Excess integral molar enthalpy

Similarly, excess integral molar entropy and enthalpy of solution may be written... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

We have calculated enthalpy, internal energy, excess molar enthalpy, and excess molar internal energy based on the integral equation theory. Validity of its use has been confirmed by the comparison of our results with those of MC calculation. Then, we have calculated the differential thermodynamic quantities of the isobaric heat capacity Cp and the excess isobaric molar heat capacity, Cp. ... 

The principles of phase equilibrium do not apply to excess adsorption variables at high pressure where the excess adsorption passes throu a maximum. Under these conditions, the pressure is no longer a single-valued function of excess adsorption so that n cannot serve as an independent variable for the determination of partial molar quantities such as activity coefficients. Additional complications which arise at high pressure are (1) the selectivity for excess adsorption (S12 = (nf/j/i)/(n2/y2)) approaches infinity as nj — 0 and (2) the differential enthalpy of the ith component has a singularity at the pressure corresponding to maximum nf. For excess variables, the diffierential functions are undefined but the integral functions for enthalpy and entropy are smooth and well-behaved (1). 

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