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 (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.[1] For example, the measurement of product conductivity is a typical way to monitor and continuously trend the performance of water purification systems.

Conductivity of Pure Water
Electrolytic conductivity of ultra-high purity water as a function of temperature.

In many cases, conductivity is linked directly to the total dissolved solids (T.D.S.). High quality deionized water has a conductivity of about 5.5 μS/m at 25 °C, typical drinking water in the range of 5–50 mS/m, while sea water about 5 S/m[2] (or 5,000,000 μS/m). Conductivity is traditionally determined by connecting the electrolyte in a Wheatstone bridge. Dilute solutions follow Kohlrausch's Laws of concentration dependence and additivity of ionic contributions. Lars Onsager gave a theoretical explanation of Kohlrausch's law by extending Debye–Hückel theory.

Units

The SI unit of conductivity is S/m and, unless otherwise qualified, it refers to 25 °C. Often encountered in industry is the traditional unit of μS/cm.

The commonly used standard cell has a width of 1 cm, and thus for very pure water in equilibrium with air would have a resistance of about 106 ohm, 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.

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, i.e., 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

Conductimetrie-schema
Principle of the 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.[3] An alternating voltage is used in order to avoid 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,[4] but may become appreciable at very high frequencies, an effect known as the Debye–Falkenhagen effect.

A wide variety of instrumentation is commercially available.[5] There are two types of cell, the classical type with flat or cylindrical electrodes and a second type based on induction.[6] Many commercial systems offer automatic temperature correction. Tables of reference conductivities are available for many common solutions.[7]

Definitions

Resistance, R, is proportional to the distance, l, between the electrodes and is inversely proportional to the cross-sectional area of the sample, A (noted S on the Figure above). Writing ρ (rho) for the specific resistance (or resistivity),

In practice the conductivity cell is calibrated by using solutions of known specific resistance, ρ*, so the quantities l and A need not be known precisely.[8] If the resistance of the calibration solution is R*, a cell-constant, C, is derived.

The specific conductance (conductivity), κ (kappa) is the reciprocal of the specific resistance.

Conductivity is also temperature-dependent. Sometimes the ratio of l and A is called as the cell constant, denoted as G*, and conductance is denoted as G. Then the specific conductance κ (kappa), can be more conveniently written as

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 Λm

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, K is an empirical constant and c 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 selected ions.

Table of limiting ion conductivity in water at 298K (approx. 25oC)[9]
Cations +o / mSm2mol−1 Cations +o / mSm2mol−1 Anions o / mSm2mol−1 Anions o / mSm2mol−1
H+ 34.982 Ba2+ 12.728 OH 19.8 SO42− 15.96
Li+ 3.869 Mg2+ 10.612 Cl 7.634 C2O42− 7.4
Na+ 5.011 La3+ 20.88 Br 7.84 HC2O41− 40.2
K+ 7.352 Rb+ 7.64 I 7.68 HCOO 5.6
NH4+ 7.34 Cs+ 7.68 NO3 7.144 CO32− 7.2
Ag+ 6.192 Be2+ 4.50 CH3COO 4.09 HSO32− 5.0
Ca2+ 11.90 ClO4 6.80 SO32− 7.2
Co(NH3)63+ 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:[10]

where A and B 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 (i.e. there are a mixture of ions and complete 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(s) of the acid dissociation constant(s) is(are) known.

For a monoprotic acid, HA, obeying the inverse square root law, with a dissociation constant Ka, an explicit expression for the conductivity as a function of concentration, c, known as Ostwald's dilution law, can be obtained.

Various solvents exhibit the same dissociation if the ratio of relative permitivities 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 inter-ionic interaction. 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. Thus the electrolyte is treated as if it were like a weak acid and a constant, K, can be derived for the equilibrium

A+ + B ⇌ A+B; K=[A+] [B]/[A+B]

Davies describes the results of such calculations in great detail, but states that K 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.[11] Various attempts have been made to extend Onsager's treatment to more concentrated solutions.[12]

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,[13] and this suggestion has received some support recently.[14][15]

Other developments on this topic have been done by T. Shedlovsky,[16] E. Pitts,[17] R. M. Fuoss,[18] Fuoss and Shedlovsky,[19] Fuoss and Onsager.[20]

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,[21][22][23] and for the ethanol at 6 molar % water.[24]

Conductivity Versus Temperature

Generally the conductivity of a solution increases with temperature, as the mobility of the ions increases. For comparison purposes reference values are reported at an agreed temperature, usually 298 K (≈ 25 °C), although occasionally 20 °C is used. So called 'compensated' measurements are made at a convenient temperature but the value reported is a calculated value of the expected value of conductivity of the solution, as if it had been measured at the reference temperature. Basic compensation is normally done by assuming a linear increase of conductivity versus temperature of typically 2% per Kelvin. This value is broadly applicable for most salts at room temperature. Determination of the precise temperature coefficient for a specific solution is simple and instruments are typically capable of applying the derived coefficient (i.e. other than 2%).

Solvent isotopic effect

The change in conductivity due to the isotope effect for deuterated electrolytes is sizable.[25]

Applications

Notwithstanding the difficulty of theoretical interpretation, measured conductivity is a good indicator of the presence or absence of conductive ions in solution, and measurements are used extensively in many industries.[26] For example, conductivity measurements are used to monitor quality in public water supplies, in hospitals, in boiler water and industries which depend on water quality such as brewing. This type of measurement is not ion-specific; it can sometimes be used to determine the amount of total dissolved solids (T.D.S.) if the composition of the solution and its conductivity behavior are known.[1] Conductivity measurements made to determine water purity will not respond to non conductive contaminants (many organic compounds fall into this category), therefore additional purity tests may be required depending on application.

Sometimes, conductivity measurements are linked with other methods to increase the sensitivity of detection of specific types of ions. For example, in the boiler water technology, the boiler blowdown is continuously monitored for "cation conductivity", which is the conductivity of the water after it has been passed through a cation exchange resin. This is a sensitive method of monitoring anion impurities in the boiler water in the presence of excess cations (those of the alkalizing agent usually used for water treatment). The sensitivity of this method relies on the high mobility of H+ in comparison with the mobility of other cations or anions. Beyond cation conductivity, there are analytical instruments designed to measure Degas conductivity, where conductivity is measured after dissolved carbon dioxide has been removed from the sample, either through reboiling or dynamic degassing.

Conductivity detectors are commonly used with ion chromatography.[27]

See also

References

  1. ^ a b Gray, James R. (2004). "Conductivity Analyzers and Their Application". In Down, R. D.; Lehr, J. H. (eds.). Environmental Instrumentation and Analysis Handbook. Wiley. pp. 491–510. ISBN 978-0-471-46354-2. Retrieved 10 May 2009.
  2. ^ "Water Conductivity". Lenntech. Retrieved 5 January 2013.
  3. ^ Bockris, J. O'M.; Reddy, A.K.N; Gamboa-Aldeco, M. (1998). Modern Electrochemistry (2nd. ed.). Springer. ISBN 0-306-45555-2. Retrieved 10 May 2009.
  4. ^ Marija Bešter-Rogač and Dušan Habe, "Modern Advances in Electrical Conductivity Measurements of Solutions", Acta Chim. Slov. 2006, 53, 391–395 (pdf)
  5. ^ Boyes, W. (2002). Instrumentation Reference Book (3rd. ed.). Butterworth-Heinemann. ISBN 0-7506-7123-8. Retrieved 10 May 2009.
  6. ^ Gray, p 495
  7. ^ "Conductivity ordering guide" (PDF). EXW Foxboro. 3 October 1999. Archived from the original (PDF) on 7 September 2012. Retrieved 5 January 2013.
  8. ^ "ASTM D1125 - 95(2005) Standard Test Methods for Electrical Conductivity and Resistivity of Water". Retrieved 12 May 2009.
  9. ^ Adamson, Aurthur W. (1973). Textbook of Physical Chemistry. London: Academic Press inc. p. 512.
  10. ^ Wright, M.R. (2007). An Introduction to Aqueous Electrolyte Solutions. Wiley. ISBN 978-0-470-84293-5.
  11. ^ Davies, C. W. (1962). Ion Association. London: Butterworths.
  12. ^ Miyoshi, K. (1973). "Comparison of the Conductance Equations of Fuoss–Onsager, Fuoss–Hsia and Pitts with the Data of Bis(2,9-dimethyl-1,10-phenanthroline)Cu(I) Perchlorate". Bull. Chem. Soc. Jpn. 46 (2): 426–430. doi:10.1246/bcsj.46.426.
  13. ^ Fuoss, R. M.; Kraus, C. A. (1935). "Properties of Electrolytic Solutions. XV. Thermodynamic Properties of Very Weak Electrolytes". J. Am. Chem. Soc. 57: 1–4. doi:10.1021/ja01304a001.
  14. ^ Weingärtner, H.; Weiss, V. C.; Schröer, W. (2000). "Ion association and electrical conductance minimum in Debye–Hückel-based theories of the hard sphere ionic fluid". J. Chem. Phys. 113 (2): 762-. Bibcode:2000JChPh.113..762W. doi:10.1063/1.481822.
  15. ^ Schröer, W.; Weingärtner, H. (2004). "Structure and criticality of ionic fluids". Pure Appl. Chem. 76 (1): 19–27. doi:10.1351/pac200476010019. pdf
  16. ^ Shedlovsky, Theodore (1932). "The Electrolytic Conductivity of Some Uni-Univalent Electrolytes in Water at 25°". J. Am. Chem. Soc. 54: 1411. doi:10.1021/ja01343a020.
  17. ^ Pitts, E.; Coulson, Charles Alfred (1953). "An extension of the theory of the conductivity and viscosity of electrolyte solutions". Proc. Roy. Soc. A217: 43. doi:10.1098/rspa.1953.0045.
  18. ^ J. Am. Chem. Soc., 80, 3163, (1958); 81, 2659, (1959)
  19. ^ J. Am. Chem. Soc., 71, 1496, (1949)
  20. ^ J. Phys. Chem., 68, 1 (1964); 69, 258, (1965)
  21. ^ T. Shedlovsky, J. Am. Chem. Soc., 54, 1411, (1932)
  22. ^ T. Shedlovsky, R. L. Kay, J. Phys. Chem., 60, 151 (1956)
  23. ^ H. Strechlow, Z. Phys. Chem., 24, 240, (1960)
  24. ^ I. I. Bezman, F. H. Verhoek, J. Am. Chem. Soc., 67, 1330, (1945)
  25. ^ Biswas, Ranjit. "Limiting Ionic Conductance of Symmetrical, Rigid Ions in Aqueous Solutions: Temperature Dependence and Solvent Isotope Effects". Journal of the American Chemical Society. 119: 5946–5953. doi:10.1021/ja970118o.
  26. ^ "Electrolytic conductivity measurement, Theory and practice" (PDF). Aquarius Technologies Pty Ltd. Archived from the original (PDF) on 12 September 2009.
  27. ^ "Detectors for ion-exchange chromatography". Retrieved 17 May 2009.

Further reading

Acid dissociation constant

An acid dissociation constant, Ka, (also known as acidity constant, or acid-ionization constant) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction known as dissociation in the context of acid–base reactions.

.

The chemical species HA, A, and H+ are said to be in equilibrium when their concentrations (written above in square brackets) do not change with the passing of time, because both forward and backward reactions are occurring at the same very fast rate. The chemical equation for acid dissociation can be written symbolically as:

where HA is a generic acid that dissociates into A, the conjugate base of the acid and a hydrogen ion, H+. It is implicit in this definition that the quotient of activity coefficients, Γ,

is a constant that can be ignored in a given set of experimental conditions.

For many practical purposes it is more convenient to discuss the logarithmic constant, pKa

The more positive the value of pKa, the smaller the extent of dissociation at any given pH (see Henderson–Hasselbalch equation)—that is, the weaker the acid. A weak acid has a pKa value in the approximate range −2 to 12 in water.

For a buffer solution consisting of a weak acid and its conjugate base, pKa can be expressed as:

The pKa for a weak monoprotic acid is conveniently determined by potentiometric titration with a strong base to the equivalence point (neutralization point) and taking the pH value measured at one-half this volume (the so-called midpoint of the titration) as being equal to pKa. That is because at this half equivalence point, the number of moles of strong base added is one-half the number of moles of weak acid originally present, while the concentrations of the conjugate base and the remaining weak acid are the same; the term in parenthesis is thus equal to unity.

Acids with a pKa value of less than about −2 are said to be strong acids. In water, the dissociation of a strong acid in dilute solutions is effectively (but not exactly) complete such that the final concentration of the undissociated acid [HA]final is extremely low. Consider a strong monoprotic acid, such as HCl (Ka = 1x107). Because of their 1:1 ratio, the final concentration of the conjugate base, [Cl]final, is taken to be equal to the concentration of the hydronium ion [H3O+], which can be directly measured by a pH meter. For strong monoprotic acids like HCl, [A]final and [H3O+] are both very nearly equal to the initial concentration of [HA]initial placed into solution (before dissociation occurs). Unfortunately, with conventional acid-base titration methods it is difficult to measure the pH of a strong acid solution and, hence, to determine the [H3O+] or [A]final, with a sufficient number of significant figures (most pH meters cannot resolve past three decimal places, or one-one thousandth of a pH unit) to accurately and precisely compute the extremely low values encountered for [HA]final ([HA]final = [HA]initial - [H3O+]), which can be as low as 10−9 mol per liter for some strong acids. Furthermore, if exactly 100% dissociation is assumed, [HA]final is exactly zero and the fraction within parenthesis in the equation above becomes undefined. Because the second expression on the right-hand side of the above equation is therefore indeterminable by conventional titration methods, the entire equation is not generally as useful a means of experimentally measuring pKa for strong acids as it is for weak acids.

However, pKa and/or Ka values for strong acids can be estimated by theoretical means, such as computing gas phase dissociation constants and using Gibbs free energies of solvation for the molecular anions. It is also possible to use spectroscopy in some cases to determine the ratio of the concentrations of the conjugate base produced and the undissociated acid. For example, the Raman spectra of dilute nitric acid (HNO3) solutions contain signals of the nitrate ion (NO3, the conjugate base) and as the solutions become more concentrated signals of undissociated nitric acid molecules also emerge.

Conductivity

Conductivity may refer to:

Electrical conductivity, a measure of a material's ability to conduct an electric current

Conductivity (electrolytic), the electrical conductivity of an electrolyte in solution

Ionic conductivity (solid state), electrical conductivity due to ions moving position in a crystal lattice

Hydraulic conductivity, a property of a porous material's ability to transmit water

Thermal conductivity, an intensive property of a material that indicates its ability to conduct heat

Einstein relation (kinetic theory)

In physics (specifically, the kinetic theory of gases) the Einstein relation (also known as Einstein–Smoluchowski relation) is a previously unexpected connection revealed independently by William Sutherland in 1904, Albert Einstein in 1905, and by Marian Smoluchowski in 1906 in their papers on Brownian motion. The more general form of the equation is

where

This equation is an early example of a fluctuation-dissipation relation.

Two frequently used important special forms of the relation are:

(Electrical mobility equation, for diffusion of charged particles)
(Stokes–Einstein equation, for diffusion of spherical particles through a liquid with low Reynolds number)

where

Electrical resistance and conductance

The electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is electrical conductance, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

The resistance of an object depends in large part on the material it is made of—objects made of electrical insulators like rubber tend to have very high resistance and low conductivity, while objects made of electrical conductors like metals tend to have very low resistance and high conductivity. This material dependence is quantified by resistivity or conductivity. However, resistance and conductance are extensive rather than bulk properties, meaning that they also depend on the size and shape of an object. For example, a wire's resistance is higher if it is long and thin, and lower if it is short and thick. All objects show some resistance, except for superconductors, which have a resistance of zero.

The resistance (R) of an object is defined as the ratio of voltage across it (V) to current through it (I), while the conductance (G) is the inverse:

For a wide variety of materials and conditions, V and I are directly proportional to each other, and therefore R and G are constants (although they will depend on the size and shape of the object, the material it is made of, and other factors like temperature or strain). This proportionality is called Ohm's law, and materials that satisfy it are called ohmic materials.

In other cases, such as a transformer, diode or battery, V and I are not directly proportional. The ratio V/I is sometimes still useful, and is referred to as a "chordal resistance" or "static resistance", since it corresponds to the inverse slope of a chord between the origin and an I–V curve. In other situations, the derivative may be most useful; this is called the "differential resistance".

Equivalent concentration

In chemistry, the equivalent concentration or normality of a solution is defined as the molar concentration ci divided by an equivalence factor feq:

Normality = ci/feq

Index of physics articles (C)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

Ionic conductivity

Ionic conductivity may refer to:

Conductivity (electrolytic), electrical conductivity due to an electrolyte separating into ions in solution

Ionic conductivity (solid state), electrical conductivity due to ions moving position in a crystal lattice

Mixing ratio

In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio or mass ratio.

Ultrapure water

Ultrapure water (also UPW or high-purity water) is water that has been purified to uncommonly stringent specifications. Ultrapure water is a commonly used term in the semiconductor industry to emphasize the fact that the water is treated to the highest levels of purity for all contaminant types, including: organic and inorganic compounds; dissolved and particulate matter; volatile and non-volatile, reactive and inert; hydrophilic and hydrophobic; and dissolved gases.

UPW and commonly used term deionized (DI) water are not the same. In addition to the fact that UPW has organic particles and dissolved gases removed, a typical UPW system has three stages: a pretreatment stage to produce purified water, a primary stage to further purify the water, and a polishing stage, the most expensive part of the treatment process.A number of organizations and groups develop and publish standards associated with the production of UPW. For microelectronics and power, they include Semiconductor Equipment and Materials International (SEMI) (microelectronics and photovoltaic), American Society for Testing and Materials International (ASTM International) (semiconductor, power), Electric Power Research Institute (EPRI) (power), American Society of Mechanical Engineers (ASME) (power), and International Association for the Properties of Water and Steam (IAPWS) (power). Pharmaceutical plants follow water quality standards as developed by pharmacopeias, of which three examples are the United States Pharmacopeia, European Pharmacopeia, and Japanese Pharmacopeia.

The most widely used requirements for UPW quality are documented by ASTM D5127 "Standard Guide for Ultra-Pure Water Used in the Electronics and Semiconductor Industries" and SEMI F63 "Guide for ultrapure water used in semiconductor processing".Ultra pure water is also used as boiler feed water in the UK AGR fleet.

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