Answer
Entropy Change Due to Mixing of Nitrogen Gas (N2)
We are mixing two samples of identical gas (N2) at the same temperature and pressure. One container has 1 mol and the other has 2 mols of nitrogen.
Important Concept:
When identical gases are mixed under the same temperature and pressure, and there is no change in volume or thermodynamic variables, there is no increase in entropy due to mixing.
Why? Because mixing identical particles doesn’t lead to any new arrangements distinguishable at the molecular level. No randomness is added to the system.
General Formula for Entropy of Mixing (for ideal gases):
ΔSmix = -R(n₁lnX₁ + n₂lnX₂ + … + nnlnXn)
However, this applies only when different gases (like O2 and N2) are mixed.
Since both containers have only nitrogen gas, the entropy change of mixing is:
ΔS = 0 J/K
Final Answer:
0 J/K
This is because there is no increase in disorder or number of microstates for identical gas mixing at the same conditions.