# Contradiction in variation of conductance and conductivity on dilution

I do conceptually understand that on dilution conductivity decreases and conductance increases but if we look at the formula of conductivity, a contradiction seems to arise.

$$\kappa=GG^*$$ where $$\kappa$$ is conductivity, $$G$$ is conductance and $$G^*$$ is cell constant.

It appears that on dilution if conductivity decreases then conductance should also decrease which is obviously wrong. Where is the problem?

• Very interesting question. I don't know the exact answer,but the reasoning may help. The $G^*$ also changes with dilution. Suppose you have a cube of volume V and of side area A and edge length L. So $G^*$ = L/A and electrolyte is filled in the cube. So for dilution cube volume should increase suppose it to be 2V after dilution. Then for constant separation between plates(L) area of plates become 2A. Thus new $G^{*'}$ become $G^*/2$. The new $G'$ is somewhat less than $2G$, so overall $\kappa$ decreases. – Manu May 14 at 10:02
• So here I assume that for dilution, plate separation remain same and only the plate area increases which causes lowering of cell constant. I don't know the reasoning behind this assumption. Perhaps there could be some different reasoning behind the observation of lowering of $\kappa$, if this assumption is not correct! – Manu May 14 at 10:06

## 1 Answer

You get it wrong.

With the dilution, both conductance and conductivity ( specific conductance ) proportionally decreases, bound by the conductometer cell constant $$G^* = \dfrac{\kappa }{ G}$$.

What increases is molar conductivity $$\Lambda_\mathrm{m}= \dfrac{\kappa }{ c}$$ toward its infinite dilution value by the Kohlrausch equation $$\Lambda_\text{m} =\Lambda_\text{m}^\circ - K\sqrt{c} = \alpha f_\lambda \Lambda_\text{m}^\circ$$.

Note that conductance is NOT the ease with which ions move. You confuse it with electrical ion mobility, that is closely linked to the molar conductivity.

In fact conductance and conductivity have nothing to do with ions at all all. Ionic solutions are just one special case how to manage these general current related quantities.

See conductance and Conductivity on Wikipedia.

• Can you elaborate on why conductance decreases? Conductance is the ease with which ions move. If we increase the space in which ions move then the "ease", therefore, conductance should increase – Robin Singh May 14 at 10:35
• No, conductance is NOT the ease with which ions move. You confuse it with ion mobility, that is closely linked to the molar conductivity. I advice you to review these basic quantities definitions, e.g. in Wikipedia. – Poutnik May 14 at 14:43