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 (S/m).
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 (TDS).
High-quality deionized water has a conductivity of μS/cm at 25 °C.
This corresponds to a specific resistivity of MΩ⋅cm.
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 (or 0.05 S/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. It is also associated with motion of ions in electric field, but the nature and solvation of ions are different, as described on the page conductivity (non-aqueous). It is usually measured with probes having low cell constant and applying low frequency electric field.
Notation is treacherous in this domain. Rho () reliably denotes specific resistivity, usually quantified in units of ohm-meter. Kappa and sigma ( and ) are inversely proportional to sigma, with kappa preferred in classical electrochemistry and sigma preferred in Maxwellian electrodynamics. Unfortunately, both kappa and sigma have prominent confounds that can trip up the unwary. In electrochemistry, kappa is also used to denote inverse Debye screening length. In electrodynamics, sigma is also used to denote double-layer charge density.
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" (omitting the distance term in the unit). 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 (in μS/cm) to the total dissolved solids (in mg/kg) 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,Marija Bešter-Rogač and Dušan Habe, "Modern Advances in Electrical Conductivity Measurements of Solutions", Acta Chim. Slov. 2006, 53, 391–395. 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.Gray, p. 495. 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 (noted on the figure above). Writing (rho) 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 (conductivity) (kappa) is the reciprocal of the specific resistance:
Sometimes the conductance (reciprocical of the resistance) is denoted as = . Then the specific conductance (kappa) 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 Strong electrolytes 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. ("Limiting" here means "at the limit of the infinite dilution".) 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, and , are the limiting molar conductivities of the individual ions.
The following table gives values for the limiting molar conductivities for some selected ions. + Table of limiting ion conductivity in water at 298 K (about 25 °C)Cations / mS m2 mol−1Cations / mS m2 mol−1Anions / mS m2 mol−1Anions / mS m2 mol−1H+34.982Ba2+12.728OH−19.815.96Li+3.869Mg2+10.612Cl−7.6347.4Na+5.011La3+20.88Br−7.844.306K+7.352Rb+7.64I−7.68HCOO−5.67.34Cs+7.687.1447.2Ag+6.192Be2+4.50CH3COO−4.095.0Ca2+11.906.807.210.2F−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 (there is a mixture of ions and neutral molecules in equilibrium). 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 (Walden's rule).
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−: A+ + B− A+B−with = . 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.
Non-polar liquids Pioneering works Onsager, Fuoss, Kraus in 20th century proved that ionization in nonpolar liquids is possible and it leads to controllable electrolytic conductivity.
Onsager created the first theory of this conductivity that takes into account formation of ion pairs predicted by Bjerrum. Ion pairs occur in non-polar liquid because of much stronger electrostatic attraction between cation and anion. This attraction brings them together, but they retain their solvation layer in such new entity called “ion pair”. Solvation layers of ions in non-polar liquids are formed by neutral molecules of amphiphile solute as described on the page Ion. Formation of ion-pairs leads to electrolytic conductivity reduction, which was taken into account by Onsager theory.
Mixed solvents systems
The limiting equivalent conductivity of solutions based on mixed solvents like water alcohol has minima depending on the nature of alcohol. For methanol the minimum is at 15 molar % water, and for the ethanol at 6 molar % water.
Conductivity versus temperature