Page 346 - Physical chemistry understanding our chemical world

ACTIVITY 313

The ionic atmosphere moves continually, so we consider its com-
‘Associated ions’ in
position statistically. Crystallization of solutions would occur if the
this context means
ionic charges were static, but association and subsequent dissocia- an association species
tion occur all the time in a dynamic process, so even the ions in a held together (albeit
dilute solution form a three-dimensional structure similar to that in transiently) via electro-
a solid’s repeat lattice. Thermal vibrations free the ions by shaking static interactions.
apart the momentary interactions.
The ions surrounding each copper cation are termed the ionic atmosphere.In the
neighbourhood of any positively charged ion (such as a copper cation), there are likely
to be more negative charges than positive (and vice versa). We say the cations are
surrounded with a shell of anions, and each anion is surrounded by a shell of cations.
The ionic atmosphere can, therefore, be thought to look much like an onion, or a
Russian doll, with successive layers of alternate charges, with the result that charges
effectively ‘cancel’ each other out when viewed from afar.
Having associated with other ions, we say the copper ion is screened from anything
else having a charge (including the electrode), so the full extent of its charge cannot be
‘experienced’. In consequence, the magnitude of the electrostatic interactions between
widely separated ions will decrease.
The electrode potential measured at an electrode relates to the
‘Coulomb potential energy’ V ‘seen’ by the electrode due to the The ‘Coulomb potential
ions in solution. V relates to two charges z 1 and z 2 (one being the energy’ V is equal to
electrode here) separated by a distance r, according to the work that must be
done to bring a charge
+ −
z z z + from infinity to a
V = (7.26) distance of r from the
4π o r r
charge z .
−
where o is the permittivity of free space and r is the relative
◦
permittivity of the solvent. In water at 25 C, r has a value of 78.54.
The magnitude of V relates to interactions between the electrode and nearby ions
nestling within the interface separating the electrode and the ionic solution. Since
the ‘effective’ (visible) charge on the ions decreases, so the electrode perceives there
to be fewer of them. In other words, it perceives the concentration to have dipped
below the actual concentration. This perceived decrease in the number of charges
then causes the voltmeter to read a different, smaller value of E Cu ,Cu .
2+
The zinc ions in the other half of the Daniell cell can similarly interact with ions
added to solution, causing the zinc electrode to ‘see’ fewer Zn 2+ species, and the
voltmeter again reads a different, smaller value of E Zn ,Zn . Since the emf represents
2+
the separation between the electrode potentials of the two half-cells, any changes in
the emf illustrate the changes in the constituent electrode potentials.

Background to the Debye–H¨ uckel theory

The interactions between the ions originally in solution and any added LiCl are
best treated within the context of the Debye–H¨uckel theory, which derives from a
knowledge of electrostatic considerations.