Question

How many microstates are there for any given compound?

Answer 1

From Boltzmann's equation of entropy:

`nbarS = k_BlnOmega`

where:

• `barS` is the molar entropy of the chosen ensemble of molecules.
• `k_B = 1.3807xx10^(-23)` `"J/K"` is the Boltzmann constant.
• `Omega` is the number of microstates available, consistent with the system's macrostates.

Solving for `Omega`:

`color(blue)(Omega = e^(nbarS"/"k_B))`

Thus, if you know the molar entropy of a compound, you can find the number of microstates it has in however many `"mol"`s you wish. As you can imagine, this number will be huge.

If you wanted, you could choose `T = "298.15 K"` and look up the standard molar entropy (`S^@`) of many compounds in the back of many general chemistry textbooks. That can be used as `barS`.