Chapter 10, Problem 10.13P

(a)

Interpretation Introduction

Interpretation:

The expressions for the partial molar volumes of species 1 and 2 at T and P.

Concept Introduction:

The expression for molar volume of a binary liquid mixture at T and P is as follows:

  $V=120x_1+70x_2+(15x_1+8x_2)x_1{x}_2$ . eq 1

(b)

Interpretation Introduction

Interpretation:

To show that when the above expressions are combined in accord with Eq 10.11, the given equation for V is recovered.

Concept Introduction:

The expression for molar volume of a binary liquid mixture at T and P is as follows:

  $V=120x_1+70x_2+(15x_1+8x_2)x_1{x}_2$ .eq 1

Eq 10.11: $M={\displaystyle \sum _i{x}_i}\overline{M_i}$

The expression for total molar volume in terms of partial molar volume is as follows:

  $V=x_1\overline{V_1}$

(c)

Interpretation Introduction

Interpretation:

To show that the above expressions satisfy Eq 10.14, the Gibbs/Duhem equation.

Concept Introduction:

The expression for molar volume of a binary liquid mixture at T and P is as follows:

  $V=120x_1+70x_2+(15x_1+8x_2)x_1{x}_2$ .eq 1

Eq 10.14:${\displaystyle \sum _i{x}_{i}d}\overline{M_i}=0$(cons T, P)

(d)

Interpretation Introduction

Interpretation:

To show that ${(d\overline{V_1}/d{x}_1)}_{x_1=1}={(d\overline{V_2}/d{x}_1)}_{x_1=0}=0$

Concept Introduction:

The expression for molar volume of a binary liquid mixture at T and P is as follows:

  $V=120x_1+70x_2+(15x_1+8x_2)x_1{x}_2$ .eq 1

(e)

Interpretation Introduction

Interpretation:

To plot the values of V, $\overline{V_1}$ and $\overline{V_2}$calculated by the given equation for V and by the equations developed in (a) vs x₁, to label points $V_1,V_2,{\overline{V}}_1^{\infty }$and ${\overline{V}}_2^{\infty }$and show their values.

Concept Introduction:

The expression for molar volume of a binary liquid mixture at T and P is as follows:

  $V=120x_1+70x_2+(15x_1+8x_2)x_1{x}_2$ .eq 1