Consider what occurs when 20 mol of pure O_2 and 80 mol of pure N_2 are allowed

Question

Consider what occurs when 20 mol of pure O_2 and 80 mol of pure N_2 are allowed to form a homogeneous mixture at a constant temperature of 25 degree C and with initial and final pressures of 1 atm. Calculate the total Gibbs free energy change delta G and entropy change delta S for this mixing process. What are the chemical potentials of N_2 and O_2 in the mixture, compared to their respective standard states at the same temperature (i.e., mu - mu degree for each gas)? An oxygen concentrator is a machine that can take in air and separate it into an oxygen-rich portion (for medical use. for example) and an oxygen-poor portion (containing mostly nitrogen), all at room temperature. Discuss with a classmate how the concepts in this problem might help to determine the minimum energy (work) that is required to operate such a machine.

Explanation / Answer

gibbs free energy change =-RT[x1lnx1+x2lnx2]

x1=0.8 and x2=0.2

Gibbs free energy change =- 8.314*(25+273.15){0.8ln0.8 +0.2 ln0.2}=1240.41 joules

2. entropy change =-R[x1lnx1+x2lnx2] =4.16 joule/K

3. change in chemical potential = u-uo = RT ln P

P= partal pressure N2 =0.8*1 =0.8atm and O2= 0.2 atm

for N2, Change in chemical potnerial = RT ln0.8 =8.314*298.16* lnP=553 adnd O2= 8.314*298.15*ln(0.2)=-3989.51

c) work done is noting but the change in gibbs free energy.

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