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I've learnt about conductivity and molar conductivity in school.

I know that conductivity is the conductance of a solution of unit volume/ of unit cross-sectional area and distance between the electrodes.

The book then goes on to say "we must define a more useful quantity called Molar Conductivity."

How is Λm more useful than κ? Though Λm=κ/c, both κ and Λm vary with concentration. What is the use of defining Λm if it varies (though in an opposite manner) like κ?

And a related question: I know that Λm increases with dilution (more ionic mobility), and that κ decreases with dilution as there are less ions per unit volume. But wouldn't more ions per unit volume decrease conductivity, as it does with Λm due to interactions between the ions?

Thank you!

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Molar conductivity reflects ion or ionic compound behaviour, while conductivity reflects rather their concentration. For high dilution, the former is nearly constant, the latter nearly proportional to c.

Compare molar conductivity of 2 different ionic compounds. Then compare just conductivities. The latter is not much useful until molar conductivity is calculated.

If you usefully compare conductivities of solutions of the same molar concentration(or different ones and recalculated), you implicitly compare molar conductivities.

Until very high concentrations, the conductivity increase due increased concentration is greater than its decrease due molar conductivity decreasing with concentration.

For not too high $c$ where Kohlrausch's law is still applicable:

$$\kappa = \Lambda_\mathrm{m}(c) c = (\Lambda_\mathrm{m}^{°} - K\sqrt{c})c$$

The Onsager's expression is:

$$\Lambda_m =\Lambda_m^0-(A+B\Lambda_m^0 )\sqrt{c}$$ 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. This is known as the Debye–Hückel–Onsager equation. However, this equation only applies to very dilute solutions and has been largely superseded by other equations due to Fuoss and Onsager, 1932 and 1957 and later.

See also a scanned article at www.ncbi.nlm.nih.gov THE FUOSS-ONSAGER CONDUCTANCE EQUATION AT HIGH CONCENTRATIONS

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  • $\begingroup$ Does anybody know the physical meaning of the parameter $K$ in front of $√c$ in Kohlrausch's law ? Is it just empirical ? Can it be justified by a reasoning ? $\endgroup$
    – Maurice
    Jun 26, 2022 at 9:55
  • $\begingroup$ In Wikipedia article is written Kohlrausch suggestion of the formula was based on experimental data. $\endgroup$
    – Poutnik
    Jun 26, 2022 at 10:07
  • $\begingroup$ @Maurice Kohlrausch's law was emprical but theoretical explanations have been given. With Debye-Hückel theory, look into Debye-Hückel-Onsager equation (1926-27). Also Fuoss-Onsager theory (1950s or so) which extends DHO. $\endgroup$ Jun 26, 2022 at 12:48
  • $\begingroup$ There is a common square root factor in them, but the relation would be more obvious if an activity coefficient were not in a logarithmic form. $\endgroup$
    – Poutnik
    Jun 26, 2022 at 12:59
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    $\begingroup$ @Poutnik. Your point of view is similar to mine. $\endgroup$
    – Maurice
    Jun 26, 2022 at 14:54

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