# Molar conductivity > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Molar_conductivity > Markdown URL: https://mediated.wiki/source/Molar_conductivity.md > Source: https://en.wikipedia.org/wiki/Molar_conductivity > Source revision: 1350355231 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Conductivity per molar concentration of electrolyte}} The '''molar conductivity''' of an [electrolyte](/source/electrolyte) solution is defined as its [conductivity](/source/Conductivity_(electrolytic)) divided by its molar concentration:''The best test preparation for the GRE Graduate Record Examination Chemistry Test''. Published by the Research and Education Association, 2000, {{ISBN|0-87891-600-8}}. p. 149.{{cite book |last1=Atkins |first1=P. W. |authorlink1=Peter Atkins|last2=de Paula |first2=J. |date=2006 |title=Physical Chemistry |url=https://archive.org/details/atkinsphysicalch00atki |url-access=limited |edition=8th |isbn=0198700725 |publisher=Oxford University Press |page=[https://archive.org/details/atkinsphysicalch00atki/page/n794 762]}} : \Lambda_\text{m} = \frac{\kappa}{c}, where : ''κ'' is the measured conductivity (formerly known as specific conductance),[http://goldbook.iupac.org/C01245.html Conductivity], IUPAC Gold Book. : ''c'' is the [molar concentration](/source/molar_concentration) of the electrolyte. The [SI unit](/source/International_System_of_Units) of molar conductivity is [siemens](/source/Siemens_(unit)) metres squared per mole (S m2 mol−1). However, values are often quoted in S cm2 mol−1. In these last units, the value of Λm may be understood as the [conductance](/source/Electrical_resistance_and_conductance) of a volume of solution between parallel plate electrodes one centimeter apart and of sufficient area so that the solution contains exactly one mole of electrolyte.[Laidler K. J.](/source/Keith_J._Laidler) and Meiser J. H., ''Physical Chemistry'' (Benjamin/Cummings 1982) p. 256. {{ISBN|0-8053-5682-7}}. ==Variation of molar conductivity with dilution== There are two types of electrolytes: strong and weak. [Strong electrolyte](/source/Strong_electrolyte)s usually undergo complete ionization, and therefore they have higher conductivity than weak electrolytes, which undergo only partial ionization. For [strong electrolyte](/source/strong_electrolyte)s, such as [salts](/source/salt_(chemistry)), [strong acid](/source/strong_acid)s and [strong base](/source/strong_base)s, the molar conductivity depends only ''weakly'' on concentration. On dilution there is a regular increase in the molar conductivity of strong electrolyte, due to the decrease in solute–solute interaction. Based on experimental data [Friedrich Kohlrausch](/source/Friedrich_Kohlrausch_(physicist)) (around the year 1900) proposed the non-linear law for strong electrolytes: : \Lambda_\text{m} =\Lambda_\text{m}^\circ - K\sqrt{c} = \alpha f_\lambda \Lambda_\text{m}^\circ, where : Λ{{su|b=m|p=∘}} is the molar conductivity at infinite dilution (or ''limiting molar conductivity''), which can be determined by extrapolation of Λm as a function of {{sqrt|''c''}}, : ''K'' is the Kohlrausch coefficient, which depends mainly on the [stoichiometry](/source/stoichiometry) of the specific salt in solution, : ''α'' is the dissociation degree even for strong concentrated electrolytes, : ''fλ'' is the lambda factor for concentrated solutions. This law is valid for low electrolyte concentrations only; it fits into the [Debye–Hückel–Onsager equation](/source/Debye%E2%80%93H%C3%BCckel_theory).{{cite book |last=Atkins |first=P. W. |title=The Elements of Physical Chemistry |publisher=Oxford University Press |year=2001 |isbn=0-19-879290-5}} For weak electrolytes (i.e. incompletely dissociated electrolytes), however, the molar conductivity ''strongly'' depends on concentration: The more dilute a solution, the greater its ''molar'' conductivity, due to increased [ionic dissociation](/source/ionic_dissociation). For example, acetic acid has a higher molar conductivity in dilute aqueous acetic acid than in concentrated acetic acid. == Kohlrausch's law of independent migration of ions== [Friedrich Kohlrausch](/source/Friedrich_Kohlrausch_(physicist)) in 1875–1879 established that to a high accuracy in dilute solutions, molar conductivity can be decomposed into contributions of the individual ions. This is known as '''Kohlrausch's law of independent ionic migration'''.Castellan, G. W. ''Physical Chemistry''. Benjamin/Cummings, 1983. For any electrolyte A''x''B''y'', the limiting molar conductivity is expressed as ''x'' times the limiting molar conductivity of A''y''+ and ''y'' times the limiting molar conductivity of B''x''−. : \Lambda_\text{m}^\circ = \sum_i \nu_i \lambda_i, where: : ''λi'' is the limiting molar ionic conductivity of ion ''i'', : ''νi'' is the number of ions ''i'' in the [formula unit](/source/formula_unit) of the electrolyte (e.g. 2 and 1 for [Na+](/source/sodium_ion) and [{{chem|SO|4|2−}}](/source/sulfate) in [Na2SO4](/source/sodium_sulfate)). Kohlrausch's evidence for this law was that the limiting molar conductivities of two electrolytes with two different cations and a common anion differ by an amount which is independent of the nature of the anion. For example, {{nowrap|Λ0(KX) − Λ0(NaX)}} = {{nowrap|23.4 S cm2 mol−1}} for X = [Cl−](/source/chloride), [I−](/source/iodide) and {{sfrac|1|2}} {{chem|SO|4|2−}}. This difference is ascribed to a difference in ionic conductivities between [K+](/source/potassium_ion) and Na+. Similar regularities are found for two electrolytes with a common anion and two cations.[Laidler K. J.](/source/Keith_J._Laidler) and Meiser J. H., ''Physical Chemistry'' (Benjamin/Cummings 1982) p. 273. {{ISBN|0-8053-5682-7}}. ==Molar ionic conductivity== The molar ionic conductivity of each ionic species is proportional to its [electrical mobility](/source/electrical_mobility) (''μ''), or [drift velocity](/source/drift_velocity) per unit [electric field](/source/electric_field), according to the equation : \lambda = z \mu F, where ''z'' is the ionic charge, and ''F'' is the [Faraday constant](/source/Faraday_constant).{{cite book |last1=Atkins |first1=P. W. |authorlink1=Peter Atkins|last2=de Paula |first2=J. |date=2006 |title=Physical Chemistry |url=https://archive.org/details/atkinsphysicalch00atki |url-access=limited |edition=8th |isbn=0198700725 |publisher=Oxford University Press |page=[https://archive.org/details/atkinsphysicalch00atki/page/n798 766]}} The limiting molar conductivity of a weak electrolyte cannot be determined reliably by extrapolation. Instead it can be expressed as a sum of ionic contributions, which can be evaluated from the limiting molar conductivities of strong electrolytes containing the same ions. For aqueous [acetic acid](/source/acetic_acid) as an example, : \begin{aligned} \Lambda_\text{m}^\circ(\ce{CH3COOH}) &= \lambda(\ce{CH3COO-}) + \lambda(\ce{H+}) \\ &= \Lambda_\text{m}^\circ(\ce{CH3COONa}) + \Lambda_\text{m}^\circ(\ce{HCl}) - \Lambda_\text{m}^\circ(\ce{NaCl}). \end{aligned} Values for each ion may be determined using measured [ion transport number](/source/ion_transport_number)s. For the cation: : \lambda^+ = t_+ \cdot \frac{\Lambda_0}{\nu^+}, and for the anion: : \lambda^- = t_- \cdot \frac{\Lambda_0}{\nu^-}. Most monovalent ions in water have limiting molar ionic conductivities in the range of {{nowrap|40–80 S cm2 mol−1}}. For example:[Laidler K. J.](/source/Keith_J._Laidler) and Meiser J. H., ''Physical Chemistry'' (Benjamin/Cummings 1982) p. 281–283. {{ISBN|0-8053-5682-7}}. {| | {| class="wikitable" ! Cation !! ''λ'', {{nowrap|S cm2 mol−1}} |- | [Li+](/source/lithium) || 38.6 |- | [Na+](/source/sodium) || 50.1 |- | [K+](/source/potassium) || 73.5 |- | [Ag+](/source/silver) || 61.9 |} | {| class="wikitable" ! Anion !! ''λ'', {{nowrap|S cm2 mol−1}} |- | [F−](/source/fluoride) || 55.4 |- | [Cl−](/source/chloride) || 76.4 |- | [Br−](/source/bromide) || 78.1 |- | [CH3COO−](/source/acetate) || 40.9 |} |} The order of the values for alkali metals is surprising, since it shows that the smallest cation Li+ moves more slowly in a given electric field than Na+, which in turn moves more slowly than K+. This occurs because of the effect of [solvation](/source/solvation) of water molecules: the smaller Li+ binds most strongly to about four water molecules so that the moving cation species is effectively {{chem|Li(H|2|O)|4|+}}. The solvation is weaker for Na+ and still weaker for K+. The increase in halogen ion mobility from F− to Cl− to Br− is also due to decreasing solvation. Exceptionally high values are found for [H+](/source/hydrogen_ion) ({{nowrap|349.8 S cm2 mol−1}}) and [OH−](/source/hydroxide) ({{nowrap|198.6 S cm2 mol−1}}), which are explained by the [Grotthuss proton-hopping mechanism](/source/Grotthuss_mechanism) for the movement of these ions. The H+ also has a larger conductivity than other ions in [alcohol](/source/Alcohol_(chemistry))s, which have a [hydroxyl](/source/hydroxyl) group, but behaves more normally in other solvents, including liquid [ammonia](/source/ammonia) and [nitrobenzene](/source/nitrobenzene). For multivalent ions, it is usual to consider the conductivity divided by the [equivalent ion concentration](/source/equivalent_concentration) in terms of equivalents per litre, where 1 equivalent is the quantity of ions that have the same amount of electric charge as 1 mol of a monovalent ion: {{sfrac|1|2}} mol Ca2+, {{sfrac|1|2}} mol {{chem|SO|4|2−}}, {{sfrac|1|3}} mol Al3+, {{sfrac|1|4}} mol {{chem|Fe(CN)|6|4−}}, etc. This quotient can be called the ''equivalent conductivity'', although [IUPAC](/source/IUPAC) has recommended that use of this term be discontinued and the term molar conductivity be used for the values of conductivity divided by equivalent concentration.Yung Chi Wu and Paula A. Berezansky, [http://nvlpubs.nist.gov/nistpubs/jres/100/5/j15wu.pdf Low Electrolytic Conductivity Standards], J. Res. Natl. Inst. Stand. Technol. 100, 521 (1995). If this convention is used, then the values are in the same range as monovalent ions, e.g. {{nowrap|59.5 S cm2 mol−1}} for {{sfrac|1|2}} Ca2+ and {{nowrap|80.0 S cm2 mol−1}} for {{sfrac|1|2}} {{chem|SO|4|2−}}. From the ionic molar conductivities of cations and anions, effective ionic radii can be calculated using the concept of [Stokes radius](/source/Stokes_radius). The values obtained for an ionic radius in solution calculated this way can be quite different from the [ionic radius](/source/ionic_radius) for the same ion in crystals, due to the effect of hydration in solution. == Applications == [Ostwald's law of dilution](/source/Law_of_dilution), which gives the dissociation constant of a weak electrolyte as a function of concentration, can be written in terms of molar conductivity. Thus, the [p''K''a](/source/pKa) values of acids can be calculated by measuring the molar conductivity and extrapolating to zero concentration. Namely, p''K''a = p({{sfrac|''K''|1 mol/L}}) at the zero-concentration limit, where ''K'' is the dissociation constant from Ostwald's law. ==References== {{reflist}} Category:Electrochemical concepts Category:Physical chemistry Category:Molar quantities --- Adapted from the Wikipedia article [Molar conductivity](https://en.wikipedia.org/wiki/Molar_conductivity) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Molar_conductivity?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.