The Phase Boundaries in Pure Substances Can Be Predicted Using Thermodynamics

1 The Phase Boundaries in Pure Substances Can Be Predicted Using Thermodynamics 

Two (or more) phases can be in physical equilibrium with one another only if they have the same temperature and pressure. In addition, the Gibbs free energies per mole, G = Gin, of the coexistin phases at the j ej uud ust also be equal. Therefore, any point of coexistei B SPlwo lrases (pna ermrpMsyj  

Using this restriction and the thermodynamic concepts developed in Chapters 7 and 8, we can predict the shape of the phase boundaries. 

A thermodynamic analysis of the pressure and temperature dependence of the Gibbs free energy shows that for Equation 9.1 to be satisfied, the slope, dPIdT, must obey 

AH - TAS = 0 across the phase coexistence line, we have AH = TAS, which means Equation 9.2 can be rewritten as 

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Figure 9.1 shows a typical phase diagram for a pure (one-component) substance. The three phase boundary lines (liquid-solid, liquid-gas, and solid-gas) meet at the triple point (the one temperature and pressure where all three phases coexist). The liquid-gas boundary line terminates at the critical point. These phase boundaries indicate how the coexistence pressure between two phases changes as the temperature changes. In this section, we will examine how we can use thermodynamics to predict the shape of phase coexistence curves for pure substances. For mixtures, more complicated phase diagrams can be constructed that indicate the dependence of the coexistence pressure and temperature upon the composition of the various phases. Phase diagrams for mixtures are discussed in Sections 9.2 and 9.3. 

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