Question

Five hundred moles of Air are mixed with 170 moles of gaseous ethanoland 45 moles of gaseous water at 150°C and 0.05 MPa. Calculate the total Gibbs’ free energy of mixing ∆Gmix and the total entropy of mixing ∆Smix. Please, clearly state and justify your assumptions.

Answer 1

a = Air

e = ethanol

w = water

Moles of air na = 500 mol

Moles of ethanol ne = 170 mol

Moles of water nw = 45 mol

Total Moles = 500 + 170 + 45 = 715 moles

Mol fraction of air Xa = 500/715 = 0.6993

Mol fraction of ethanol Xe = 170/715 = 0.2378

Mol fraction of water Xw = 45/715 = 0.0629

total entropy of mixing

∆Smix = - R [Xa lnXa + Xe lnXe + Xw lnXw]

= - 8.314 [0.6993*ln(0.6993) + 0.2378*ln(0.2378) + 0.0629* ln(0.0629)]

= - 8.314 [-0.25012 - 0.34156 - 0.17399]

= - 8.314 x (-0.76567)

= 6.3657 J/mol·K

total Gibbs’ free energy of mixing

∆Gmix = RT [na lnXa + ne lnXe + nw lnXw]

∆Gmix = 8.314 x (150+273)K x [500*ln(0.6993) + 170*ln(0.2378) + 45* ln(0.0629)]

= 3516.822 x [-547.49]

= - 1925433.43 J/mol

= - 1925.433 kJ/mol