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9. Consider a container of volume 5.0 L, which is divided into two compartments

ID: 907934 • Letter: 9

Question

9. Consider a container of volume 5.0 L, which is divided into two compartments of equal size. In the left compartment there is nitrogen at 3.0 atm and 25 C. In the right compartment there is oxygen at 1.0 atm and 25 C. What are the changes in the entropy and the Gibbs free energy function of the system when the partition is removed and the gases are allowed to mix? Assume the gases to be ideal. 10. In a similar experiment (see the previous problem), the left compartment initially contains nitrogen at 3.0 atm, while the right compartment contains also nitrogen, but at 1.0 atm, all at 25 C. Find delta S and delta G in this case.

Explanation / Answer

Moles of nitrogen gas in the first compartment n= PV/RT= 3*2.5/(25+298.15)*0.08206 =0.3065

Moles of oxygen gas in the second compartment = PV/RT= 1*2.5/(25+298.15)= 0.102181

Total moles after mixing = 0.3065+0.102181= 0.408727 moles

Volume after mixnig = 5 L temerature =25 Deg.C =25+273.15= 298.15K

P= nRT/V= 0.408727*0.08206*298.15/ 5=2 atm

Mole fraction of Nitrogen xa = 0.306545/0.408727= 0.75 Xb= 1-0.75= 0.25

delG=PV (xa* lnxa+ xblnxb)= 2*1.01325*105Pa*5 *10-3 m3 (0.75ln0.75+0.25ln0.25)=-569.78Joules

Entropy change due to mixing = -delG/T =569.78/298.15= 1.1911

10. Entopy change

Final pressure in this case

total moles of nitrogen is same as that of nitrogen and oxygen = 0.408727 moles

P= 2 atm( same as the previous case)

DelS/R = -ln(2/3) + (-ln(2/1)= -0.28768

delS= 0.28768*8,314 joules/K=-2.39179 J/K

delG= -TDelS= -298.15*(-2.39179)=713.112 Joules