Residual Entropy

[Nicole Filbert 1D]

What is residual entropy? How is it different from normal entropy and how do you calculate it?
For example HW 9.75, where did Avogadro's number come from?

[Yvonne Tran 2F]

Residual entropy is entropy at T=0 K. You will have to use S=kB lnW to solve it. Degeneracy, W, is #orientations^#molecules. You need Avogadro's # to get molecules.

[Jade Bowman 1A]

Can someone explain this further? I don't really understand this answer.

[Saira Shahid 3K]

Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance at a temperature close to 0 K. I believe you use the equation S=KblnW to solve for it, where S is entropy, K is a constant, and W is degeneracy.

[Chem_Mod]

Jade, one way to conceptually understand residual entropy is to imagine this scenario: take a room full of people of party and you suddenly freeze time. If "order" is considered to be when everybody is facing in the same direction, then our "disorder" is measured by the amount of different orientations people are in. As you can imagine in a party, there will be a bunch of different circles of people, stragglers brooding in the corner, people camping out at the table of food, etc. So even when time is frozen, there is still disorder in our system/party.

Residual entropy is the disorder that still exists at absolute zero when molecular motion just stops. As you can expect in a party, the molecules, though frozen, are oriented randomly rather than in a uniform pattern. Even when nothing can move at absolute zero, there is still disorder. So we calculate entropy as we normally do with the Boltzmann formula where our W degeneracy is the number of orientations that our molecule could possibly be in raised to the power of the number of molecules. This gives us the number of possible different combinations of a group of molecules with a certain orientation for each one. Think of it like tossing three coins. The number of combinations is 2³, 2 because our coin can either be heads or tails and 3 because we have three coins.

[Crystal Ma]

Then how do we know the number of possible orientation?