Question

How do you calculate microstates in chemistry?

Answer 1

Well, you can calculate the NUMBER of microstates at `"298.15 K"` with tabulated standard molar entropies.

• I go over what microstates are, here.
• An example that should be easy to follow is here.
• A much more detailed calculation example with methane is gone into here.

---

Boltzmann's formulation of entropy states:

`S = k_BlnOmega`

where `Omega` is the number of microstates, and `k_B = 1.38065 xx 10^(-23) "J/K"` is the Boltzmann constant.

There is a more complicated formula for `Omega` that works for systems where the number of available states is much larger than the number occupied:

`Omega = "exp"{sum_(i=1)^(N) [N_iln(g_i/N_i) + N_i]}`

where `N_i` is the number of particles with energy `epsilon_i` in a state with degeneracy `g_i`.

For simplicity, we can calculate the value of `Omega` indirectly.

`Omega = e^(S//k_B) = "exp"(S//k_B)`

As an example, `"O"_2` has `S^@ = "205.15 J/mol"cdot"K"` at `"298.15 K"` and `"1 bar"`. So, in those conditions:

`color(blue)(Omega) = "exp"((205.15 cancel"J""/"cancel"mol"cdotcancel"K")/(1.38065 xx 10^(-23) cancel"J""/"cancel"molecule"cdotcancel"K" xx (6.0221413 xx 10^(23) cancel"molecules")/(cancel"1 mol")))`

`= color(blue)(5.197 xx 10^10)`

So, there are `5.197 xx 10^10` ways for `"O"_2` to exist such that it has an entropy of `"205.15 J/mol"cdot"K"`.