
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
164.1k+ views
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.
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.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
Types of Solutions

Degree of Dissociation and Its Formula With Solved Example for JEE

Classification of Drugs

Instantaneous Velocity - Formula based Examples for JEE

JEE Main Chemistry Question Paper with Answer Keys and Solutions

JEE Main Chemistry Online Mock Test for Class 12

Other Pages
Haloalkanes and Haloarenes

Alcohol Phenol and Ether Class 12 Notes: CBSE Chemistry Chapter 7

Coordination Compounds Class 12 Notes: CBSE Chemistry Chapter 5

NCERT Solutions for Class 12 Chemistry In Hindi Chapter 10 Haloalkanes and Haloarenes In Hindi Mediem

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates
