Induction generator

2014-01-22T20:12:07Z

89.168.132.115: Corrected grammar

'''Molar conductivity''' is defined as the [[Conductivity (electrolytic)|conductivity]] of an [[electrolyte]] [[solution]] divided by the [[molar concentration]] of the electrolyte, and so measures the efficiency with which a given electrolyte conducts electricity in solution. Its units are [[Siemens (unit)|siemens]] per meter per [[molarity]], or siemens meter-squared per mole. The usual symbol is a capital lambda, Λ, or Λm.

== History ==

[[Friedrich Kohlrausch]] established that to a high accuracy in dilute solutions, molar conductivity is composed of individual contributions of ions. This is known as the ''law of independent migration of ions''.<ref>Castellan, G.W. ''Physical Chemistry''. Benjamin/Cummings, 1983.</ref>

== Description ==

From its definition, the molar conductivity is given by:<ref>''The best test preparation for the GRE Graduate Record Examination Chemistry Test.'' Published by the Research and Education Association, 2000, ISBN 0-8789-600-8. p. 149.</ref>

:<math>\Lambda_{\mathrm{m}} = \frac{\kappa}{c}</math>

where:
* κ is the measured conductivity
* ''c'' is the electrolyte concentration.

Two cases should be distinguished: strong electrolytes and weak electrolytes.

For [[strong electrolyte]]s, such as [[salt]]s, [[strong acid]]s and [[strong base]]s, the molar conductivity depends only ''weakly'' on concentration. Based on experimental data [[Friedrich Kohlrausch]] (around the year 1900) proposed the non-linear law for strong electrolytes:

:<math>\Lambda_{\mathrm{m}} =\Lambda_{\mathrm{m}}^\circ - K\sqrt{c}</math>

where
* <math>\Lambda_{\mathrm{m}}^\circ</math> is the molar conductivity at infinite dilution (or ''limiting molar conductivity'')
* ''K'' is the Kohlrausch coefficient, which depends mainly on the stoichiometry of the specific salt in solution.
This law is valid for low electrolyte concentrations only; it fits into the [[Debye-Hückel-Onsager equation]] :.<ref>{{cite book|last=Atkins|first=P. W.|title=The Elements of Physical Chemistry|publisher=Oxford University Press|year=2001|isbn=0-19-879290-5}}</ref>

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]]. (This, for example, is the case of SDS-coated proteins in the stacking gel of an [[SDS-PAGE]].)

The limiting molar conductivity can be decomposed into contributions from the different ions (Kohlrausch's law of independent migration of ions):

:<math>\Lambda_{\mathrm{m}}^\circ = \Sigma_i \nu_i \lambda_i</math>

where:
* <math>\lambda_i</math> is the molar ionic conductivity of ion ''i''.
* <math>\nu_i</math> is the number of ions ''i'' in the formula unit of the electrolyte (e.g. 2 and 1 for Na+ and SO42- in Na2SO4)

== Applications ==
[[Law of dilution|Ostwald's 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 [[pKa]] values of acids can be calculated by measuring the molar conductivity and extrapolating into zero concentration. Namely, pKa = p(K/(1 mol dm−3)) at the zero-concentration limit, where K is the dissociation constant from Ostwald's law.

==References==
<references />

[http://www.iupac.org/publications/pac/pdf/1994/pdf/6608x1739.pdf]

[[Category:Electrochemistry]]
[[Category:Physical chemistry]]

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Induction generator