Page 20 - Battery Reference Book

Electromotive force 1/5
the metal, as neutral metal atoms, is negligibly small.
In the solution the salt is dissociated into positive ions
of the metal and negative anions, e.g.
CuSO4 = CuZi + SO:-
and the electrical conductivity of metals shows that
they are dissociated, at any rate to some extent, into
metal ions and free electrons, thus:
cu = CU*+ + :!e (a) P>P b) P <P
The positive metal ions are thus the only constituent Figure 1.2 The origin of electrode potential difference
of the system that is common to the two phases. The
equilibrium of a metal and its salt solution therefore
differs from an ordinary case of solubility in that only The metal and the solution will be in equilibrium
one constituent of the metal, the metal ions, can pass and no electric field will arise at the interface.
into solution. When a metal and its solution are not initially in
Nernst, in 1889, supposed that the tendency of a equilibrium, there is thus formed at the interface an
substance to go into solution was measured by its electrical double layer, consisting of the charge on the
solution pressure and its tendency to deposit from surface of the metal and an equal charge of opposite
the solution by its osmotic pressure in the solution. sign facing it in the solution. By virtue of this double
Equilibrium was supposed to be reached when these layer there is a difference of potential between the
opposing tendencies balanced each other, i.e. when metal and the solution. The potential difference is
the osmotic pressure in the solution was equal to the measured by the amount of work done in taking unit
solution pressure. positive charge from a point in the interior of the liquid
In the case of a metal dipping into a solution to a point inside the metal. It should be observed that
containing its ions, the tendency of the metal ions to the passage of a very minute quantity of ions in the
dissolve is th'us determined by their solution pressure, solution or vice versa is sufficient to give rise to the
which Nemst called the electrolytic solution pressure, equilibrium potential difference.
P, of the metal. The tendency of the metal ions to Nernst calculated the potential difference required
deposit is measured by their osmotic pressure, p. to bring about equilibrium between the metal and
Consider what will happen when a metal is put in the solution in the following way. We determined the
contact with a solution. The following cases may be net work obtainable by the solution of metal ions by
distinguished : means of a three-stage expansion process in which
1. P > p The electrolytic solution pressure of the the metal ions were withdrawn from the metal at the
metal is greater than the osmotic pressure of electrolyte solution pressure P, expanded isothermally
to the osmotic pressure p, and condensed at this
the ions, so that positive metal ions will pass into
the solution. As a result the metal is left with pressure into the solution. The net work obtained in
a negative charge, while the solution becomes this process is
positively charged. There is thus set up across the w' = RT In Plp per mol (1.3)
interface an electric field which attracts positive
ions towards the metal and tends to prevent any If V is the electrical potential of the metal with
more passing into solution (Figure 1.2(a)). The ions respect to the solution (V being positive when the
will continue to dissolve and therefore the electric metal is positive), the electrical work obtained when
field to increase in intensity until equilibrium is 1 mol of metal ions passes into solution is nVF, where
reached, i.e. until the inequality of P and p, which n is the number of unit charges carried by each ion.
causes the solution to occur, is balanced by the The total amount of work obtained in the passage of
electric field. 1 mol of ions into solution is thus
2. P < p The osmotic pressure of the ions is now RT In Plp + n VF (1.4)
greater than the electrolytic solution pressure of the
metal, so that the ions will be deposited on the and for equilibrium this must be zero; hence
surface of the latter. This gives the metal a positive RT
charge, w.hile the solution is left with a negative V = - lnP/p
charge. Tlhe electric field so arising hinders the nF
deposition of ions, and it will increase in intensity Objection can be made to this calculation on the
until it balances the inequality of P and p, which grounds that the three-stage process employed does
is the cause of the deposition (Figure L.2(b)). not correspond to anything that can really occur and
3. P = p The osmotic pressure of the ions is equal is really analogous in form only to the common three-
to the ele'ctrolytic solution pressure of the metal. stage transfer. However, a similar relation to which