At 600 degree C, copper and gold form a regular solid solution for which the exc

Question

At 600 degree C, copper and gold form a regular solid solution for which the excess molar Gibbs free energy of mixing is given by: delta G_mix^xs = -28, 280 X_AuX_Cu J/mole The saturated vapor pressure of solid copper is given by: In p degree _Cu = - 40, 920/T - 0.86lnT + 21.67 and the saturated vapor pressure of solid gold is given by: In p degree _Au = - 45, 650/T - 0.306lnT + 10.81 with T in K and p degree in atm. Does this solid solution exhibit a positive or negative deviation from ideal behavior at 600 degree C? Explain your answer. Find an expression for the heat of sublimation of pure copper as a function of temperature. Calculate the heat of sublimation of pure copper at 600 degree C. Calculate the partial pressures of copper and gold (in atm) exerted by a solid solution in which X_cu = 0.6 at 600 degree C.

Explanation / Answer

At 600deg.c, the vapor pressures

lnCu= -40920/(600+273)-0.86*ln(873)+21.67, Cu vapor pressre at 600 deg.c=3.35*10-14 atm

for Au, lnAu = -45650/873-0.306*ln(873)+10.81, Au= 1.21*10-19 atm

given deltaGmix= -28280 XAu*XCu

lnYAu= -28280XCu2 and lnYCu= -28280XAu2

for ideal solution P= XCuPCu+XAu*PCu

let XCu=0.1,XAu=1-0.1= 0.9

P= 0.1*3.35*10-14 +0.9*1.21*10-19 = 3.35*10-15 atm

For real solution,   P= XCuPCu*YCu +XAu*Pau*YAu

YAu= exp(-28280*0.1*0.1)= 1.518*10-123

YCu= exp(-28280*0.9*0.9)= 0

P = 0.9*1.21*10-19* 1.518*10-123 < P ( ideal solution)

Since the mixture pressure is lower than ideal solution, the solution shows –ve deviation.

d(lnPCu)= 40920/T2 -0.86/T

d(lnPCu)= deltaH/RT2 = (deltaG+ TdeltaS)/T2 = deltaG/T2 +deltaS/T

similalty for Au, d(lnPAu)= 45650/T2 -0.306/T= deltaG/T2 +deltaS/T

deltaG= 40920 and deltaS= -0.86 for Cu

deltaH= heat of sublimation at 600 deg,c = deltaG-TdeltaS= 40920-873*(-0.86) =41671 energy units/mole

when Xcu=0.6, XAu= 1-0.6=0.4

lnYCu = -28280*0.6*0.6 YCu= 0

and lnYAu= 0

so the solution is ideal

Partial pressure of Au= xAu*Pau = 0.4*1.21*10-19 atm =4.84*10-20 atm

Partial pressure of Cu =0.6*3.35*10-14= 2.01*10-14 atm

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