Second virial cross coefficients for (ammonia + water) derived from gas phase excess enthalpy measurements

A flow-mixing calorimeter has been used to measure the excess molar enthalpy HmEof gaseous (ammonia + water) at the mole fraction y= 0.5, at standard atmospheric pressure, and over the temperature range 383.15 K to 493.15 K. The excess molar enthalpy is negative, indicating that the strength of the ammonia–water hydrogen bond is greater than that of the water–water hydrogen bond. The measurements were analysed first in terms of a purely thermodynamic model which assumes that the second virial cross coefficient B12and the related isothermal Joule–Thomson coefficient φ12are adequately described by an empirical equation of square well form. Information about the strength of the ammonia–water hydrogen bond was obtained by analysing the measurements on the basis of a quasi-chemical association model. It was shown that hydrogen bonding in ammonia is so slight that to use an association model for the second virial coefficient B11would be inappropriate. The second virial coefficient B22of water was written B22=B22ns−R·T·K22. The non-specific interaction B22nsbetween water molecules was calculated from the Stockmayer potential with parameters appropriate to a water–nonpolar fluid interaction, and the specific (hydrogen bonding) forces were described by the association model in terms of an equilibrium constant K22(298.15 K) = 0.36 MPa−1and an enthalpy of formation of ΔH22=−(16.2 ± 2)kJ · mol−1for the water–water hydrogen bond. The second virial cross coefficient was written B12=B12ns− (R·T·K12)/2, and from the temperature dependence of lnK12the enthalpy of formation of the ammonia–water hydrogen bond was found to be ΔH12=−(19.7 ± 3)kJ · mol−1, and K12(298.15 K) = 0.827 MPa−1. Values of B12derived from the measurements are given by the equation:B12/(cm3· mol−1)= 38 − 43059 · (K/T) − 1.993 ·exp{1900 · (K/T)}.