Obtain a relation between conductivity (K) and molar conductivity `(^^_(m))`.

Explanation

Conductivity or specific conductance (K) is the conductance of 1 `cm^(3)` of the solution in C.G.S. units, while molar conductivity is the conductance of a solution containing one mole of an electrolyte.
Consider C molar solution i.,e. C moles of an electrolyte present in 1 liter or `1000 cm^(3)` of the solution .
`because` C moles of an electrolyte are present in `1000cm^(3)` solution.
`therefore` 1 mole of an electrolyte is present in`(1000)/(c) cm^(3)` solution .
Now,
`because` Conductance of `1 cm^(3)` of this solution is k .
`therefore` Conductance of `(1000)/(c) cm^(3)` of these solution is `(k xx 1000)/(C)`
This represent molar conductivty `^^_(m)`
`therefore ^^_(m) = (k xx 100)/(C) Omega^(-1) cm^(2) mol^(-1)` ( in C.G.S units).