Question

What is the SI unit of conductivity?
a.) Sm
b.) $S{ m }^{ -1 }$
c.) $S{ m }^{ 2 }$
d.) $S{ m }^{ -2 }$

Answer 1

Hint: For determining the SI unit of any function, we should first determine the factors on which the concerned function depends upon. Conductivity of an electrolyte solution is related to its conductance as well as the cell constant.

Complete step by step solution:
Let us first look into the definition of conductivity.
The ability of a solution of an electrolyte to conduct electricity due to the free ions of the electrolyte (that are no longer bound in the lattice) is called the conductivity (or specific conductance) of that electrolyte’s solution. Its SI unit is Siemens per meter (S/m) and is denoted by the symbol ‘$\kappa $’.
Conductivity and Resistance are related to each other.
Resistance of a sample is directly proportional to the distance ‘l’ between the electrodes and is inversely proportional to the cross-sectional area ‘A’ of the sample. $\rho $ (rho) is the proportionality constant and is called specific resistance (or resistivity).
${ R=\rho \cfrac { l }{ A } . }$
The fraction ‘l/A’ is called the cell constant ‘${ G }^{ \ast }$’ which is found by using solutions of known specific resistance ‘${ \rho }^{ \ast }$’. If the resistance of such a solution is ${ R }^{ \ast }$, then the cell constant will be:

${ G }^{ \ast }=\cfrac { { R }^{ \ast } }{ { \rho }^{ \ast } } $
The reciprocal of the specific resistance is conductivity or specific conductance.
${ \kappa ={ \dfrac { 1 }{ \rho } }={ \cfrac { { G }^{ \ast } }{ R } } }$
The value of conductivity depends upon the temperature, concentration of the ions in solution, type of electrolyte. There is also a relation between the conductance (G) (which is inverse of resistance) and the conductivity of a solution.
${\displaystyle \kappa =G^{*}\times G}$
From the above equation it is clear that the SI unit of conductivity is S/m since the SI unit of conductance is Siemens (S) and the SI unit of cell constant is per metre (${ m }^{ -1 }$).

So, the correct answer is “Option B”.

Note: The conductance of an electrolytic solution increases as the number of ions present in the solution increases. The number of ions that a particular electrolyte produces on dissociation depends upon its nature. Since strong electrolytes completely dissociate into their respective ions in solution, they show high conductance. Whereas the solutions of weak electrolytes show low conductance since weak electrolytes do not dissociate completely. As the temperature of an electrolytic solution increases, its conductance increases.