Question

If the specific conductance and conductance of a solution are the same, then its cell constant is equal to _______.
(A) $1$
(B) $0$
(C) $10$
(D) $100$

Answer 1

Hint: Conductance is defined as the tendency of a material to allow the flow of current through it, while resistance is the tendency of a material to stop the flow of current. Conductance is the reciprocal of resistance.

Complete step by step answer:
Specific conductance is also referred to as conductivity; it is described as the conductance of the solution between two electrodes having a cross-sectional area of $1\,c{m^2}$ separated by a distance of $1\,cm$. It is the reciprocal of resistivity.
$\kappa \, = \,\dfrac{1}{\rho }$
Where $\kappa $ is the conductivity and $\rho $ is the resistivity
Conductivity depends upon the nature of the solution it increases as we increase the concentration of electrolyte and decreases on decreasing the concentration. Conductivity is measured in $ohm{.^{ - 1}}c{m^{ - 1}}$
The cell constant is the ratio of the distance between the electrodes, $l$ to the cross-sectional area, $A$ of the electrodes.
${{Cell}}\,{{constant}}\left( {G*} \right)\, = \,\,\dfrac{l}{A}$
As we know
$ {{conductance(G)}}\,{{ = }}\,\dfrac{{{1}}}{{{{Resistance(R)}}}}\, \\
    \\ $}
And
$R\, = \,\rho \dfrac{1}{A}$
Where $R$ is the resistance, $\rho $ is resistivity, and $A$ cross-sectional area.
So,
$G\, = \,\kappa \dfrac{A}{l}$
Or
$\dfrac{l}{A}\, = \,\dfrac{\kappa }{G}$
And as given in question we know $\kappa \, = \,G$
so,
$\,\dfrac{\kappa }{G}\, = \,1$
Hence the value of $\dfrac{l}{A}\,$ or cell constant will be $1$.
Hence the correct option is (A).

Additional Information: According to ohm’s law, the resistance offered by a substance is directly proportional to its length $(l)$ and inversely proportional to its cross-sectional area $(A)$.

Note:
The conductance increases when you increase the concentration of ions. It is also affected by temperature. On increasing the temperature, It has been observed that higher temperature enhances the solubility of electrolytes. Conductance is also affected by the nature of electrolytes. Strong electrolytes like \[{ }KN{O_3}\] possess a high degree of dissociation and due to this their solutions have a high concentration of ions, Hence they are good electrolytic conductance.