We have to find the equivalent conductivity of a solution, which can be called the conductivity of a substance per gram
The equivalent of the same substance. This can be written as:
Equivalent conductivity \(=\frac{\text { conductivity }}{\text { gram equivalent }}\)
Now, we know that one gram equivalent of a substance is the number of gram equivalents per unit volume.
Gram equivalents \(=\frac{\text { No. of gram equivalents }}{\text { Volume }}\)
Here, we will consider the volume to be in \(m^{3}\) as it is the same as the volume in liters which is regularly considered to
Calculate the gram equivalents. Thus, taking the units for the gram equivalent:
Gram equivalents \(=\frac{g \text { equiv }}{m^{3}}\)
Substituting these units in the formula for equivalent conductivity we get,
Equivalent conductivity \(=\frac{\frac{S}{m}}{\frac{g \text { equiv }}{m^{3}}}\)
Now solving and simplifying, we get,
Equivalent conductivity \(=\frac{S}{m} \times \frac{m^{3}}{g \text { equiv }}\)
Equivalent conductivity \(=\frac{S m^{2}}{g \text { equiv }}\)
Equivalent conductance \(=\mathrm{cm}^{2} gm\) equiv \(^{-1}\)