Question

The specific conductance of a ${}^{N}/{}_{10}$ KCl at $25{}^\circ C$ is $0.0112oh{{m}^{-1}}c{{m}^{-1}}$. The resistance of the cell containing solution at the same temperature was found to be 55 ohms. 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 concepts of electrochemistry will give you the required pathway to solve the above given problem. As it is a numerical based explanation, only one answer will be correct from the above options.

Complete step by step solution:
Let us understand the concepts of electrochemistry and cell constants.
Electrochemistry- It is part of physical chemistry which studies the relationship between electricity and chemical changes taking place. The concept of electrochemistry is used to make electrical batteries which store the chemical energy which can be utilised in the electrical form when required. In electrochemistry, the electrodes are involved in the cell for recording the chemical changes and producing electricity. Thus, the concept of cell constant is evolved.
Cell constant- The cell constant is the ratio of distance between the electrodes by the area of the cross section of the electrode. It has a unit of per centimeter. In other words, cell constant is defined as the ratio of distance between conductance-titration electrodes to the area of electrodes which is measured from the determined resistance of the solution of some specific conductance.
It is given as,
Cell constant = $\dfrac{conductivity}{conduc\tan ce}$ = conductivity $\times $ resistance
It is more convenient to obtain the value of cell constant, by measuring the conductance of a standard solution whose conductivity is known.
Thus, for given illustration,
Given that,
Resistance = 55 ohms
Specific conductivity = $0.0112oh{{m}^{-1}}c{{m}^{-1}}$
Thus, using above mentioned formula we get,
Cell constant = $0.0112oh{{m}^{-1}}c{{m}^{-1}}\times 55ohm=0.616c{{m}^{-1}}$
Therefore, cell constant is $0.616c{{m}^{-1}}$.

Hence, option (B) is correct.

Note: Consider the calculations with proper units. All the options are numerically similar with differences in their tenth powers. Do note that we should not make any mistake while calculating an answer as every type of answer arising even from mistake will be present in the options.