Conductivity (electrolytic)

Conductivity or specific conductance of an electrolyte solution is a measure of its ability to conduct electricity. The SI unit of conductivity is siemens per meter.
Conductivity measurements are used routinely in many industrial and environmental applications as a fast, inexpensive and reliable way of measuring the ionic content in a solution. For example, the measurement of product conductivity is a typical way to monitor and continuously trend the performance of water purification systems.
In many cases, conductivity is linked directly to the total dissolved solids.
High-quality deionized water has a conductivity of
This corresponds to a specific resistivity of
The preparation of salt solutions often takes place in unsealed beakers. In this case the conductivity of purified water often is 10 to 20 times higher. A discussion can be found [|below].
Typical drinking water is in the range of 200–800 μS/cm, while sea water is about 50 mS/cm.
Electrolytic conductivity varies from about 10E-10 S/m for purified toluene up to about 10 S/m for recently discovered highly concentrated “water-in-salt” solutions.
Conductivity of aqueous and other polar solutions is traditionally determined by connecting the electrolyte in a Wheatstone bridge. Dilute solutions follow Kohlrausch's law of concentration dependence and additivity of ionic contributions. Lars Onsager gave a theoretical explanation of Kohlrausch's law by extending Debye–Hückel theory.
Conductivity of low- and non-polar solutions is very low and usually measured with probes having high cell constant and applying low frequency electric field.

Units

The SI unit of conductivity is S/m, and unless otherwise qualified, it refers to 25 °C. More generally encountered is the traditional unit of μS/cm.
The commonly used standard cell has a, and thus for very pure water in equilibrium with air would have a resistance of about 10⁶ ohms, known as a megohm. Ultra-pure water could achieve 18 megohms or more. Thus in the past, megohm-cm was used, sometimes abbreviated to "megohm". Sometimes, conductivity is given in "microsiemens". While this is an error, it can often be assumed to be equal to the traditional μS/cm. Often, by typographic limitations μS/cm is expressed as uS/cm.
The conversion of conductivity to the total dissolved solids depends on the chemical composition of the sample and can vary between 0.54 and 0.96. Typically, the conversion is done assuming that the solid is sodium chloride; 1 μS/cm is then equivalent to about 0.64 mg of NaCl per kg of water.
Molar conductivity has the SI unit S⋅m²⋅mol⁻¹. Older publications use the unit Ω⁻¹⋅cm²⋅mol⁻¹.

Measurement

The electrical conductivity of a solution of an electrolyte is measured by determining the resistance of the solution between two flat or cylindrical electrodes separated by a fixed distance. An alternating voltage is generally used in order to minimize water electrolysis. The resistance is measured by a conductivity meter. Typical frequencies used are in the range 1–3 kHz. The dependence on the frequency is usually small, but may become appreciable at very high frequencies, an effect known as the Debye–Falkenhagen effect.
A wide variety of instrumentation is commercially available. Most commonly, two types of electrode sensors are used: electrode-based sensors and inductive sensors. Electrode sensors with a static design are suitable for low and moderate conductivities and exist in various types, having either two or four electrodes, where electrodes can be arranged oppositely, flat or in a cylinder. Electrode cells with a flexible design, where the distance between two oppositely arranged electrodes can be varied, offer high accuracy and can also be used for the measurement of highly conductive media. Inductive sensors are suitable for harsh chemical conditions but require larger sample volumes than electrode sensors. Conductivity sensors are typically calibrated with KCl solutions of known conductivity. Electrolytic conductivity is highly temperature-dependent, but many commercial systems offer automatic temperature correction. Tables of reference conductivities are available for many common solutions.

Definitions

Resistance is proportional to the distance between the electrodes and is inversely proportional to the cross-sectional area of the sample . Writing for the specific resistance, or resistivity,
In practice the conductivity cell is calibrated by using solutions of known specific resistance, so the individual quantities and need not be known precisely, but only their ratio. If the resistance of the calibration solution is, a cell constant, defined as the ratio of and , is derived:
The specific conductance is the reciprocal of the specific resistance:
Sometimes the conductance is denoted as =. Then the specific conductance is
Conductivity is also temperature-dependent.

Theory

The specific conductance of a solution containing one electrolyte depends on the concentration of the electrolyte. Therefore, it is convenient to divide the specific conductance by concentration. This quotient, termed molar conductivity, is denoted by :

Strong electrolytes

s are hypothesized to dissociate completely in solution. The conductivity of a solution of a strong electrolyte at low concentration follows Kohlrausch's Law:
where is known as the limiting molar conductivity, is an empirical constant, and is the electrolyte concentration. In effect, the observed conductivity of a strong electrolyte becomes directly proportional to concentration at sufficiently low concentrations, i.e. when
As the concentration is increased, however, the conductivity no longer rises in proportion.
Moreover, Kohlrausch also found that the limiting conductivity of an electrolyte,
are the limiting molar conductivities of the individual ions.
The following table gives values for the limiting molar conductivities for some selected ions.

Cations	/ mS m² mol⁻¹	Cations	/ mS m² mol⁻¹	Anions	/ mS m² mol⁻¹	Anions	/ mS m² mol⁻¹
H⁺	34.982	Ba²⁺	12.728	OH⁻	19.8		15.96
Li⁺	3.869	Mg²⁺	10.612	Cl⁻	7.634		7.4
Na⁺	5.011	La³⁺	20.88	Br⁻	7.84		4.306
K⁺	7.352	Rb⁺	7.64	I⁻	7.68	HCOO⁻	5.6
	7.34	Cs⁺	7.68		7.144		7.2
Ag⁺	6.192	Be²⁺	4.50	CH₃COO⁻	4.09		5.0
Ca²⁺	11.90				6.80		7.2
	10.2			F⁻	5.50

An interpretation of these results was based on the theory of Debye and Hückel, yielding the Debye–Hückel–Onsager theory:
where and are constants that depend only on known quantities such as temperature, the charges on the ions and the dielectric constant and viscosity of the solvent. As the name suggests, this is an extension of the Debye–Hückel theory, due to Onsager. It is very successful for solutions at low concentration.

Weak electrolytes

A weak electrolyte is one that is never fully dissociated. In this case there is no limit of dilution below which the relationship between conductivity and concentration becomes linear. Instead, the solution becomes ever more fully dissociated at weaker concentrations, and for low concentrations of "well behaved" weak electrolytes, the degree of dissociation of the weak electrolyte becomes proportional to the inverse square root of the concentration.
Typical weak electrolytes are weak acids and weak bases. The concentration of ions in a solution of a weak electrolyte is less than the concentration of the electrolyte itself. For acids and bases the concentrations can be calculated when the value or values of the acid dissociation constant are known.
For a monoprotic acid HA obeying the inverse square root law, with a dissociation constant, an explicit expression for the conductivity as a function of concentration, known as Ostwald's dilution law, can be obtained:
Various solvents exhibit the same dissociation if the ratio of relative permittivities equals the ratio cubic roots of concentrations of the electrolytes.

Higher concentrations

Both Kohlrausch's law and the Debye–Hückel–Onsager equation break down as the concentration of the electrolyte increases above a certain value. The reason for this is that as concentration increases the average distance between cation and anion decreases, so that there is more interactions between close ions. Whether this constitutes ion association is a moot point. However, it has often been assumed that cation and anion interact to form an ion pair. So an "ion-association" constant can be derived for the association equilibrium between ions A⁺ and B⁻:
Davies describes the results of such calculations in great detail, but states that should not necessarily be thought of as a true equilibrium constant, rather, the inclusion of an "ion-association" term is useful in extending the range of good agreement between theory and experimental conductivity data. Various attempts have been made to extend Onsager's treatment to more concentrated solutions.
The existence of a so-called conductance minimum in solvents having the relative permittivity under 60 has proved to be a controversial subject as regards interpretation. Fuoss and Kraus suggested that it is caused by the formation of ion triplets, and this suggestion has received some support recently.
Other developments on this topic have been done by Theodore Shedlovsky, E. Pitts, R. M. Fuoss, Fuoss and Shedlovsky, Fuoss and Onsager.