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Question: The cell constant of a given cell is \[{\text{0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}}\]. The r...

The cell constant of a given cell is 0.47 cm - 1{\text{0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}}. The resistance of a solution placed in this cell is measured to be 31.6 ohm. The conductivity of the solution (in Scm - 1{\text{Sc}}{{\text{m}}^{{\text{ - 1}}}}where S has usual meaning) is
A) 0.15
B) 1.5
C) 0.015
D) 150

Explanation

Solution

The ability of a solution to conduct electricity is known as the conductivity of the solution. The conductivity of the solution is inversely proportional to the resistance of a solution. Use the equation related to cell constant, resistance and conductivity of the solution and calculates the conductivity.

Formula Used:
k = 1R× cell constant{\text{k = }}\dfrac{{\text{1}}}{{\text{R}}} \times {\text{ cell constant}}

Complete step-by-step answer:
Here, we have given the cell constant of the cell and the resistance of the solution placed in the cell and we have to calculate the conductivity of the solution.
Cell constant of cell = 0.47 cm - 1{\text{0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}}
Resistance =31.6 ohm
The equation related to the conductivity of the solution, cell constant and resistance is:
k = 1R× cell constant{\text{k = }}\dfrac{{\text{1}}}{{\text{R}}} \times {\text{ cell constant}}
Where,
k{\text{k}} = conductivity
R = resistance
Now, we have to substitute 0.47 cm - 1{\text{0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}} for cell constant, 31.6 ohm for resistance and calculate the conductivity of the solution.
k = 131.6 ohm× 0.47 cm - 1=0.015 ohm - 1cm - 1=0.015 Scm - 1{\text{k = }}\dfrac{{\text{1}}}{{31.6{\text{ ohm}}}} \times {\text{ 0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}} = 0.015{\text{ oh}}{{\text{m}}^{{\text{ - 1}}}}{\text{c}}{{\text{m}}^{{\text{ - 1}}}} = 0.015{\text{ Sc}}{{\text{m}}^{{\text{ - 1}}}}
Thus, the conductivity of the solution having cell constant 0.47 cm - 1{\text{0}}{\text{.47 c}}{{\text{m}}^{{\text{ - 1}}}}and resistance 31.6 ohm is0.015 Scm - 10.015{\text{ Sc}}{{\text{m}}^{{\text{ - 1}}}}.

Hence, correct option is (C) 0.015.

Note: The resistance of the solution is very important to determine the conductivity of the solution. In solution current flow due to the migration of ions. The opposition to the current flow through the solution is known as the resistance of the solution. The greater the resistance of the solution lower is the conductivity of the solution. The resistance of the solution is expressed in ohm.