The unit of equivalent conductivity `(Lambda_(eq.))` are

Options

A. `ohm^(-1)cm^(2)eq^(-1)`
B. `ohm^(-2)cm^(2)`
C. `ohm^(-1)cm^(-1)`
D. `ohm^(-1)cm^(-2)`

Answer

A

Explanation

Imagine `1 c.c.` of a solution of `1` equivalent of an electrolyte placed between two large electrodes `1 cm` apart. In this case
Conductance `(G)` = specific conductivity `(k)`
= Equivalent conductivity `(Lambda_(eq.))`
Suppose the solution is now diluted to `1000 cm^(3)`. We will be having now `1000 cm` cubes of the solution. Therefore, the conductance of the resulting solution will be `1000` times its specific conductance.
But even now, as the solution contain only `1 grams` equivalent of the electrolyte between the electrodes, the conductance measured will be equivalent conductance. Thus, in this case,
`Lambda_(eq.) = 1000 xx k`
If the solution is further diluted to say, `5000 cm^(3)`, there will be `5000 cm` cubes of the solution and hence the equivalent conductance of the resulting solution will be `5000` times its specific conductance. In general,
`Lambda_(eq) = kV`
where `V` (called dilution) is the volume of the solution in `c.cs`, containing `1 gram` equivalent of the electrolyte.
Since the units of conductivity are `Omega^(-1) cm^(-1)` and the units of volume are `cm^(3)`, units of equivalent conductance are :
`(Omega^(-1) cm^(-1)) (cm^(3) = Omega^(-1) cm^(2)`
In `SI` system, the units of equivalent conductance are `S m^(2)`.
Truly speaking the unit of equivalent conductance should be `S m^(2) "equiv"^(-1)` or `ohm^(-1) cm^(2) "equiv"^(-1)`