Liquid-vapor equilibria at constant pressure

The thermodynamic treatment of data obtained from the study of the liquid-vapor equilibria at constant pressure differs from that used in constant-temperature experiments in the treatment of the standard states. This difference arises because we cannot calculate the change in the chemical 

We can subtract from each side, p T, P,y= 1], the chemical potential of the pure, real gas at the same temperature and pressure as the experiment. We then have 

The difference between the chemical potentials of the pure component in the liquid and gas phases is calculated, with the knowledge that the chemical potentials must be equal at the boiling point of the pure substance, T, at the pressure P. We choose the series of changes of state 

values of AjufT, P, x] can be calculated from the measured values of the equilibrium temperature T and the two mole fractions, x, and jq. The same equation with change of subscripts is valid for the second component when its standard state can be taken as the pure liquid component. 

The values of An [T, P, x] at different compositions obtained by the case of Equation (10.86) are not isothermal, because in the univariant system the temperature is a function of the mole fractions. Corrections must be made to obtain isothermal values of An. We choose some arbitrary temperature T0. Then, according to Equation (11.120), 

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