09.09 - Calculation of Fugacity (Solids)

The fugacity of a solid (uakron, 19min) follows a similar trend to that of a liquid, but there can be unexpected implications. The impact of pressure requires careful consideration. NIST Webbook lists the melting temperature of xenon as 161.45K and the Antoine equation as log₁₀P^sat(bars) = 3.80675 - 577.661/(T(K)-13.0), Cp^V=22.7 J/mol-K, Cp^L=44.4 J/mol-K, ρ^L=2.9662 g/cm3. Wikipedia lists the solid density as 3.540 g/cm3 (and the liquid density as 3.084) and the heat of fusion as 2270 J/mol. You may assume Cp^L=Cp^S. Use Eq. 7.06 to describe the vapor phase. You may assume ω = 0 for the purpose of these calculations. This screencast shows a sample calculation to solve for: (a) the vapor fugacity at 162 K and 0.085 MPa (b) the liquid fugacity in equilibrium with the same vapor at 162 K and 0.085 MPa (c) the liquid fugacity at 162 K and 8.5 MPa (d) the solid fugacity at 161.45 K and 0.082 MPa (e) the solid fugacity at 162 K and 8.5 MPa. If you are still having trouble understanding the ways that all these fugacities relate, you might like to view the phase diagram implications of VLSE (uakron, 9min).

Comprehension Questions:

1. How much did raising the pressure to 8.5 MPa change the liquid fugacity (bars)?
2. Estimate the fugacity (MPa) of the vapor at 162 K and 1.15 MPa and compare it to the liquid. Which is smaller? Which state do you think best characterizes the fluid (ie. V or L or S)?
3. Estimate the fugacities (MPa) of methane vapor, liquid, and solid at its triple point using PREOS. Compare the vapor pressure from PREOS at the triple point to that from NIST.
4. Assuming V^S=V^L/1.1, estimate the fugacity of solid methane at 92K and 10 MPa using PREOS for all fluid properties. Consult the NIST Webbook for T and H_fus at the triple point.