An informal definition of Henry’s Law states that the solubility of a compound in a solvent is directly proportional to the partial pressure of the compound in the vapour phase, at low partial pressures. In a plot of concentration dissolved vs. partial pressure, the slope of the curve is the Henry’s Law Constant (HLC). The system is taken to be at equilibrium; that is the Gibbs free energy is at a global minimum so the macroscopic properties of the system are static. Unfortunately this definition is often too simplistic to be used in most practical applications for reasons which will be explained later.
The formal definition of the HLC is:
lim┬(x_i→0)〖(f ̂_i^L)/x_i 〗=H_ij (1)
where f ̂_i^L is the liquid fugacity of the solute i, xi is the mole fraction, and Hij is the HLC of the solute, in the solvent j. It is important to mention that the HLC is specific a particular solute-solvent pair. A common mistake is to use the vapour-phase fugacity instead of the liquid-phase one, and simply to take the HLC as the ratio of the vapour-phase fugacity to liquid phase composition. This is incorrect as it assumes that the activity coefficients are equal to one, and the HLC is the reference fugacity (Carroll, 1991). The most common form of Henry’s Law used assumes that the vapour is at a pressure low enough such that it acts as an ideal gas. When this assumption is made both the activity coefficient, γ, and the fugacity coefficient, φ ̂, are equal to unity.
x_i H_ij=y_i P (2)
This form of Henry’s Law can be used up to a pressure of about 200 kPa and liquid concentrations of 1 mol% (Carroll, 1991). This shows that at low partial pressures a plot of mole fraction of a compound vs. partial pressure of the compound in the gaseous phase would be linear. When the vapour pressure of the solute increases, non-idealities occur and eq. 2 is no longer valid. However it is not necessary to confine the applicability of the Henry’s Law to such strict limits. With the inclusion of some extra terms the Henry’s law can be used over the entire range of compositions and pressures.
γ_i x_i H_ij exp[∫_(P_j^0)^P▒((v_i^(-∞))/RT)dP]=y_i φ ̂_i P (3)
The exponential term in eq. 3 is the Poynting correction factor and is only necessary at very high pressures, thus it can be excluded and the equation is still valid up to pressure of 10,000 kPa.
From these definitions we can see that compounds with a higher HLC are more volatile at a given temperature. Therefore the HLC is a measure of the relative affinity of a compound for the vapour phase and the liquid phase.
The expressions above are useful for binary systems however many industrial applications do not deal with pure binary systems. The presence of multiple components affects the value of the HLC. In these cases a more involved approach must be taken in determining the HLC. Carroll (1992) has written an introductory article on the various approaches and models used when dealing with other systems:...