# How do you calculate the number of microstates a compound has?

##### 1 Answer

**DISCLAIMER:** *The answer isn't that long, but has a link to extra info at the bottom for you extra, extra hard-working people.*

A convenient equation is:

#\mathbf(S = k_BlnOmega)# where:

#S# is thestatistical entropyat a specified temperature. For example, we can use#S^@ = "191.6 J/mol"cdot"K"# for#"N"_2(g)# at#"298.15 K"# . As long as you shoot for#"298.15 K"# , you can look it up in the appendix of your textbook.#k_B# is theBoltzmann constant,#1.3806xx10^(-23)# #"J/K"# .#Omega# is thenumber of microstatesconsistent with a given macrostate.

So, if we can calculate or if we know the compound's entropy at a given temperature, we can calculate the number of microstates.

Note though, that **we shouldn't be surprised if** **is absurdly large**, because

Using

#color(blue)(Omega) = e^(S"/"k_B)#

#= "exp"(191.6 cancel("J/")"mol"cdotcancel("K")"/"1.3806xx10^(-23) cancel("J/molecule"cdot"K") xx cancel"1 mol"/(6.0221413 xx 10^23 cancel"molecules"))#

#~~ color(blue)(1.019 xx 10^10 " accessible microstates")#

So really, the hard part is figuring out what the entropy for the system is if we don't have the number readily available. If you want to know how to do it, there's a *very involved process*, shown below.

**Fortunately, if you want it at** **it's already been done for you**: you can find

For you extra hard-working people:

Deriving Entropy at a Given Temperature