Mathematical Expression for Limiting Molar Conductivity [closed]








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I have been fiddling around with the theory of electrolytes, specifically molar conductivity, and ways of calculating limiting molar conductivity $\Lambda^0$.


I was able to come up with the following expression:


$$\Lambda^0 = \frac{\lambda}{mT}|z\_+z\_-|\, ,$$


where $m$ – mass of a single ion in solution (in $\pu{kg}$); $T$ – absolute temperature (in $\pu{K}$); $z\_i$ – charge of a single ion (positive or negative); $\lambda$ is a constant given by


$$\lambda = \frac{N\_\mathrm{A}he^2}{k\_\mathrm{B}} = \frac{hF^2}{R} = \pu{7.42e-25 S kg m2 K mol-1}\, .$$


The above formula works for some chemical species, but fails for others.


Using my formula, $\Lambda^0$ for $\ce{HCl}$ at $\pu{298 K}$ ($m = \pu{6.06e-26 kg}$) is $\pu{0.0411 S m2 mol-1}$, which agrees well with the experimental value of $\pu{0.0426 S m2 mol-1}$.


Constants in the expression for $\lambda$ should be familiar to anyone who studies physical chemistry.


Have I found a new (easier!) approach of calculating $\Lambda^0$, or is my discovery just a coincidence (or, has this already been discovered)?


If it is indeed novel, any ideas on how to get a more accurate formula?


**EDIT (in response to closed post)**: Theory suggests that the above equation should also depend on the (dimensionless) dielectric constant (relative permittivity) of water (when dealing with aqueous solutions) which is 78.4 at 298 K, and this is also expressed in the comments.


