the glass with lithium, and the calcium with strontium or barium, the error can be reduced by about one
order of magnitude. So-called 'wide range' glass electrodes which have alkaline errors as low as 0.1 of a
pH unit in a 2 M sodium solution are commercially available. Below pH 1, the electrode is unlikely to
have a Nernstian or a reproducible response, the effect being known as the acid error.
Glass Electrodes for the Determination of Cations Other Than Hydrogen
The alkaline error shown by a soda-glass membrane has been exploited in developing membranes with
a high selectivity for sodium and other cations. For example, a study of glass composition has shown
that the presence of A1 2 O 3 or B 2 O 3 can enhance the response to sodium ions relative to hydrogen ions.
The membrane potential is then given by
where K is the equilibrium constant for the reaction
and is known as the selectivity ratio, μNa+ and μH+ being the mobilities of the sodium and hydrogen ions
within the gel layers. For large values of K and at high pH, such an electrode exhibits a Nernstian
response to sodium ions. Sodium and other cation-sensitive glass electrodes are available commercially;
those with a high selectivity for H+, Na+, Ag+ or Li+ have proved to be the most satisfactory.
(b)—
Solid-state Electrodes
These incorporate membranes fabricated from insoluble crystalline materials. They can be in the form
of a single crystal, a compressed disc of micro-crystalline material or an agglomerate of micro-crystals
embedded in a silicone rubber or paraffin matrix which is moulded in the form of a thin disc. The
materials used are highly insoluble salts such as lanthanum fluoride, barium sulphate, silver halides and
metal sulphides. These types of membrane show a selective and Nernstian response to solutions
containing either the cation or the anion of the salt used. Factors to be considered in the fabrication of a
suitable membrane include solubility, mechanical strength, conductivity and resistance to abrasion or
corrosion.
In all cases the mechanism by which the membrane responds to changes in the activity of the
appropriate ion in the external solution is one of ionic conduction. Lattice defects in the crystals allow
small ions with a low formal charge a degree of mobility within the membrane. It is this shift in charge
centres which gives rise to the membrane potential, the process resembling the movement of sodium
ions in the dry glass layer of a glass membrane. A fluoride electrode, in which the membrane is a single
crystal of lanthanum fluoride doped with europium to increase the conductivity, is one of the