This problem concerns a compound for which the following information is available:

Question

• The triple point is located at P=0.8 atm and T=300 K.
• The critical point is located at P=40 atm and T=650 K.
• The acentric factor is 0.25.
• At atmospheric pressure, it boils at 314 K.
• At atmospheric pressure, the molar volume is 0.12 L/mol for solid and 0.132 L/mol for liquid.
• At atmospheric pressure, the enthalpy of fusion/melting is 400 J/mol.

Give your best estimate of each of the following:

A) The enthalpy of vaporization at the triple point.
B) The vapor pressure at 305 K.
C) The vapor pressure at 500 K.
D) Estimate the melting point at atmospheric pressure.

Answer 1

Apply Clausius-Clapeyron equation and solve for ??H^vap:



Use data that agrees with the assumptions associated with the Clausius-Clapeyron equation, such as a small temperature range and low pressures. Let P_1^sat=0.8 atm , P_2^sat=1 atm , T_1=300 K , and T_2=314 K:



Apply Clausius-Clapeyron equation which is valid in this case since the temperature range is small:



Clausius-Clapeyron equation is not valid in this case because it is modeled using the ideal gas law which is not valid at higher pressures. The unknown P_2^sat will be high compared to P_1^sat because T_2 is much greater than T_1. Apply the shortcut vapor pressure equation:



Where ?=0.25, P_c=40 atm, T_c=650 K and T=500K, which is the temperature at which the vapor pressure P^sat is being solved for:



Apply the Clapeyron equation:



Separate variables and integrate:



Where state 1 will correspond to the triple point, and state 2 will correspond to the melting point at atmospheric pressure. ??H^fusis assumed to be constant with respect to temperature within this range.