# Mathematical Expression for Limiting Molar Conductivity

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?

• Welcome to chemistry.SE! If you have any questions about the policies of our community, please ‎visit the help center. – airhuff Jan 4 '18 at 5:06
• Did you come across your expression by guesswork, or does it have some physical motivation? The latter might present a path for further generalization. Do you notice a pattern among the species for which your expression is accurate and among the species for which it is not? If you do, that might tell you about what interactions you should consider to get a better approximation. – a-cyclohexane-molecule Jan 4 '18 at 5:58
• Actually, based on electrolyte theory, limiting molar conductivity increases with temperature. In my expression, it is inversely proportions to temperature... haven't found anything to explain this yet... but it's remarkable that the expression has the same order of magnitude and correct units nonetheless. – compbiostats Jan 4 '18 at 6:17
• Please visit this page, this page and this one on how to format your future posts better with MathJax and Markdown. I see you are an advanced $\rm \LaTeX$ user, but MathJax is a bit different:) – andselisk Jan 4 '18 at 9:06
• I actually determined the equation from guesswork, so I know of no way to verify it from theory. – compbiostats Jan 5 '18 at 18:58