You are interested in finding the pressure at which the first bubble of vapor will form from a liquid mixture of ethanol (1) and benzene (2) (49% by mole ethanol) at 313 K. The Margules parameters for this mixture are A12 = 2.173 and A21 = 1.539, while the Wilson parameters for this mixture are a12/R = 653.13 K and a21/R = 66.16 K. Find the pressure and vapor-phase composition using three ways.
A. The 2-parameter Margules equation
B. The Wilson equation
C. Ideal solution
(A)
Interpretation:
The pressure and vapour-phase composition using 2-parameter Margules equation.
Concept Introduction:
Write the expression to obtain the liquid mole fraction of benzene
Here, liquid mole fraction of ethanol is
Write the expression to obtain the activity coefficient of component 1
Here, Margules parameters are
Write the expression to obtain the activity coefficient of component 2
Write the expression of vapor pressure using Antoine equation.
Here, temperature in degree Celsius is
Write the expression to obtain the pressure
Write the expression to obtain the vapor phase composition.
Here, mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Explanation of Solution
Given information:
Margules parameters are
Write the expression to obtain the liquid mole fraction of benzene
Substitute 49% mole for
Write the expression to obtain the activity coefficient of component 1
Substitute
Write the expression to obtain the activity coefficient of component 2
Substitute
Write the expression of vapor pressure using Antoine equation.
From Appendix E, “Antoine Equations”, write the following properties for component 1 and 2 as in Table (1).
Parameters | Ethanol | Benzene |
A | 8.321 | 6.905 |
B | 1718.10 | 1211.03 |
C | 237.52 | 220.79 |
Convert the unit of temperature.
Substitute
Substitute
Write the expression to obtain the pressure
Substitute
Thus, the pressure at which the first bubble of vapor will form is
Write the expression to obtain the vapor phase composition.
Substitute
Thus, the mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Substitute
Thus, the mole fraction of component 2 is
(B)
Interpretation:
The pressure and vapour-phase composition using the Wilson equation.
Concept Introduction:
Write the expression to obtain the temperature dependent parameters of the Wilson equation
Here, Wilson parameter is
Write the expression to obtain the temperature dependent parameters of the Wilson equation
Here, Wilson parameter is
Write the expression to obtain the activity coefficient of component 1
Write the expression to obtain the activity coefficient of component 2
Write the expression to obtain the pressure
Write the expression to obtain the vapor phase composition.
Here, mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Explanation of Solution
Given information:
Wilson parameters are
Refer appendix C.1, “Critical point, enthalpy of phase change, and liquid molar volume”, obtain the liquid molar volume
Compound |
liquid molar volume |
Ethanol (1) | 58.68 |
Benzene (2) | 89.41 |
Write the expression to obtain the temperature dependent parameters of the Wilson equation
Substitute
Write the expression to obtain the temperature dependent parameters of the Wilson equation
Substitute
Write the expression to obtain the activity coefficient of component 1
Substitute
Write the expression to obtain the activity coefficient of component 2
Substitute
Write the expression to obtain the pressure
Substitute
Thus, the pressure at which the first bubble of vapor will form is
Write the expression to obtain the vapor phase composition.
Substitute
Thus, the mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Substitute 0.392 for
Thus, the mole fraction of component 2 is
(C)
Interpretation:
The Ideal solution.
Concept Introduction:
Write the expression to obtain the pressure
Write the expression to obtain the vapor phase composition.
Here, mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Explanation of Solution
Write the expression to obtain the pressure
Substitute
Thus, the pressure at which the first bubble of vapor will form is
Write the expression to obtain the vapor phase composition.
Substitute
Thus, the mole fraction of component 1 is
Write the expression to obtain the mole fraction of component 2
Substitute 0.415 for
Thus, the mole fraction of component 2 is
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Chapter 11 Solutions
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