Thermodynamics and Chemistry

CHAPTER 9 MIXTURES

9.4 LIQUID ANDSOLIDMIXTURES OFNONELECTROLYTES 249

gas mixture fi

liquid mixture xi

Figure 9.6 Equilibrated liquid and gas mixtures. Substanceiis present in both

phases.

9.4.4 Henry’s law

Consider the system shown in Fig.9.6, in which a liquid mixture is equilibrated with a gas
phase. Transfer equilibrium exists for substancei, a constituent of both phases. Substance
iis assumed to have the same molecular form in both phases, and is not, for instance, an
electrolyte. We can vary the mole fractionxiin the liquid and evaluate the fugacityfiin
the gas phase.
Suppose we allowxito approach zero at constantTandpwhile the relative amounts
of the other liquid constituents remain constant. It is found experimentally that the fugacity
fibecomes proportional toxi:

fi!kH;ixi as xi! 0 (9.4.14)

(constantTandp)

This behavior is calledHenry’s law. The proportionality constantkH;i is theHenry’s
law constantof substancei. The value ofkH;idepends on the temperature and the total
pressure, and also on the relative amounts of the constituents other thani in the liquid
mixture.
If the liquid phase happens to be an ideal liquid mixture, then by definition constituent
iobeys Raoult’s law for fugacity at all values ofxi. In that case,kH;iis equal tofi, the
fugacity when the gas phase is equilibrated with pure liquidiat the same temperature and
pressure as the liquid mixture.
If we treat the liquid mixture as a binary solution in which solute B is a volatile non-
electrolyte, Henry’s law behavior occurs in the limit of infinite dilution:

fB!kH,BxB as xB! 0 (9.4.15)

(constantTandp)

An example of this behavior is shown in Fig.9.7(a) on page 251. The limiting slope of the
plot offBversusxBis finite, not zero or infinite. (The fugacity of a volatileelectrolyte, such
as HCl dissolved in water, displays a much different behavior, as will be shown in Chap.
10 .)

Equation9.4.15can be applied to a solution of more than one solute if the combination

of constituents other than B is treated as the solvent, and the relative amounts of these

constituents remain constant asxBis varied.

Since the mole fraction, concentration, and molality of a solute become proportional to
one another in the limit of infinite dilution (Eq.9.1.14), in a very dilute solution the fugacity