# Summary

Relative volatility is a comparative measure of the vapour pressures of components in a liquid mixture. It is commonly used in the design of absorption and separation processes such as distillation as it allows the difficulty of separating components to be quickly assessed.

# Definitions

: | Partial pressure | |

: | Pressure | |

: | Liquid Mole Fraction | |

: | Vapour Mole Fraction | |

: | Relative Volatility | |

: | Activity Coefficient |

# Introduction

The partial pressures or composition of components in an ideal mixture can be easily calculated using simplified relationships such as Dalton's Law, Raoult's Law and Henry's Law. While these methods are adequate for either low or high concentrations of subject components they break down when non-ideal ('real') behaviour is encountered.

Consider the graph below, here our simplified relationships Henry's law and Raoul's law can be applied over the range A-B and C-D respectively, however they break down in the middle where non-ideal behaviour is encountered, B-C.

To adequately estimate the properties of mixtures over a wide range of conditions a more accurate approach is required. For this we can use relative volatility calculations in conjunction with activity coefficients.

# Relative Volatility

To determine the relative volatility of an ideal binary mixture the volatility of a component is first defined as the ratio of its partial pressure to its liquid mole fraction:

The relative volatility, of a binary mixture is then calculated by taking the ratio of the volatilities for each component and as follows:

Using Raoult's law the liquid and vapour mole fractions can then be related to each other via the relative volatility:

# Activity Coefficients

In non-ideal systems, an additional component called the activity coefficient is introduced to the equations presented above to account for a real mixtures deviation from ideal behaviour.

The activity coefficient is a function of concentration, temperature and pressure and therefore complex to calculate. Detailed usage of activity coefficients is outside the scope of this article as they are not well suited to simple calculations and are best left to computer simulation packages.