Question

If conductivity (unit Siemens, S) is directly proportional to the area of the vessel and the concentration of the solution in it, and is inversely proportional to the length of the vessel, then the unit of constant of proportionality is:

• A. S m mol${}^{-1}$
• B. S m${}^2$ mol${}^{-1}$
• C. S${}^{-2}$ m${}^2$ mol
• D. S${}^{-2}$ m${}^2$ mol${}^{-2}$

Answer 1

Answer: (B)

S m${}^2$ mol${}^{-1}$

Conductivity $\propto$ Area,

$\propto$ Concentration, and

$\propto \frac{1}{length}$

$\therefore$ Conductivity $\propto \frac{Area\times \left[concentration\right]}{length}$

Conductivity = $constant\times \frac{A\times Conc.}{l}$

$S=constant\times \frac{m^2}{m^1}\times \frac{mol}{m^3}$

$\therefore$ Constant $=S{m}^{2}mo{l}^{-1}$.

Hence, option B is correct.