# How many microstates are there for any given compound?

Feb 4, 2017

From Boltzmann's equation of entropy:

$n \overline{S} = {k}_{B} \ln \Omega$

where:

• $\overline{S}$ is the molar entropy of the chosen ensemble of molecules.
• ${k}_{B} = 1.3807 \times {10}^{- 23}$ $\text{J/K}$ is the Boltzmann constant.
• $\Omega$ is the number of microstates available, consistent with the system's macrostates.

Solving for $\Omega$:

$\textcolor{b l u e}{\Omega = {e}^{n \overline{S} \text{/} {k}_{B}}}$

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

If you wanted, you could choose $T = \text{298.15 K}$ and look up the standard molar entropy (${S}^{\circ}$) of many compounds in the back of many general chemistry textbooks. That can be used as $\overline{S}$.