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294 CHAPTER 3

decrease, begins to exceed the value of unity characteristic of the reference state of
noninteraction, i.e., of infinite dilution.
A qualitative picture of the events leading to these apparently anomalous happen-
ings has already been given in Chapter 2. There it has been argued that ions exist in
solution in various states of interaction with solvent particles. There is a consequence
that must therefore follow for the effectiveness of some of these water molecules in
counting as part of the solvent. Those that are tightly bound to certain ions cannot be
effective in dissolving further ions added (Fig. 3.38). As the concentration of electro-
lyte increases, therefore the amount of effective or free solvent decreases. In this way
the apparently anomalous increase in the activity coefficient occurs. The activity
coefficient is in effect that factor which multiplies the simple, apparent ionic concen-
tration and makes it the effective concentration, i.e., the activity. If the hydration of the
ions reduces the amount of free solvent from that present for a given stoichiometric
concentration, then the effective concentration increases and the activity coefficient
must increase so that its multiplying effect on the simple stoichiometric concentration
is such as to increase it to take into account the reduction of the effective solvent.
Experiment shows that sometimes these increases more than compensate for the
decrease due to interionic forces, and it is thus not unreasonable that the activity
coefficient should rise above unity.
Some glimmering of the quantitative side of this can be seen by taking the number
of waters in the primary hydration sheath of the ions as those that are no longer effective
solvent particles. For NaCl, for example, Table 2.18 indicates that this number is about
7. If the salt concentration is, e.g., the moles of water per liter withdrawn from
effect as free solvent would be 0.07. Since the number of moles of water per liter is
1000/18 = 55.5, the number of moles of free water is 55.43 and the effects arising from
such a small change are not observable. Now consider a 1 N solution of NaCl. The
water withdrawn is and the change in the number of moles of free water
is from 55.5 in the infinitely dilute situation to 48.5, a significant change. At 5 N NaCl,

Fig. 3.38. The distinction be-
tween free water and hydration
water that is locked up in the
solvent sheaths of ions.