Download Topic 2275 Ionic Mobilities: Aqueous Solutions. A classic subject in

Topic 2275
Ionic Mobilities: Aqueous Solutions.
A classic subject in physical chemistry concerns the electric conductivities of salt
solutions, most interest being centred on the aqueous salt solutions. Although the
electric conductivities of these systems, transport properties, do not come under the
heading ‘thermodynamic properties’, these conductivities have played a major part in
the task of understanding the thermodynamic properties of salt solutions.
Generally however interest in the electric conductivities of salt solutions has waned
as spectroscopic properties in all its form have moved to a dominant position in
physical chemistry. Nevertheless the contributions made by research into the electric
properties of salt solutions have been and remain enormously important.
Conductivities
At this point there is merit in commenting on the technique, mass spectrometry. In
this important experimental technique, ions are produced in an ion source and then
subjected to an electric field gradient, where (usually) cations are accelerated. The
ions pass through a magnetic field, the path of a given ion depending on the charge
and mass of the ion.
Descriptions of the electrical conductivities of salt solutions start out from a quite
different basis. To understand the point we consider a reasonably concentrated
aqueous solution of sodium chloride;
i.e. 0.1 mol dm-3 ≅ 0.1 mol salt in water, mass 1 kg ≅ 0.1 mol salt in (1.0/0.018) mol
water ≅ 0.1 mol Na+ ions + 0.1 mol Cl- ions + 55.6 mol water( l ).
In other words, for every sodium ion there are 556 molecules of water in this aqueous
solution. The contrast with the mass spectrometer experiment could not be more
dramatic. Further in conventional experiments studying the electric conductivities of
salt solutions, the effect of a modest electric potential gradient is simply to bias the
otherwise Brownian motion of the ion in a direction depending on the sign of the
charge on a given ion. As each ion makes its way through the solution it is jostled and
impeded by the large number of solvent molecules. Nevertheless in theoretical
treatments of the electric conductivities of salt solutions the theory envisages a slow
direct progress through the solution, in the case of, for example, a cation down the
electric potential gradient. The key experimental fact is that the electric properties of
salt solutions at low electric currents and low electric potential gradients obey the
phenomenological law, Ohm’s Law. Deviations from this law are observed for
example at high electrical field gradients; e.g. Wien Effects.
Molar Conductivities
The key term in the context of the electric conductivities of a salt solution,
concentration of salt cj is the molar conductivity Λ defined by equation (a) where κ
is the electrolytic conductivity [1,2].
Λ = κ/cj
(a)
For a salt solution prepared using a 1:1 salt , the molar conductivity can be expressed
as the sum of ionic conductivities , λ+ and λ-.
Thus Λ = λ + + λ −
(b)
Using equation (a), the electrolytic conductivity κ is related to the ionic conductivities
using equation (c)
κ = c j ⋅ (λ + + λ − )
(c)
The electric mobility of a given ion, uj is related to the mobility vj using equation (d)
[3].
uj = vj /E
(d)
Footnotes
κ = (electric current density) /(electric field strength )
[1]
= [j]/[E]
= [A m -2 ] /[V m -1 ] = [S m -1 ]
[2] Λ = [S m -1 ] /[mol m -3 ] = [S m 2 mol -1 ]
[3]
uj =[m s-1 ]/[V m-1] = [m2 s-1 V-1]