# Where does the relation Λm=κV come from? is it experimental?

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).

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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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