# 5.1: Introduction

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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.