1. Consider a container of volume 250 mL that is divided into two compartments o

Question

1.    Consider a container of volume 250 mL that is divided into two compartments of

equal size. In the left compartment there is argon at 10.0 mbar and 0?C. In the right compartment, there is neon. The system is under both mechanical and thermal equilibrium. Calculate the entropy and Gibbs energy of mixing when the partition is removed. Assume that the gases are perfect.

Consider a container of volume 250 mL that is divided into two compartments of equal size. In the left compartment there is argon at 10.0 mbar and 0?C. In the right compartment, there is neon. The system is under both mechanical and thermal equilibrium. Calculate the entropy and Gibbs energy of mixing when the partition is removed. Assume that the gases are perfect.

Explanation / Answer

deltaG = nRT [ Xa*ln(Xa) + Xb*ln(Xb)]

deltaG = PV[Xa*ln(Xa) + Xb*ln(Xb)] where Xa and are mole fraction of argon and neon

Since equal amount is mixed hence Xa = 1/2 and Xb = 1/2

Now,

10mbar = 9.87 x 10^-4 atm , V = 0.25 L

PV = 2.45 x 10^-4 atmL = 0.02533 J

deltaG = 0.02533(0.5*ln(0.5) + 0.5*ln(0.5))

deltaG = -0.0175 J

deltaS = -deltaG/T = 0.0175/273.15 = 6.42 x 10^-5 J/K

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