachael_1H
Posts: 31
Joined: Fri Sep 25, 2015 3:00 am

### Ideal Monatomic Gas Entropy

Why does "1 mol of the atoms of an ideal monatomic gas" have a greater change in entropy than "1 mol of atoms bound together as diatomic molecules" when temperature in increased?

The book's answer key says it is because the 1 mol of atoms of an ideal monatomic gas has "a greater number of particles." Why is this? Can someone please explain why 1 mol of atoms of an ideal monatomic gas has more particles than 1 mol of atoms bound together as diatomic molecules?

Ryan Williams 1E
Posts: 20
Joined: Fri Sep 25, 2015 3:00 am

### Re: Ideal Monatomic Gas Entropy

Its easiest to explain this with an example. Take diatomic fluorine. F2 is always in equilibrium with its monatomic form, F, as shown below:

F2 <--> 2F

When diatomic fluorine is heated, not only will it gain entropy due to the energy transfer, but some of the diatomic molecules will split, effectively increasing the moles of gas. This is why the book says there are "more particles".

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