What is the Gibbs free energy of pure solid Al at 400K? What is the Gibbs free e

ID: 3281270 • Letter: W

Question

What is the Gibbs free energy of pure solid Al at 400K? What is the Gibbs free energy of liquid Ga at 400K?

consider:

heat capacity of solid Al: 23.25449 + 5.32e-3*T -1.09e5/T^2 + 5.34e-6*T^2

heat capacity of solid Ga: 27.8 - 26e-3*T - 7.5046e5/T^2 + 7.64e-5*T^2

heat capacity of liquid Al: 31.751

heat capacity of liquid Ga: 24.986 + 1.83e-3*T + 267050/T^2 - 5.50e-7*T^2

standard entropy of Al: 28.275 J/molK

standard entropy of Ga: 40.838 J/molK

temperature of melting of Al: 934K

temperature of melting of Ga: 303K

latent heat of melting of Al: 1.07e4 J/mol

latent heat of melting of Ga: 5.60e3 J/mol

Gibbs free energy of Aluminium = GAl

GAl = HAl - T*SAl

HAl = (Heat Capacity of Solid Al) * T = (23.25449 + 5.32e-3*T -1.09e5/T^2 + 5.34e-6*T^2) * T

T*SAl = T * (28.275)

GAl = (23.25449 + 5.32e-3*T -1.09e5/T^2 + 5.34e-6*T^2) * T - T * (28.275)

GAl (at T = 400) = ( (23.25449 + 5.32e-3*T -1.09e5/T^2 + 5.34e-6*T^2) * T - T * (28.275) ) at T = 400

put value of T = 400 and get the answer.

Gibbs free energy of liquid Ga = GGa

GGa = HGa - T*SGa

melting point of Ga = 303K

HGa = (heat capacity of solid Ga) * Tmelting point + (latent heat of melting of Ga) + (heat capacity of liquid Ga) * T (=400-303)

HGa = (27.8 - 26e-3*T - 7.5046e5/T^2 + 7.64e-5*T^2) * 303 + (5.60e3 ) + (24.986 + 1.83e-3*T + 267050/T^2 - 5.50e-7*T^2) * T (=400-303)

solve above equation to get the answer.

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