Interpretation:
Does the mixture form a miscibility gap? If so, how does your value is compared with the experimental value at this temperature?
Concept Introduction:
The expression of solubility parameters for methanol (1) and hexane (2) is,
Here, molar volume of methanol (1) and hexane (2) is
The expression of change in molar internal energy of vaporization is,
Here, change in molar enthalpy of vaporization is
The expression of natural logarithmic activity coefficient of component methanol is,
Here, mole fraction of component methanol is
The expression of natural logarithmic activity coefficient of component hexane is,
The phase equilibrium relationship for phase 1 and 2 is,
Here, mole fraction of component 1 in phase
Explanation of Solution
Write the expression of solubility parameters for methanol (1) and hexane (2).
Write the expression of change in molar internal energy of vaporization.
Rewrite Equations (1) and (2) using Equation (3).
Refer Appendix C.1, “Critical point, Enthalpy of phase change, and liquid molar volume”; obtain the following properties at 300 K for methanol (1) and n-hexane (2).
Substitute
Substitute
Write the expression of the parameter
Substitute
Write the expression of the parameter
Substitute
Write the expression of natural logarithmic activity coefficient of component methanol.
Write the expression of natural logarithmic activity coefficient of component hexane.
Write the phase equilibrium relationship for phase 1 and 2.
Write the expression of the molar Gibbs free energy of mixing.
If we plot the graph of
By using this approach, obtain the nearest values of
When the SH approach does, a miscibility gap is predicted. That is the gap over a bigger range is experimentally observed. Actually, it predicts an immiscible liquid system.
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