Explain how conductance measurements can be used to determine the solubility of sparingly soluble salts.
Answers
Answer:
Determination of the solubility product and enthalpy of dissolution of sparingly
soluble salts by conductometry
Introduction
The electrical resistance is a property of the materials. The resistance R is constant for a given
temperature, geometry and material. Therefore, the resistance of an object can be defined as the
ratio of voltage to current, in accordance with Ohm's law:
R = U / I
Specific resistance, or resistivity, is the resistance in ohms offered by a unit volume (the circular-
mil- foot or the centimeter cube) of a substance to the flow of electric current: resistivity of a 1 m
long, object with a cross section area of 1 mm2
. In electrochemistry, it is more practical to use the
reciprocal unit: the reciprocal of resistance is conductivity (G = R-1, the unit is Siemens, 1 S = 1 Ω-
1
).
By definition the specific conductivity (κ) of electrolyte solutions is the conductivity of a 1 cm3
liquid cube, measured between two parallel, 1cm2
first-order electrodes in the distance of 1 cm. The
material of the first-order electrode is usually an inert metal, e.g. often gold or platinum.
The specific conductivity is = l R-1A
-1 where l is the distance between the surface of the two
electrodes, so the unit of S m-1, or S cm-1. Specific conductivity depends on the quality of the
electrolyte material, the concentration, and the temperature.
Molar specific conductivity (m) is the conductivity d
divided by the concentration of the
electrolyte. The entire conductance is measured perpendicular to the electrode surface. As noted
above,
(1)
where c is the solution concentration (mol dm-3) and V is the dilution. The conductance is closely
related to the ions' mobility: if it is connected to the voltage measuring electrodes, the electrolyte
ion migration starts. The migration speed depends on the magnitude of the electric field, so the
migration rate of 1 V/cm relates to network power. The distance traveled by the ion in an electric
filed of 1 V/cm magnitutde is the electric mobility of the ion (u). Since in a binary electrolyte, both
the anions and cations contribute to the conductivity of the solution, the specific conductivity
concentration dependence
= z c (ua + uc ) /1000
form can be written for diluted solutions of strong electrolytes. If the solution is highly diluted, the
electrostatic interaction is not significant (does not occur) between the dissolved ions, and the solute
completely dissociates, then the concentration of the solution can be calculated from the
conductance:
uc,0 ua,0
1000
where, uc0 and ua0 are the mobility of cations and anions in dilute solution.
The mobility of dissolved substances varies significantly with temperature. In aqueous solution 1oC
temperature increase results about 2% rise (the temperature coefficient in case of cations is 1.94
%/°C, while 2.19%/°C for the anions). The solubility also varies with temperature, of course. Its
quantitative description is given by the Clausius-Clapeyron equation:
2
dT RT
dlnc H
=
where H is the enthalpy of the dissolution, c is the solubility in the T temperature. If the solubility
data of a sparingly soluble salt is available on multiple temperatures, using the Clausius-Clapeyron
equation, the enthalpy of dissolution can be calculated. If T1 and T2 (given in Kelvin) are the two