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Answer :
Final answer:
A mixture of nitrogen and argon gases results in an increased number of microstates and hence increased system entropy due to larger volume occupancy and matter dispersal. This change is explained by Avogadro's law, stating that equal volumes of gases at the same temperature and pressure house the same number of molecules.
Explanation:
The change in entropy of a system when two gases mixtures can be calculated using Boltzmann's entropy formula, S = k * ln(W), where k is Boltzmann's constant and W is the number of microstates. When 6.00 mole of nitrogen (N2) gas and 6.00 mole of argon (Ar) gas in separate, equal-sized, insulated containers at the same temperature mix, the number of microstates increases, hence resulting in an increase in the entropy of the system According to Avogadro's law, equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. So, nitrogen and argon gases occupy a volume twice as large as that which each occupied before mixing, causing matter dispersal and hence an increase in entropy. Since the gases can diffuse into each other's previously occupied space and occupy a larger volume, there are significantly more ways to arrange the gas molecules, leading to a higher number of microstates, which ultimately means a higher entropy.
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