Page 160 - Essentials of physical chemistry

122 Essentials of Physical Chemistry

to other properties such as the chemical potential. What does it mean? As a student, the author did
not understand this but gradually came to appreciate it in the following sense.

If you want to believe that a chemical property is the simple sum of its parts you have to allow that
property to adjust to the presence of the other components!

This seemingly strange departure from ordinary experience is due to the microscopic nature of the
molecular world just as Dalton’s law of partial pressures needs to be interpreted in terms of very
small atoms=molecules, which can intermingle and seem to occupy the same volume. By the way,
just what is the molarity (M) of water when we have 1 L of just water? In most laboratory situations,
the concentration of the solute is in the range of 0.01 M or even less so we tend to ignore the solvent.
However, by definition of molarity (M) we can write:

(1000 gH O=L)=(18:01528 g=mol) ¼ 55:508 M:
2
This is usually ignored when dealing with water solutions of inorganic ions but if you think about it
even simple salt solutions involve at least one solvent shell around each ion as an ‘‘aqueous ion’’ but
this is a small amount of the water, which still leaves a large concentration of water capable of
dissolving more=other solutes.

NaCl þ H 2 O ƒ Na þ þ Cl
aqueous aqueous
ƒ!
Example 4
Although the ammonia solution has a volume we expect from common sense, let us consider the next
more complicated case of NaCl dissolved in water. Starting with 1000 g of water we can dissolve
varying amounts of NaCl in the solvent and now we have to be aware of the fact that water is quite
‘‘polar’’ with a dipole moment of 1.8546 debyes [5] so the negative (O lone pairs) end of the water
molecules will be attracted to the Na ions and the positive end of the water dipoles (H-atoms) will be
þ
attracted to the Cl ions. There may also be an effect that short range order is induced in the H-bonding

of the second layer of water molecules around a solvated ion. In addition, there may be some long range
repulsion between ions with the same charge, but this will be a very small effect in dilute solutions. Thus,
we come to realize that there are electrical effects within the solution as well as the usual consideration of
H-bonding in aqueous solutions. Suppose careful laboratory measurements of the total volume of 1000
g of water and various moles (m)of NaClsolute can be fitted to a polynomial in m of NaCl [7].

3 2
V tot ¼ 1003:00 þ 16:62m þ 1:77m 2 þ 0:12m :
Then it is easy to calculate the ‘‘partial molal volume’’ of NaCl in terms of the molal
concentration as:

3
qV tot 1
(1:77)m 2 þ 2(0:12)m (mL=mol):
V NaCl ¼ 16:62 þ
qm 2
Then we can obtain the differential of the NaCl concentration as:

1 3 1
(1:77)m 2 þ 2(0:12) dm:
dV NaCl ¼
2 2
But what about the partial molal volume of the water as affected by the charged ions?
The Gibbs–Duhem equation gives us another relationship to allow the partial molal volume of
the water to actually vary with the concentration of the NaCl using n H 2 O dV H 2 O þ n NaCl dV NaCl ¼ 0.