# Logical reasoning behind the formula for molar conductance of an electrolyte [closed]

I am studying some introductory material on electrochemistry. My book and all standard websites I've found define the molar conductance of an electrolyte as "conductivity of an electrolyte solution divided by the molar concentration of the electrolyte."

I am unable to figure out how this definition was arrived at. Can anyone provide a logical, beginner-level, step-wise approach to how this definition was reached?

• Arrived to what? If sth is defined, then that's the definition... – Mithoron Apr 10 '17 at 15:03
• If it's defined , there has to be a logic behind it. How can be a definition just be without logic and brought in from plain air ? – Pyro Recorcinol Apr 10 '17 at 15:06
• For my clarification, do you have trouble understanding some part of the definition or you don't understand why this particular definition is used? – J. Ari Apr 10 '17 at 15:15
• @J.Ari I have trouble understanding why this definition is used . – Pyro Recorcinol Apr 10 '17 at 15:20
• I also don't know if I see the problem. It seems reasonable that the molar conductance would be the conductivity per molar. What else would molar conductance be? It seems to be a reasonable measure of how much conductivity you get per molar of electrolyte. – Tyberius Apr 10 '17 at 15:48

For most physical properties of substances, it's useful to know how those properties depend on other parameters. For example, the various coefficients of thermal expansion (CTEs) indicate how rapidly the dimension(s) of a substance change when the temperature is changed by a given amount. A common CTE used when working with materials is the linear CTE:

$$\alpha_\mathrm L = {1\over L} {dL \over dT}$$

When thermal expansion occurs, if the temperature change is relatively small the amount of thermal expansion is roughly proportional to the original length $L$. So, the definition of $\alpha_\mathrm L$ divides the length dependence $dL/dT$ by $L$ to yield a parameter that is approximately constant within a particular temperature range.

A similar rationale underlies the definition of the molar conductance (also called the 'molar conductivity') as:

$$\Lambda_\mathrm m = {\kappa \over c}$$

The conductivity $\kappa$ of an electrolyte is a strong function of the concentration $c$ of the electrolyte of interest. However, for electrolytes containing only strong acids and/or bases (or salts of these), $\kappa$ is nearly a linear function of $c$ over a very wide concentration range, and thus $\Lambda_\mathrm m$ for these electrolytes is nearly constant.

Thus, for species that show this strong linearity, defining $\mathbf{\Lambda_m}\equiv\kappa / c$ is useful because a single $\mathbf{\Lambda_m}$ value can be employed to calculate the absolute conductivity $\mathbf\kappa$ across a wide range of electrolyte concentrations $c$, as:

$$\kappa = \Lambda_\mathrm m c$$