# 5.1: Introduction

In the previous chapter, we began our study of macroscopic mass and mole balances for multicomponent systems. There we encountered a variety of measures of concentration and here we summarize these measures as

$\rho_{A} =\left(\begin{array}{c} {\text{mass of species } A} \\ {\text{per unit volume}} \end{array}\right)$

$\rho =\sum_{A = 1}^{A = N}\rho_{A} , \quad \text{ total mass density}$

$\omega_{A} ={\rho_{A} / \rho } , \quad \text{ mass fraction}$

$c_{A} ={\rho_{A} / MW_{A} } , \quad \text{ molar concentration}$

$c=\sum_{A = 1}^{A = N}c_{A} , \quad \text{ total molar concentration}$

$y_{A} \text{ or } x_{A} ={c_{A} / c} , \quad \text{ mole fraction}$

In the analysis of gas-phase systems it is often important to relate the concentration to the pressure and temperature. This is done by means of an equation of state, often known as a $$p-V-T$$ relation. In this chapter we will make use of the ideal gas relations; however, many processes operate under conditions such that the ideal gas laws do not apply and one must make use of more general $$p-V-T$$ relations. Non-ideal gas behavior will be studied in a subsequent course in thermodynamics.