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My book says ratio of molar conductance at a given concentration of solute and molar concentration at infinite dilution is equal to degree of dissociation for weak electrolytes. I understand it intuitively but I feel like I need a proof to believe it which i cannot find anywhere on internet.

Can you prove the relation indicated by the equation below?

$$\alpha = \dfrac{\Lambda_\mathrm{M}}{\Lambda^{\circ}_\mathrm{M}}$$

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    $\begingroup$ Note that using photos/screenshots of text instead of typing text itself is highly discouraged. The image text content cannot be indexed nor searched for, nor can be reused in answers. Specifically handwritten scripts can be difficult to decipher. Consider copy/pasting or rewriting of at least essential parts. Suitable formatting can be done according to formatting math/chem expressions/equations. $\endgroup$
    – Poutnik
    Commented Jul 22, 2022 at 11:07
  • $\begingroup$ I have written what it says exactly in questions and I am a newbie here so i can't seem to get around formating yet, sorry $\endgroup$
    – Gaurav
    Commented Jul 22, 2022 at 11:10
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    $\begingroup$ No problem, that is why those comments are posted, to be handy for you for future cases. $\endgroup$
    – Poutnik
    Commented Jul 22, 2022 at 11:10
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    $\begingroup$ Note that terms "proof" and "science" do not like much each other, unless you mean the formal mathematical proof of consistence of theoretical model. Considering matching theory and experiment, there are used terms experimental confirmation or refutation of theoretical claims of models, hypothesis or theories. $\endgroup$
    – Poutnik
    Commented Jul 22, 2022 at 11:16

1 Answer 1

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The expression follows (1) from the principle that ions forming due to dissociation of electrolytes are the charge carriers responsible for the conductance of electrolyte solutions, (2) from an empirical observation (Kohlrausch's law of independent migration of ions), and (3) from the definition of the limiting value of the molar conductivity as the concentration of an electrolyte as the value of the molar conductivity as the electrolyte concentration goes to zero.

The limiting conductivity of electrolytes is more than just a definition, of course, it has the important property that it is a constant, which is consistent with the independent behavior of individual ions as the electrolyte concentration goes to zero, and is therefore consistent with Kohlrausch's law.

The introduction of the degree of dissociation reflects the fact that ions are charge carriers, whereas undissociated neutral species are not. Therefore only the fraction of electrolyte that has dissociated contributes to the molar conductivity.

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