Question

A solution of concentration ‘C’ g equiv/litre has a specific resistance R. The equivalent conductance of the solution is-
(A) $\dfrac{1000}{RC}$
(B) $\dfrac{C}{R}$
(C) $\dfrac{R}{C}$
(D) $\dfrac{1000R}{C}$

Answer 1

Hint: We can use the relation equivalent conductance, ${{\Lambda }_{eq}}=\dfrac{\kappa \times 1000}{concentration}$ where $\kappa =$ specific conductance. And also, specific conductance is the inverse of specific resistance.

Complete step by step solution:
We know that reciprocal of specific resistance (denoted by $\rho$) is the specific conductance(denoted by $\kappa$). Mathematically,
\[\kappa =\dfrac{1}{\rho }\]
Here in the question, we are given that,
\[\rho =R\]
Therefore, \[\kappa =\dfrac{1}{R}\]
Equivalent conductance (denoted by${{\Lambda }_{eq}}$) is defined as the conductance of all the ions produced by one gram equivalent of an electrolyte in a given solution.
Also, ${{\Lambda }_{eq}}=\kappa \times V$ where V is the volume in mL containing 1 g equivalent of the electrolyte.
If the concentration of the solution is ‘C’ gram equivalent per litre, then the volume containing 1 g equivalent of the electrolyte will be 1000/C.
So equivalent conductance can be written as,
${{\Lambda }_{eq}}=\dfrac{\kappa \times 1000}{C}$
Putting value of specific conductance in the above equation,
${{\Lambda }_{eq}}=\dfrac{1000}{R\times C}$

Therefore, the value of equivalent conductance of the solution is $\dfrac{1000}{RC}$ . Hence the correct option is (A)$\dfrac{1000}{RC}$.

Note: One must not confuse between the terms conductance and conductivity. The conductance(G) of a component tells us about how good a conductor it is. The higher the conductance, the better the component is at conducting. Conductance is just the inverse of resistance, that is, $G=\dfrac{1}{\text{Resistance}}$ . Whereas conductivity is the other name for specific conductance, which is the inverse of specific resistance or resistivity and is given by \[\kappa =\dfrac{1}{\rho }\] . Such that, conductance is an extrinsic property while conductivity is an intrinsic property.