Chapter 1, Problem 1.3P

Interpretation Introduction

Interpretation:

The given expression for density of a mixture is to be proven.

Concept Introduction:

For a mixture containing $n$ components, the mass fraction of the component $i$

in the mixture is given as:

  $x_i=\frac{m_i}{{\displaystyle \sum _i^n{m}_i}}$ ........(1)

Here, $m_i$ is the mass of component $i$ .

For a fluid, its density $\left(\rho \right)$ is defined as:

  $\rho =\frac{m}{V}$ ........(2)

Here, $m$ is the mass of the fluid and $V$ is the volume of the fluid.

Density of a mixture $\left({\rho }_{mixture}\right)$ containing $n$

components is defined as:

  ${\rho }_{mixture}=\frac{{\displaystyle \sum _i^n{m}_i}}{{\displaystyle \sum _i^n{V}_i}}$ ........(3)