Chapter 4, Problem 4.23P

Interpretation Introduction

Interpretation:

A description about the changes observed when a mixture of composition $b_3$ is heated, at each stage giving the number, composition and relative amounts of phases present has to be done.

Concept Introduction:

A state of matter that is uniform throughout in chemical composition and physical state is known as phase.

Phase diagram is a graphical representation of all the equilibrium phase as a function of temperature, pressure and composition.

The lever rule is mainly used to determine compositions of phases and the relative proportions of phases to each other in Binary diagrams of compounds and using the lever rule we can determine quantitatively the relative composition of a mixture in a two phase region in a phase diagram. 

According to lever rule, we can write,

$n=n^{\text{'}}+n^{\text{'}\text{'}}$

Where,

$n^{\text{'}}:$ Total amount of molecule in one

$n^{\text{'}\text{'}}:$ Total amount of molecule in other phase

The total amount of A in the sample is $n{x}_A$ where $x_A$ it is the overall mole fraction of A in the sample. The overall amount of A is also the sum of its amounts in the two phases, where it has the mole fractions $x_A^{\text{'}}and{x}_A^{\text{'}\text{'}}$ respectively.

Thus,

$\begin{array}{l}n{x}_A=n^{\text{'}}{x}_A^{\text{'}}+n^{\text{'}\text{'}}{x}_A^{\text{'}\text{'}}\\ \\ n^{\text{'}}\left(x_A^{\text{'}}-x_A\right)=n^{\text{'}\text{'}}\left(x_A-x_A^{\text{'}\text{'}}\right)\end{array}$