Single-component systems Clapeyron equation

A sublimation process is controlled primarily by the conditions under which phase equilibria occur in a single-component system, and the phase diagram of a simple one-component system is shown in Figure 15.30 where the sublimation curve is dependent on the vapour pressure of the solid, the vaporisation curve on the vapour pressure of the liquid, and the fusion curve on the effect of pressure on the melting point. The slopes of these three curves can be expressed quantitatively by the Clapeyron equation ... 

Single-component systems are useful for illustrating some of the concepts of equilibrium. Using the concept that the chemical potential of two phases of the same component must be the same if they are to be in equilibrium in the same system, we were able to use thermodynamics to determine first the Clapeyron and then the Clausius-Clapeyron equation. Plots of the pressure and temperature conditions for phase equilibria are the most common form of phase diagram. We use the Gibbs phase rule to determine how many conditions we need to know in order to specify the exact state of our system. 

The Clapeyron equation (5.19) is valid for all forms of phase equilibrium in single-component systems, i.e. evaporation, condensation, melting, solidification, sublimation, and transformation (see table 4.1). 

The Clapeyron equation (5.19) applies to equilibrium between two arbitrary phases in a single-component system. If one of the phases is an ideal gas, it can be useful to rewrite the Clapeyron equation. For the rewriting it shall be used that the molar volume of a condensed phase is normally negligible compared to the molar volume of a gas phase. If we consider, for example, the equilibrium between water and water vapom at 25 °C, we have the following numerical values. Molar volume of water Ci 18 10 m /mol molar volume of saturated water vapour 0.78m /mol. In this system the molar volume of the gas phase is approximately 40000 times the volume of the condensed phase. Therefore, the difference Ay included in the Clapeyron equation can to a good approximation be expressed... 

For this single-component system with one condensed phase and one ideal gas phase, and according to the Clausius-Clapeyron equation (5.24), we obtain... 

If we consider two phases of a single component (e.g., solid hydrogen-liquid hydrogen) then the system pressure depends only on the tempera-ture. Accordingly, we can write the Clapeyron equation... 

In the previous chapter we obtained a number of relations, such as the Clausius-Clapeyron equation, which are correct whatever the natme of the phases which are in equilibrium, provided that there is only a single component. The question arises whether any equations of a comparable generality may be obtained for the case of a multi-component system. 

In Chapter 6, we introduced some important concepts that we can apply to systems at equilibrium. The Clapeyron equation, the Clausius-Clapeyron equation, and the Gibbs phase rule are tools that are used to understand the establishment and changes of systems at equilibrium. However, so far we have considered only systems that have a single chemical component. This is very limiting, because most chemical systems of interest have more than one chemical component. They are multiple-component systems. 

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