Chapter 4, Problem 4C.1E

Interpretation Introduction

Interpretation:

The total volume of the given mixture  of total mass $1.000kg$ which contains propanone and trichlormethane has to be determined.

Concept introduction:

The number of moles of any substance can be determined using the equation

$\text{Number}\text{of}\text{mole}\text{=}\frac{\text{Given}\text{mass}\text{of}\text{the}\text{substance}}{\text{Molar}\text{mass}}$

The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mole (g/mol).

Partial molar quantity is a thermodynamic quantity which indicates how an extensive property of a mixture or solution varies with changes in the molar composition of the mixture at constant temperature and pressure. These quantities are usually indicated by the lower case letter.

For example,

$\begin{array}{c}{v}_i={\left(\frac{\partial V}{\partial n_i}\right)}_{T,P,n_{i,j}}\\ n_i{v}_i=V\end{array}$

This is the partial molar volume of component i.

A mixture contains two components; A and B and $V_{A}and{V}_B$ are their partial molar volumes respectively, then the total volume V of the mixture can be determined using the following equation,

$\text{V}={\text{n}}_{\text{A}}{\text{V}}_{\text{A}}\text{+}{\text{n}}_{\text{B}}{\text{V}}_{\text{B}}\boxed{\begin{array}{l}Where,\\ n_A:numberofmolesofcomponentA\\ n_B:numberofmolesofcomponentB\end{array}}$

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture. Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,

  $\text{molecule}\text{fraction}\text{of}\text{A,}\text{(}{\text{χ}}_{\text{A}}\text{) }\text{=}\frac{\text{numbers}\text{of moles of}\text{molecule A}{\text{(n}}_{\text{A}}\text{)}}{\text{total number of moles}{\text{(n}}_{\text{A}}{\text{+n}}_{\text{B}}{\text{+n}}_{\text{C}}\text{) }}$