Relation between k and ∧

Conductivity $k$ is the electrical conductance of $\mathrm{1\ cm^3}$ of solution. If $V$ is the volume of solution in $\mathrm{cm^3}$ containing 1 mole of dissolved electrolyte, its electrical conductance is $\Lambda$. Each $\mathrm{1\ cm^3}$ portion of the volume $V$ has conductance $k$; hence the total conductance of $V\ \mathrm{cm^3}$ is $kV$, which is the molar conductivity. Thus we have

The concentration of the solution is $c\ \mathrm{mol\,L^{-1}}$; converting to the cm-based unit,

The volume $V$ of solution in $\mathrm{cm^3}$ containing 1 mole of electrolyte is the reciprocal of this concentration. Therefore, …