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I was learning about molar conductivity in electrochemistry and this relation

                                      Λm=κV

came up in my textbook. it somehow 'derives' this relation from a known relation except it does not do it very well. (or am i lacking something to understand that?.in that case please let me know which topic). this is my textbook's explanation

I just do not get how it equated area to volume. please educate me on this bit too. I will be very thankful.

Thank You!

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    – Poutnik
    Nov 14 at 12:18
  • $\begingroup$ Numerical value 1 does not mean being unitless, Two quantities with the same numerical value but different units are not equal. B the numerical value and the unit are integral part of physical quantity value. If L = 1 m and m = 1 kg then L <> m. $\endgroup$
    – Poutnik
    Nov 14 at 12:23

1 Answer 1

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These equations are definitions:

\begin{align} \kappa &= G \cdot \frac{L}{A}\\ \Lambda &= \frac{\kappa }{ c} = G \cdot \frac{L}{Ac}\\ c &= n/V\\ \Lambda &= \frac{\kappa V }{ n} = G \cdot \frac{LV}{An} = G \cdot \frac{LV_\text{m}}{A} \end{align}

$$\Lambda[\pu{S m2 mol-1}]=G[S] \frac {L[\pu{m}]}{\pu{1 m2} \cdot c [\pu{mol m-3}] }$$

If $L=c$ numerically then $\Lambda = G$ numerically.
If $A=1 \pu{m2}$ then $L = V $ numerically.

The formula $\Lambda m = \kappa V$ would be correct, if there was $n$ (molar amount) instead of $m$ (mass).

Symbol Quantity
G Conductance
$\kappa$ Conductivity
$\Lambda$ Molar conductivity
L Length
A Area
c Amount concentration
V volume
n Molar amount
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