How Many Phases Can Coexist in a Given Equilibrium Situation

1 HOW MANY PHASES CAN COEXIST IN A GIVEN EQUILIBRIUM SITUATION  

Could all three phases of water coexist over some finite range of temperatures Could the vapor-liquid equilibrium exist over a range of pressures at one temperature, instead of at just one pressure for any given temperature We have all been told, in previous courses, that the answer is no. But how would you prove that The answer is that we would use the phase rule, often called Gibbs phase rule after Josiah Willard Gibbs (1790-1861). 

For the simple case of asking whether three phases of a single pure substance can coexist over a finite range of pressures, it is instructive to study the problem by Clapeyron s equation before we take up the phase rule. Consider the possibility of three phases of some single pure substance (like water or propane) coexisting over some finite range of temperature and pressure. For the three combinations of two phases each we can write Clapeyron s equation (Eq. 5.5) three times for the three binary equilibria (1 = solid, 2 = liquid, 3 = gas) 

But if the three phases coexist over some finite range of temperatures, then dP/dT must be the same for the three combinations indicated above, or 

Physical and Chemical Equilibrium for Chemical Engineers, Second Edition. Noel de Nevers. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

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