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Question: The specific conductance of a N/10 KCl at \({{25}^{0}}C\) is \(0.0112oh{{m}^{-1}}c{{m}^{-1}}\) . the...

The specific conductance of a N/10 KCl at 250C{{25}^{0}}C is 0.0112ohm−1cm−10.0112oh{{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) 6.16cm−16.16c{{m}^{-1}}
(B) 0.616cm−10.616c{{m}^{-1}}
(C) 0.0616cm−10.0616c{{m}^{-1}}
(D) 616cm−1616c{{m}^{-1}}

Explanation

Solution

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 25oC{{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= 1R\dfrac{1}{R}
Where R = resistance
Units of conductance = mho or ohm−1orΩ−1oh{{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.
RαlA⇒R=ρlAR\alpha \dfrac{l}{A}\Rightarrow R=\rho \dfrac{l}{A} --- (1)
Where ρ\rho is called specific resistance and lA\dfrac{l}{A} = cell constant
The reciprocal of specific resistance is called specific conductance.
Specific conductance, κ=1ρ\kappa =\dfrac{1}{\rho } -- (2)
From equation (1) and (2),
κ=lAC\kappa =\dfrac{l}{A}C
Hence, specific conductance, κ=cellconstant×conductance(C)\kappa = {cell constant \times conductance (C) }
Cellconstant=specificconductance×Resistance(R)Cell constant = specific conductance \times Resistance (R)
Given resistance R = 55ohms
Specific conductance, κ=0.0112ohm−1cm−1\kappa =0.0112oh{{m}^{-1}}c{{m}^{-1}}
Then cell constant = 55×0.0112=0.616cm−155\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.