Question

The electrodes of a conductivity cell are 3 cm apart and have a cross-sectional area of 4 cm². The cell constant of the cell ( in cm⁻¹ ) is.
(a) \[4 \times 3\]
(b) \[4 / 3\]
(c) \[3 / 4\]
(b) \[9 / 4\]

Answer 1

Hint: The cell constant is the measure of the theoretical distance between electrodes and the area of the cross-section. Whereas specific conductance is defined as the conductance of a substance to conduct electricity. And it is the reciprocal value of specific resistance.

Complete Step by Step Solution:
The value of the cell constant (\[K\]) can be calculated in the following way.
We know cell constant is \[K = \frac{l}{A}\], where l is the length in \[{\rm{cm}}\] and A is the area in \[{\rm{c}}{{\rm{m}}^2}\].
Therefore, the value of cell constant will be in \[{\rm{c}}{{\rm{m}}^{ - 1}}\] i.e, \[K = \frac{{cm}}{{c{m^2}}} = c{m^{ - 1}}\].

Also, \[R \propto \frac{l}{A}\] or \[R = \rho \frac{l}{A}\] where\[\rho \] is specific resistant.
The reciprocal value of specific resistance is known as specific conductance (\[k\]) or conductivity i.e., \[k = \frac{l}{\rho }\].
Hence mathematically, \[\frac{l}{R} = \frac{l}{\rho }.\frac{A}{l}\]

On rearranging,
\[\frac{l}{R} = k.\frac{A}{l}\]
\[\frac{l}{A} = k.R\]
\[K = k.R\] (relation between cell constant and specific conductance)
or
(Cell constant \[ = \] Specific conductance\[ \times \] Resistant) Eq. 1
Here, \[K = \] cell constant
          \[k = \] Specific conductance
           \[R = \] Resistant

Given in question,
The distance between the electrode \[3cm\] and cross-sectional area is \[4c{m^2}\]. Therefore, we know cell constant is \[K = \frac{l}{A}\], where l is the length in \[{\rm{cm}}\]and A is the area in \[{\rm{c}}{{\rm{m}}^2}\]. Hence the value of cell constant calculated as:
\[K = \frac{{3cm}}{{4c{m^2}}}\]
Hence, \[K = 3 / 4c{m^{ - 1}}\].
Hence, the above explanation denotes that options C is correct.

Note: The value of cell constant is depending upon the cross-section area of electrodes, the distance between the electrodes and on the nature of the electric fields. The value of the cell constant of a conductivity cell stays constant for a cell.