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I would like to give an alternative derivation for theorist's answer. You can get the same answer with statistical mechanics using a lattice model. Let us discretize the container into $M_1$ respective $M_2$ cells. The volume of a cell is $V_{cell}$. Each gas particle fits exactly into one cell and can hop from cell to cell in a discrete manner. Since we are ...
There's a simple way to solve this: We know that, for an ideal gas at constant T: $$\Delta S = -nR \ln \frac{p_f}{p_i}= nR \ln \frac{p_i}{p_f}$$ And since ideal gases ignore each other, we can calculate the entropy change for gas 1 and gas 2 separately, and simply sum the two. [At any given $T$, the chemical potential of an ideal gas is determined only by ...