The ideal gas is a convenient starting point to introduce the calculation of mixture properties because the calculations are simple. Since ideal gas molecules do not have intermolecular potentials, the internal energy consists entirely of kinetic energy. When components are mixed at constant temperature and pressure, the internal energy is simply the sum of the component internal energies (kinetic energies), which can be written using y as a gas phase composition variable:
The total volume of a mixture is related to the number of moles by Amagat’s law:
We can thus see that the energy of mixing and the volume of mixing for an ideal gas are both zero. Combining U and V to obtain the definition of H, H = U + PV, and using Eqns. 3.26 and 3.27,
Therefore the enthalpy of a mixture is given by the sum of the enthalpies of the components at the same temperature and pressure and the enthalpy of mixing is zero. On a molar basis,
Furthermore, we can add the component enthalpies and internal energies for ideal gas mixtures using the mole fractions as the weighting factors. The energy of mixing, volume change of mixing, and enthalpy change of mixing are all zero.
The enthalpy of mixing is zero for an ideal gas.
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