Page 347 - Physical chemistry understanding our chemical world

314 ELECTROCHEMISTRY

Firstly, we assume the ions have an energy distribution as defined by the Boltzmann
distribution law (see p. 35). Secondly, we say that electrostatic forces affect the
behaviour and the mean positions of all ions in solution. It should be intuitively clear
that ions having a larger charge are more likely to associate strongly than ions having
a smaller charge. This explains why copper ions are more likely to associate than
are sodium ions. The magnitude of the force exerted by an ion with a charge z 1 on
another charge z 2 separated by an inter-ion distance of r in a medium of relative
permittivity r is the ‘electrostatic interaction’ φ, as defined by

z z
+ −
φ = (7.27)
4π o r r 2
Note how this equation states that the force is inversely proportional to the square
of the distance between the two charges r, so the value of φ decreases rapidly as r
increases.
Since cations and anions have opposite charges, φ is negative.
The force between two anions will yield a positive value of φ.We
Positive values of φ see how a positive value of φ implies an inter-ionic repulsion and
imply repulsion, and a a negative value implies an inter-ionic attraction.
negative value attrac-
tion. The Debye–H¨ uckel theory suggests that the probability of find-
ing ions of the opposite charge within the ionic atmosphere increa-
ses with increasing attractive force.

Why does adding NaCl to a cell alter the emf, but
adding tonic water doesn’t?

The effects of ion association and concentration on γ

Sodium chloride – table salt – is a ‘strong’ ionic electrolyte because it dissociates
fully when dissolved in water (see the discussion of weak and strong acids in
Section 6.2). The only electrolytes in tonic water are sugar (which is not ionic) and
sodium carbonate, which is a weak electrolyte, so very few ions are formed by adding
the tonic water to a cell.
The ratio of perceived to real concentrations is called the activity coefficient γ
(because, from Equation (7.25), γ = a ÷ c). Furthermore, from the definition of activ-
ity in Equation (7.20), γ will have a value in the range zero to one. The diagram
in Figure 7.9 shows the relationship between γ and concentration c for a few ionic
electrolytes.
Adding NaCl to solution causes γ to decrease greatly because the number of ions
in solution increases. Adding tonic water does not decrease the activity coefficient
much because the concentration of the ions remains largely unchanged. The change
in γ varies more with ionic electrolytes because the interactions are far stronger. And
if the value of γ does not change, then the real and perceived concentrations will
remain essentially the same.