Question

The specific conductance of a N/10 KCl at ${{25}^{0}}C$ is $0.0112oh{{m}^{-1}}c{{m}^{-1}}$ . the resistance of cell-containing solution at the same temperature was found to be 55ohm. The cell constant will be:
(A) $6.16c{{m}^{-1}}$
(B) $0.616c{{m}^{-1}}$
(C) $0.0616c{{m}^{-1}}$
(D) $616c{{m}^{-1}}$

Answer 1

Hint: The measurement of an electrolyte solution ability to conduct electricity is known as conductivity or specific conductance of an electrolyte solution. The SI unit of conductivity is Siemens per meter, S/m, and refers to ${{25}^{o}}C$ .

Complete answer:
The property of electrolyte solution when electricity passes through it, the flow of ions is known as conductance and it is reciprocal of resistance.
Conductance, C= $\dfrac{1}{R}$
Where R = resistance
Units of conductance = mho or $oh{{m}^{-1}}or{{\Omega }^{-1}}$
There are three types of conductance of an electrolyte,
(i) Specific conductance
(ii) Equivalent conductance
(iii) Molar conductance
Specific conductance or conductivity:
The resistance of any conductor is directly portioned to its length and inversely proportional to its cross-sectional area.
$R\alpha \dfrac{l}{A}\Rightarrow R=\rho \dfrac{l}{A}$ --- (1)
Where $\rho $ is called specific resistance and $\dfrac{l}{A}$ = cell constant
The reciprocal of specific resistance is called specific conductance.
Specific conductance, $\kappa =\dfrac{1}{\rho }$ -- (2)
From equation (1) and (2),
$\kappa =\dfrac{l}{A}C$
Hence, specific conductance, $\kappa = {cell constant \times conductance (C) }$
$ Cell constant = specific conductance \times Resistance (R) $
Given resistance R = 55ohms
Specific conductance, $\kappa =0.0112oh{{m}^{-1}}c{{m}^{-1}}$
Then cell constant = $55\times 0.0112=0.616c{{m}^{-1}}$

Hence, the correct answer is option B.

Note:
Many industrial and environmental applications in conductivity measurements are routinely used and inexpensive and reliable ways of measuring the ionic content in a solution. Various factors are affecting the electrolytic conductance which is the nature of the electrolyte, the concentration of the solution, migration of ions, and temperature.