The Phase Equilibria Problem

As we learned in Chapter 1, for a system to be in thermal equilibrium, there are no temperature gradients in the system. Similarly, in mechanical equilibrium there cannot be a pressure gradient. Therefore, we can write. 

These two criteria for equilibrium are obvious and therefore straightforward to formulate they deal with measurable properties. To see that these conditions represent criteria for equilibrium, you may ask, for example, What would happen if T T Energy flows from hot to cold and will, therefore, flow from phase a to )8 until the temperatures equilibrate. A similar argument can be made for pressure and mechanical equilibrium.  

The driving force for species transfer is not so apparent. This chapter will focus on the following questions  

Before we begin, note that neither mole fraction nor concentration, both measurable properties, represents the driving force for species transfer between phases (as temperature difference represents the driving force for energy transfer between phases). For example, consider an air-water system in phase equilibrium between the vapor and liquid phases. It would be absurd to think that oxygen will transfer from the air into the water until the mole fraction was 0.21 in the water, or conversely that water would transfer into the air until the vapor was almost all water Unfortunately, the thermodynamic property that drives a system toward chemical equilibrium, unlike thermal or mechanical equilibrium, is not a measurable property. 

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We will take thermal and mechanical equilibrium for granted in the following discussion hence, in formulating the phase equilibria problem, we need only measure the temperature and pressure of one phase, and these values must apply to the entire system. This concept is illustrated schematically in Figure 6.1, where temperature and pressure measurements that are made only to phase a apply to the entire system. A piston-cylinder assembly is used to remind us that the system must be able to change in volume to accommodate thermal and mechanical equilibrium. 

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