Q1. At 20 °C and atmospheric pressure, the molar volume (in cm 3 /mol) of liquid mixtures of compound 1 and compound 2 can be described by: V = 12.38x 1 2 + 45.37x 1 + 19.55 Note that x 1 is mole...

Q1. At 20 °C and atmospheric pressure, the molar volume (in cm³/mol) of liquid mixtures of compound 1 and compound 2 can be described by:

                                    V = 12.38x₁
² + 45.37x₁+ 19.55

Note that x₁ is mole fraction of compound 1 and x₂= 1 - x₁ is mole fraction of compound 2.

a) Find expressions for the partial molar volumes of compound 1 and 2 at this T and P.

b) Show that when these partial molar volume expressions are combined in accord with SVA Equation 10.11 the given equation for V is recovered.

c) Show that the expression satisfies (or doesn’t), the Gibbs-Duhem Equation

d) Plot values of molar volume, partial molar volume of compound 1, and partial molar volume of compound 2 versus x₁.  Label the pure component molar volumes and the partial molar volumes at infinite dilution.

e) What is thetotal volume(cm³) of a mixture containing 4 moles of component 1 and 6 moles of component 2?

f) What is the
partial molar volume of component 1(cm³/mol) of a mixture containing 4 moles of component 1 and 6 moles of component 2?

g) What is theexcess volume(cm³) of a mixture containing 4 moles of component 1 and 6 moles of component 2?

h) What would be the volume (cm³) of a mixture containing 4 moles of component 1 and 6 moles of component 2if the solution were an ideal solution?

***HINT: Recall one common model for V is:
V=V1x1+V2x2+Ax1x2,
where
V₁ and V₂ are the molar volumes of the pure components***