Why does electrolytic conductance increase with dilution?

Question

We are only talking about strong electrolytes.

According to my book, conductance increases slightly due to dilution.

Explanation given by my book:

On the one hand, in a dilute solution, the number of ions present in $1\rm\,cm^3$ solution is less than that of a concentrated solution. So, conductivity decreases with dilution. [I agree with this explanation.]

On the other hand, in a dilute solution, the number of ions present in between two electrodes remains the same as that in a concentrated solution ... (1). However, the ions remain farther apart due to dilution. Thus opposing forces decrease. So, conductance increases slightly. [I don't agree with this explanation.]

My comments:

I disagree with (1). Suppose, the volume of the entire solution before dilution is $500\rm\,cm^3$. The volume of solution between the two electrodes is $100\rm\, cm^3$. After dilution, the volume of the entire solution becomes $750\rm\,cm^3$, but the volume of the solution between the two electrodes will remain the same ($100\rm\,cm^3$). As I understand it, conductance depends solely on the solution between the electrodes ($100\rm\,cm^3$). Before dilution, the $100\rm\,cm^3$ will contain more ions. After dilution, the $100\rm\,cm^3$ will contain fewer ions. So, the number of ions between the two electrodes doesn't stay the same. What is my book talking about then? As the number of ions decreases in $100\rm\,cm^3$ in a diluted solution, conductance should also decrease along with conductivity.

I agree that with dilution, specific conductance or conductivity decreases. Conductivity is the conductance of $1\rm\,cm^3$ solution present in between the two electrodes with a cross-sectional area of $1\rm\,cm^2$ and with $1\rm\,cm$ distance between them. In other words, conductivity is the conductance per unit volume ($\rm\,cm^3$).

So, if conductance per unit volume decreases with dilution, the conductance of the solution, in general, should also decrease. Is my understanding correct?

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Related:

1. Why conductivity of electrolyte decreases on dilution, but molar conductivity increases?
2. Effect of concentration on molar conductance

Answer 1

Conductivity is a measure how fast charges can travel in medium, i.e. $$ \sigma = -q \mu $$ where charge mobility is defined as : $$ \mu ={\frac {q\ell }{m^{*}v_{_{\rm {F}}}}}, $$ where $v_{_F}$ is Fermi velocity, $m^*$ is effective mass and $\ell$ is mean free path of charges. In diluted solution average distance between charges increases, so they can acquire greater drift velocities due to the fact that neighboring charges Coulomb force will be reduced due to greater separations between charges. Not to mention that collision rates and scattering rates between charges will be reduced too. So as mean free path of charges increases in more diluted solution,- charge mobility $\mu$ increases too, and as such conductivity increases. Thus, answer (B).