# 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
Commented May 14, 2020 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
Commented May 14, 2020 at 10:06

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 $$\Lambda_\text{m} =\Lambda_\text{m}^\circ - K\sqrt{c} = \alpha f_\lambda \Lambda_\text{m}^\circ$$.