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versus N (or H ) partial pressure above the solution. Up to 100 atm, the N plot obeys Section 9.9
2
2
2
1
l
Henry’s law x K P and is essentially linear. Above 100 atm, the N plot shows in- Summary
i
i
2
i
creasing deviations from the Henry’s law line (the dotted line) because of the depen-
dence of K on pressure and deviations of the gas from ideal-gas behavior. H obeys
i
2
Henry’s law up to 200 atm.
At the low solute concentrations for which Henry’s law applies, the solute’s mo-
lality m and molar concentration c are each essentially proportional to its mole frac-
i
i
tion x (Prob. 9.8). Therefore molalities or concentrations can be used instead of mole
i
fractions in Henry’s law: P K m or P K c , where K i,m and K are constants
i,m
i
i,c i
i,c
i
i
related to K in (9.65).
i
Some values of K for gases in water and in benzene at 25°C are
i
i H 2 N 2 O 2 CO Ar CH 4 C H 6
2
K i,H 2 O /kbar 71.7 86.4 44.1 58.8 40.3 40.4 30.3
K /kbar 3.93 2.27 1.24 1.52 1.15 0.49 0.068
i,C 6 H 6
From (9.65), the larger the K value, the smaller the solubility of the gas. Note the
i
much greater solubility of these gases in benzene as compared with water.
The solubility of most nonpolar gases (and liquids) in water goes through a mini-
mum as T increases. Figure 9.23 plots K at 1 bar for several gases in water versus T.
i
The maxima in K correspond to minima in solubility since the solubility is proportional
i
1
to K . Also plotted are K 1 for O and N in water versus T. The solubilities increase
i
2
2
i
strongly as the critical temperature 374°C of water is approached.
Henry’s law does not apply to a dilute aqueous HCl solution. Even in the limit of
infinite dilution, m of a strong electrolyte such as HCl(aq) does not have the form
i
m m° RT ln x used in deriving Henry’s law. See Prob. 10.71 for this case.
i
i
i
Partial Molar Quantities
The partial molar properties of the ideally dilute solution’s components are derived
from their chemical potentials. See Probs. 9.55–9.57.
Reaction Equilibrium
For a chemical reaction in an ideally dilute solution, we can substitute m m° Figure 9.23
i
i
RT ln x into the equilibrium condition n m 0 to derive a mole-fraction equilib- Henry’s law constant K (at 1 bar)
i
i
i
i
i
n
rium constant K (x ) i , where x i,eq is the equilibrium mole fraction of species for several gases in water plotted
x
i
i,eq
i; see Prob. 9.59 for details. versus T (upper figure) and 1/K i
For most equilibria in aqueous solutions, some of the reacting species are ions, for O and N in water versus T.
2
2
which makes the ideally dilute solution approximation poor. Ionic equilibria are con-
sidered in Chapter 11.
9.9 SUMMARY

The volume of a solution is given by V n V i , where the partial molar volume of

i
i
component i in the solution is defined by V 10V>0n 2 . Similar equations hold
i
i T,P,n j i
for other extensive properties of the solution (for example, U, H, S, G, C ). The par-

P

tial molar properties G i ( m ), , S ,H i i and V i obey relations analogous to the relations
i
between the corresponding molar properties G, H, S, and V of pure substances. The
chemical potentials m are the key thermodynamic properties of a solution.
i
The volume change V for forming a solution of volume V from its pure com-
mix
ponents at constant T and P is ¢ mix V V V* n (V i V* ). The mixing quan-
i
i
m,i
tities ¢ mix G, ¢ mix H, ¢ mix S, and ¢ mix V obey relations analogous to the relations be-
tween the corresponding properties of pure substances [Eqs. (9.33) to (9.35)].