# Constant in the molar conductivity equation

For the variation of conductivity with concentration for strong electrolytes there is this equation relating molar conductivity and concentration:

$$\Lambda_\mathrm{M}=\Lambda^{\circ}_\mathrm{M} - A \sqrt{c}$$

Could someone explain what factors determine the value of the constant A in this expression?

• Chem+Math Expression formatting reference: MathJax Basics / Chem+Math expressions/formulas/equations / Upright vs italic / Math SE Mathjax tutorial // MathJax is preferred not to be used in CH SE Q titles. Commented May 11, 2023 at 14:01
• Hello! I encourage you to read the Debye-Hückel-Onsager theory to undestand the two constants of that equation. It may or may not be an easy trip, depending on where are you right now at university. Kohlrausch's law is the name of the equation, but it was an empircal formulation, so there is no way we can get a good grasp of what the two constants represent. Commented May 11, 2023 at 14:03
• I'm currently in high school so it might be a little difficult for me but I'll check it out. Thanks!
– ria
Commented May 13, 2023 at 2:21

Around each ion is a cloud of nonzero net charge density of the opposite charge, as ions statistically repulse the like and attract the opposite charges.

When the external potential gradient is applied, the a ion and its "cloud" move in the opposite directions and the "cloud" effectively decreases the gradient for the moving ion. This causes decreasing the ion mobility and molar conductivity.

Another factor, decreasing the effective ion mobility and molar conductivity, is partial forming ionic pairs that are indifferent to the potential gradient. It occurs mainly for higher concentrations and/or for electrolytes with higher charges (like magnesium sulphate in sea water).

Different electrolytes have generally different $$A$$ parameter for the Kohlrausch equation. As both complementing ions are contributors to the molar conductivity, the electrolytes with the common ion have generally more similar coefficient values, compared to ones without a common ion.

The effects contributing to the $$A$$ value via the affecting ion mobility:

• Ions with higher mobility have bigger dynamic bias of their "anti ion cloud" leading to bigger $$A$$.
• Ions with bigger charge have stronger "ion clouds" and ionic pair formation tendency, leading to bigger $$A$$.
• Ions with bigger hydrated radius (note the opposite trend compared to naked ion radius) have weaker ion cloud", leading to bigger $$A$$. It correlates with the ion mobility.

The Kohlrausch law equation parameters may be found tabulated, or they can be determined experimentally from conductivity of solutions of different amount concentration.

• Is the constant dependent on nature of the compound? Like for e.g, would KCl and NaCl have the same/ similar vales for the constant 'A' ?
– ria
Commented May 13, 2023 at 2:24
• See the question update. Commented May 13, 2023 at 9:50
• Alright, thank you!
– ria
Commented May 14, 2023 at 23:21