Final answer:
The correct formula for the entropy of mixing two perfect gases is ΔS = -R(x1 ln(x1) + x2 ln(x2)), representing the increased disorder when gases mix due to the greater number of possible microstates.
Step-by-step explanation:
Entropy of Mixing for Perfect Gases
The entropy of mixing for two perfect gases is captured by the formula: ΔS = -R(x1 ln(x1) + x2 ln(x2)), where ΔS represents the change in entropy, R is the universal gas constant, and x1 and x2 are the mole fractions of the two gases. When gases are mixed, there is an increase in the number of possible microstates for the system, which leads to an increase in entropy. The correct option from those provided is A) ΔS = -R(x1 ln(x1) + x2 ln(x2)). This relationship is derived from the statistical interpretation of entropy, considering that the gases do not interact and the volume for mixing is the addition of the original volumes of the gases.
The various forms of the entropy change equation provided, including those for standard entropy change (AS°) and the specific example of mixing, are all based on the fundamental concept that entropy reflects the disorder or distribution of energy and matter within a system. Significant increases in entropy occur when going from solid to liquid to gas states. Moreover, entropy increases with the complexity of molecules and when solutions form due to the additional possibilities for arrangement (microstates) in the system.
Thus, the entropy change for mixing reflects the increased disorder when two different substances are combined, leading to a larger number of microstates and, hence, a greater entropy.