I came across these equations (boxed in red) in a book:

$$ \begin{align} &\therefore & t_\mathrm{c} &= \frac{u_\mathrm{c}}{u_\mathrm{c} + u_\mathrm{a}}\\ &\text{and} & t_\mathrm{a} &= \frac{u_\mathrm{a}}{u_\mathrm{c} + u_\mathrm{a}} \end{align} $$ At infinite dilution, $$\text{Also,} \quad t_\mathrm{c}^\infty = \frac{u_\mathrm{c}^\infty}{u_\mathrm{c}^\infty + u_\mathrm{a}^\infty}$$ Since, $\lambda_\mathrm{c}^\infty = u_\mathrm{c}^\infty\times F$ and $\lambda_\mathrm{a}^\infty = u_\mathrm{a}^\infty\times F$ $$ \bbox[3px,border:1px solid red]{ \begin{align} &\therefore & t_\mathrm{c}^\infty \times \Lambda_\mathrm{elecrolyte}^\infty &= \lambda_\mathrm{c}^\infty\\ &\text{and} & t_\mathrm{a}^\infty \times \Lambda_\mathrm{elecrolyte}^\infty &= \lambda_\mathrm{a}^\infty \end{align} } $$

Where $t$ refers to the transport number of an ion, and the subscripts $\mathrm{a}$ and $\mathrm{c}$ refer to an anion and cation, respectively.

From what I've learnt, the uppercase lambda $\Lambda$ refers to molar conductivity. But then what does the lowercase lambda $\lambda$ stand for?

Different sections within the same book give different definitions for $\lambda$, one being 'ionic conductance' and another being 'ionic conductivity', and I'm pretty sure 'conductance' and 'conductivity' are not the same thing.

I did try looking it up online, but Wikipedia wasn't much help.

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    $\begingroup$ @andselisk Thanks for the edit! This question was from before the time I learned to (somewhat) use LaTex, my apologies. Have a badge! ;-) $\endgroup$ – paracetamol Dec 29 '17 at 2:23
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    $\begingroup$ You are very welcome, no need to apologize. I also like to practice in formatting various stuff:) $\endgroup$ – andselisk Dec 29 '17 at 2:35

Look in the Wikipedia article Ion transport number.

Lower case lambda, $\lambda$, is the molar ionic conductivity

Upper case lambda, $\Lambda$, is the molar conductivity.

$\lambda = t \dfrac{\Lambda}{\nu}$

Where $\nu$ is the number of ions for the cation or anion in the molecule. So $\ce{Na3PO4}$ would have 3 cations per molecule, but only 1 anion per molecule.


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