0.16 Phase equilibrium and intermolecular forces

Introduction

Our study of phase equilibrium between the liquid and gas phases has opened a door to a world of information about how molecules interact in a liquid. Recall that we would like to relate the properties of individual molecules to the properties of bulk samples of a substance. Our studies of the properties of gases were a little disappointing towards this goal. We found that the properties of a mole of gas molecules are the same, accurately predicted for all substances by the Ideal Gas Law except under extreme conditions. This means that the properties of individual molecules are largely irrelevant to the properties of gases.

By contrast, we now know that each liquid has a characteristic vapor pressure at each temperature and a characteristic boiling point at each pressure, and these properties differ from one substance to the next. These differences must be related to differences in the properties of the individual molecules in the liquid phase. Furthermore, we developed a model for phase equilibrium based on a dynamic view. The rate of condensation must equal to the rate of evaporation at equilibrium. And the rate of evaporation must differ from one liquid to the next and must also vary as the temperature changes. These experimental clues will help us develop a model to account for the differences in physical properties arising from differences in the attractions of individual molecules in the liquid phase.

In this study, we will further develop the concept of phase equilibrium, including solids in our discussion. We will experimentally determine the conditions under which one of the phases is the most stable and conditions under which two or all three of the phases are stable at equilibrium. We will then build a model to describe the interactions between molecules, accounting for which types of molecules have strong attractions and which have weaker attractions.

Observation 1: liquid-vapor phase diagram

In the previous study, we examined experimental data on the vapor pressures of different liquids as a function of their temperature. We found that the vapor pressure of a liquid depends strongly on what the liquid substance is. These variations reflect the differing "volatilities" of the liquids: those with higher vapor pressures are more volatile.

In addition, there is a very interesting correlation between the volatility of a liquid and the boiling point of the liquid. Without exception, the substances with high boiling points have low vapor pressures and vice versa. If we look more closely at the connection between boiling point and vapor pressure, we can find an important relationship.

Let’s consider the specific case of water, with its vapor pressure given in Figure 1. We know from experiment that water boils at 1 atm pressure at 100 ºC. Note in Figure 1 that, at 100 ºC, the vapor pressure of water is 760 torr = 1 atm. Thus, the boiling point of water at 1 atm is the temperature at which the vapor pressure of water is equal to 1 atm. This is a general result. The boiling point of each liquid at 1 atm pressure is equal to the temperature at which the vapor pressure of that liquid is equal to 1 atm.