# Decrease in molar conductivity with increase in concentration

Why does molar conductivity $$Λ$$ for strong electrolytes decrease with increase in concentration? I mean, more concentration would mean higher number of solute particles present in the solution, and as it is a strong electrolyte all of them would disassociate and can help in conduction of electricity, so the $$Λ$$ should ultimately increase, but $$Λ$$ is given by

$$Λ_\mathrm{m} = Λ^°_\mathrm{m} - Ac^{1/2}$$

What am I missing here?

• If I understand the question correctly, first, it's getting too crowded in the solution as the concentration rises (so that solvated ions interfere with each other), and second, note that this is an expression for molar (hence subscript "m") conductivity. – andselisk Jun 15 '19 at 10:09

The equation you quote is the empirical relationship discovered by Kohlrausch (1907) for the conductivity of strong electrolytes, and is valid for concentrations up to $$\sqrt{c} \approx 0.3$$. $$\Lambda_m$$ is the molar conductivity usually given with units $$\mathrm{\Omega^{-1}\,cm^2\,mol^{-1}}$$ ($$\Omega$$ = ohm). The $$\Lambda_m^0$$ is the molar conductivity at infinite dilution which effectively means that of pure water.
Each ion is surrounded by a 'cloud' of oppositely charged ions and when a field is applied there is simultaneous movement of an ion in one direction and of the opposite movement of the ionic atmosphere; the electrophoretic effect. Both the central ion and its atmosphere drag solvent molecules along with them and this results in a retardation of the movement of the central ion. The effect can be evaluated using Stoke's Law $$v=f/6\pi\eta L$$, where velocity is $$v$$ and force $$f=zeE$$ for an ion of charge $$z$$ in field $$E$$. The solution viscosity is $$\eta$$ and $$L$$ the Debye length which is the effective radius of the ionic atmosphere, typically a few nm in millimolar solution. The velocity is identified with the deceleration of the ion caused by the ionic atmosphere moving in the opposite direction.
When the ion is under the influence of the applied field the time average of the forces on the ion are therefore no longer zero. The external field driving the ions through solution is reduced by the continual effect of the relaxation field. This seems strange since this field relaxes so very rapidly compared to motion of the central ion through its atmosphere, $$\approx 10^{-3}$$ sec, however, its magnitude is huge $$10^5$$ V/cm compared to the applied field and even small changes in symmetry do have a measurable effect in acting against the external field.