The enthalpy of mixing (J/mol) of Au-Pt solid solutions can be approximately giv

Question

The enthalpy of mixing (J/mol) of Au-Pt solid solutions can be approximately given by the following relation: ?H m= 22,500(XPt ? X 2 Pt) . Since the enthalpy of mixing is positive, solid solutions of Au and Pt will exhibit phase separation at low temperatures. Compute the following quantities.(total of 5 points) (a) The T above which single-phase solutions of Au and Pt can exist for any composition. For this solution use the Gibbs energy of mixing relation ?G m = RT(XAulnXAu + XPtlnXPt) + ?H m , where ?H m is the heat of mixing (3 points) (b) At what composition of Au and Pt does the free energy of mixing given by the form in part (a) have its maximum magnitude for any given temperature. (2 points)

Explanation / Answer

a.
T above which single phase solutions can exist critical temperature is constant/2R = 22500/2*8.314 = 1353.13 k
b.
d/dx [x[1-x]] = 0 :x=0.5 that is at 50 percent each of Au and Pt

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