Henry's law has been shown to apply to a wide range of solutes in the limit of
infinite dilution (
x → 0), including non-volatile substances such as
sucrose. In these cases, it is necessary to state the law in terms of
chemical potentials. For a solute in an ideal dilute solution, the chemical potential depends only on the concentration. For non-ideal solutions, the activity coefficients of the components must be taken into account: :\mu = \mu_c^\circ + RT\ln\frac{\gamma_c c}{c^\circ}, where \gamma_c = \frac{H_{\rm v}}{p^*} for a volatile solute;
c° = 1 mol/L. For non-ideal solutions, the infinite dilution activity coefficient
γc depends on the concentration and must be determined at the concentration of interest. The activity coefficient can also be obtained for non-volatile solutes, where the vapor pressure of the pure substance is negligible, by using the
Gibbs-Duhem relation: :\sum_i n_i d\mu_i = 0. By measuring the change in vapor pressure (and hence chemical potential) of the solvent, the chemical potential of the solute can be deduced. The
standard state for a dilute solution is also defined in terms of infinite-dilution behavior. Although the standard concentration
c° is taken to be 1 mol/L by convention, the standard state is a hypothetical solution of 1 mol/L in which the solute has its limiting infinite-dilution properties. This has the effect that all non-ideal behavior is described by the activity coefficient: the activity coefficient at 1 mol/L is not necessarily unity (and is frequently quite different from unity). All the relations above can also be expressed in terms of
molalities b rather than concentrations, e.g.: :\mu = \mu_b^\circ + RT\ln\frac{\gamma_b b}{b^\circ}, where \gamma_b = \frac{H_{\rm v}^{pb}}{p^*} for a volatile solute;
b° = 1 mol/kg. The standard chemical potential
μm°, the activity coefficient
γm and the Henry's law constant
Hvpb all have different numerical values when molalities are used in place of concentrations.
Solvent mixtures Henry's law solubility constant H_{\rm s,2,M}^{xp} for a gas 2 in a mixture M of two solvents 1 and 3 depends on the individual constants for each solvent, H_{\rm s,2,1}^{xp} and H_{\rm s,2,3}^{xp} according to: : \ln H_{\rm s,2,M}^{xp} = x_1 \ln H_{\rm s,2,1}^{xp} + x_3 \ln H_{\rm s,2,3}^{xp} + a_{13} x_1 x_3 Where x_1, x_3 are the molar ratios of each solvent in the mixture and a13 is the interaction parameter of the solvents from Wohl expansion of the excess chemical potential of the ternary mixtures. A similar relationship can be found for the volatility constant H_{\rm v,2,M}^{px}, by remembering that H_{\rm v}^{px}=1/H_{\rm s}^{xp} and that, both being positive real numbers, \ln H_{\rm s}^{xp}=-\ln (1/H_{\rm s}^{xp}) = -\ln H_{\rm v}^{px} , thus: : \ln H_{\rm v,2,M}^{px} = x_1 \ln H_{\rm v,2,1}^{px} + x_3 \ln H_{\rm v,2,3}^{px} - a_{13} x_1 x_3 For a water-ethanol mixture, the interaction parameter a13 has values around 0.1 \pm 0.05 for ethanol concentrations (volume/volume) between 5% and 25%. == Miscellaneous ==