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Why does the molar conductivity (Λₘ) of an electrolyte increase while its conductivity (κ) decrease with a decrease in concentration (or with an increase in dilution)? It's really counterintuitive. Don't they both imply somthing similar? If yes, how can they show completely opposite behaviour in this case?

As per Wikipedia, Λₘ increases due to a decrease in solute–solute interaction. I would like to have an elaborative explanation for this. A decrease in κ (in case of a strong electrolyte) upon dilution can be clearly understood by the fact that there is a decrease in number of ions per unit volume. But the fact that there is an increase in Λₘ upon dilution is just too counterintuitive for me and thus I can't shove this fact down my throat. A lesser math ridden and a more mechanism based answer would be highly appreciated.

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  • $\begingroup$ @Poutnik Yeah, I can get it, but kindly explain how conductivity and molar conductivity can manifest such contrasting results provided they both mean something very similar, i.e. ability of an electrolyte to conduct electricity. $\endgroup$
    – Gaurav Kumar
    Commented Mar 28, 2022 at 4:57
  • $\begingroup$ So, as per your analogy x:sinx:[(sinx)/x]::c:κ:Λₘ , isn't it? well, do sinx and [(sinx)/x] mean something similar? $\endgroup$
    – Gaurav Kumar
    Commented Mar 28, 2022 at 5:34
  • $\begingroup$ This analogy, no doubt, fits well mathematically but fails to address the idea that despite κ and Λₘ mean something similar, they show opposite variation upon dilution. $\endgroup$
    – Gaurav Kumar
    Commented Mar 28, 2022 at 5:37
  • $\begingroup$ Yeah, I think this party baloon analogy/example is giving me a better idea. I just couldn't think that way. Thanks a lot :) $\endgroup$
    – Gaurav Kumar
    Commented Mar 28, 2022 at 5:48
  • $\begingroup$ Comments deleted and converted to the answer. $\endgroup$
    – Poutnik
    Commented Mar 28, 2022 at 7:03

1 Answer 1

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Ion electromobility decreases with concentration due several effects slowing them down. Major ones are these:

  • The close ion neigbourhood has statistically slightly nonzero net charge of the opposite sign. When these opposite ions move in the opposite directions than "our" ion, there is nonzero net electrostatic force acting against the ion motion.
  • At higher concentrations ions has (weaker or stronger) tendency to form hydrated ion pairs, that are neutral and do not participate in conductivity.

As the consequence, conductivity curve, being initially proportional to concentration, bends to increase progressively slower with increasing concentration.

If concentration increases 10 times, conductivity does not increase 10 times, but (illustratively) just 8 times. As molar conductivity is conductivity divided by concentration, it is 0.8 times smaller than for the diluted solution.

As analogy, if you are compressing slowly leaking party balloon, the gas mass decreases, but the gas specific mass (density) increases, while both meaning something similar.

Another analogy at buying cables, imagine the price per meter decreases with a bought amount. So while the specific price = price/length decreases with the length, absolute price increases with length.

For low concentrations, by the Kohlrausch equation, the dependence of conductivity and molar conductivity on molar concentration is approximately:

$$\kappa=\Lambda.c=\Lambda_0.c - a.c^{(\frac{3}{2})}$$

$$\Lambda=\Lambda_0 - a \sqrt{c}$$

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