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Hi in the quiz we had a question that stated "which molecule, when a single crystal, would you predict to have a larger molar entropy T=0K". Two crystals were then given with the same geometry. I know that you had to take the r the positional/residual entropy and degeneracy into account. What I am confused about is that the third law of thermodynamics states that the entropy of a perfect crystal at absolute zero is exactly equal to zero. Therefore, shouldn't both crystals have the same entropy of zero?
You're right; the third law of thermodynamics states that the entropy of a perfect crystal at absolute zero is exactly equal to zero. However, a "perfect crystal" is achieved when there is only one microstate possible. If that's the case, W = 1, and then the entropy would be zero. The third law of thermodynamics is used to explain the residual/positional entropy of a substance at 0K. Bringing it to absolute zero, we wouldn't have to worry about thermal entropy, and can therefore determine which substance has a larger entropy at 0K. I don't know which two substances you were given, but even if they were the same geometry, you should find that at least one of them would have multiple micro states because the atoms of the whole molecule could shift around, creating new micro states and thus having the higher residual entropy.
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