Chemical potential change with pressure

The first equation simply states the balance in chemical potentials inside and outside of the cell. The expression for the chemical potential inside the protocell separates into a term involving the mole fraction and the chemical potential associated with the pressure difference. The work done by the cell in opposing the pressure change, assuming that the cell remains at constant volume, is given below, where the change in pressure is from p to p + tv. 

One method of calculating fugacity and hence y is based on the measured deviation of the volume of a real gas from that of an ideal gas. Considet the case of a pute gas The ftee energy F and chemical potential /i changes with pressure according to the equation... 

Escobedo and de Pablo have proposed some of the most interesting extensions of the method. They have pointed out [49] that the simulation of polymeric systems is often more troubled by the requirements of pressure equilibration than by chemical potential equilibration—that volume changes are more problematic than particle insertions if configurational-bias or expanded-ensemble methods are applied to the latter. Consequently, they turned the GDI method around and conducted constant-volume phase-coexistence simulations in the temperature-chemical potential plane, with the pressure equality satisfied by construction of an appropriate Cla-peyron equation [i.e., they take the pressure as 0 of Eq. (3.3)]. They demonstrated the method [49] for vapor-liquid coexistence of square-well octamers, and have recently shown that the extension permits coexistence for lattice models to be examined in a very simple manner [71]. 

WhUe Eq. (2.5.1) is satisfactory it does relate the chemical potential to reference values that change with pressure. A greater degree of uniformity may be achieved by referring all chemical potentials of solutions to the chemical potentials of the pure constituents under standard conditions, P = 1 bar, as follows ... 

For this choice of reference, we write the chemical potential change as A/r) to distinguish it from the previous case relative to a 0 K reference. In this way, A A = 0 corresponds to the surface in equilibrium with the gas-phase reservoir at the same temperature and the reference pressure. Negative values of A ) would indicate equilibrium with a pressure less than P and positive values with a pressure greater than P. We have already defined, Pa) in eqn (2.34),... 

Vapour pressure osmometry is the second experimental technique based on colligative properties with importance for molar mass determination. The vapour pressure of the solvent above a (polymer) solution is determined by the requirement that the chemical potential of the solvent in the vapour and in the liquid phase must be identical. For ideal solutions the change of the vapour pressure p of the solvent due to the presence of the solute with molar volume V/1 is given by... 

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