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Two volatile liquids A (P A pure= 165 Torr) and B (PB pure= 85.1 Torr) are confined in a piston/cylinder assembly. Initially only the liquid phase is present. As the external pressure is reduced, vapor is first observed at a total pressure of 110 Torr. Calculate the mole fraction of component A in the solution (XA) and the mole fraction of component A in the vapor (YA).

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sebassandin

Answer:

[tex]y_A=0.467\\x_A=0.312[/tex]

Explanation:

Hello,

In this case, one could use the following equations to compute the required mole fractions (fugacity equality for both A and B):

[tex]p_A^{vap}x_A=y_AP\\p_B^{vap}(1-x_A)=(1-y_A)P\\p_B^{vap}-x_Ap_B^{vap}=P-y_AP\\y_AP-x_Ap_B^{vap}=P-p_B^{vap}[/tex]

Therefore, the 2x2 system of equations turns out:

[tex]\left \{ {{165x_A-110y_A=0} \atop {110y_A-85.1x_A=24.9}} \right.\\ \\y_A=0.467\\x_A=0.312[/tex]

Best regards.

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