Page 325 - Physical Chemistry

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Chapter 10 Equations (10.4), (10.28), and (10.31) give as the activities on the molality and
Nonideal Solutions molar-concentration scales

a m,i g m,i m >m°, a g c >c° (10.32)*
i
c,i i
c,i
which may be compared with a g x [Eq. (10.5)].
i i
i
Some values of g , g , and g for sucrose in water at 25°C and 1 atm are plotted
c
m
II
in Fig. 10.6.
For solute i, one has the choice of expressing m using the mole-fraction scale
i
(Convention II), the molality scale, or the molar concentration scale. None of these
scales is more fundamental than the others (see Franks, vol. 4, pp. 4, 7–8), and which
scale is used is simply a matter of convenience. In dilute solutions, g , g , and g are
II
c
m
nearly equal to one another, and each measures the deviation from ideally dilute be-
havior (no solute–solute interactions). In concentrated solutions, these activity coeffi-
cients differ from one another, and it is not meaningful to say which one is the best
measure of such deviations.
The solute activity coefficients g II,i (often denoted by g ), g , and g are some-
c,i
x,i
m,i
times called Henry’s-law activity coefficients since they measure deviations from
Henry’s law. The activity coefficient g is called a Raoult’s-law activity coefficient.
I,i
Table 11.1 in Sec. 11.8 summarizes the standard states used for solutions and pure
substances.
10.5 SOLUTIONS OF ELECTROLYTES
Figure 10.6
Electrolyte Solutions
g , g , and g of the solute An electrolyte is a substance that yields ions in solution, as evidenced by the solution’s
c
II
m
sucrose in water at 25°C and
1 atm plotted versus solution showing electrical conductivity. A polyelectrolyte is an electrolyte that is a polymer.
composition. Ionization of acidic groups in DNA and acidic and basic groups in proteins makes these
molecules polyelectrolytes (see Sec. 15.6). For a given solvent, an electrolyte is classi-
fied as weak or strong, according to whether its solution is a poor or good conductor of
electricity at moderate concentrations. For water as the solvent, some weak electrolytes
are NH ,CO , and CH COOH, and some strong electrolytes are NaCl, HCl, and MgSO .
3
2
3
4
An alternative classification, based on structure, is into true electrolytes and po-
tential electrolytes. A true electrolyte consists of ions in the pure state. Most salts are
true electrolytes. A crystal of NaCl, CuSO , or MgS consists of positive and negative
4
ions. When an ionic crystal dissolves in a solvent, the ions break off from the crystal
and go into solution as solvated ions. The term solvated indicates that each ion in so-
lution is surrounded by a sheath of a few solvent molecules bound to the ion by elec-
trostatic forces and traveling through the solution with the ion. When the solvent is
water, solvation is called hydration (Fig. 10.7).
Some salts of certain transition metals and of Al, Sn, and Pb have largely covalent bond-
ing and are not true electrolytes. Thus, for HgCl , the interatomic distances in the crystal
2

show the presence of HgCl molecules (rather than Hg 2 and Cl ions), and HgCl is
2
2
largely molecular in aqueous solution, as evidenced by the low electrical conductivity. In
contrast, HgSO , Hg(NO ) , and HgF are ionic.
2
3 2
4
A potential electrolyte consists of uncharged molecules in the pure state, but when
dissolved in a solvent, it reacts with the solvent to some extent to yield ions. Thus,

acetic acid reacts with water according to HC H O H O ∆ H O C H O ,
2 3 2 2 3 2 3 2
yielding hydronium and acetate ions. Hydrogen chloride reacts with water according

to HCl H O ∆ H O Cl . For the strong electrolyte HCl, the equilibrium lies
Figure 10.7 2 3
far to the right. For the weak electrolyte acetic acid, the equilibrium lies far to the left,
Hydration of ions in solution. except in very dilute solutions.