Question

Express the relation among cell constant, resistance of the solution in the cell and conductivity of the solution. How is molar conductivity of a solution related to its conductivity?

Answer 1

Hint: We have learnt that conductance is the property of a conductor that supports the flow of currents. It depends upon temperature and concentration and fuel cells work like a battery by producing electricity and heat. Resistance is basically those properties which oppose the flow of current.

Complete step by step answer:
Resistance of the solution in a cell is that property which opposes the flow of current flowing through it in a substance. Resistance is directly proportional to the length and it is inversely proposal to the area of cross section of a wire and we can explain this relation as follows:
$
  R\propto l \\
  R\propto \dfrac{1}{A} \\
  R\propto \dfrac{l}{A} \\
  R = \rho \dfrac{l}{A}
 $
We just got to know that conductivity is the conductance of $1\,c{m^3}$of a conductor, also called specific conductance and Conductance of a solid conductor depends only on the temperature and conductance of a liquid conductor depends upon the concentration of the electrolyte as well as the temperature. When temperature and concentration are increased, conductance increases. We can resistance and conductance as:
$
  R = \rho \dfrac{l}{A} \\
  \dfrac{1}{R} = \dfrac{1}{\rho } \times \dfrac{A}{l} \\
  \dfrac{1}{R} = c \\
  c = k\dfrac{A}{l}
 $
Now, if we say that length is $1cm$and area of cross section is $1c{m^2}$then$c = k$
Let us talk about the cell constant which is equivalent to the distance between two electrodes for an electrolyte solution divided by the effective area of electrodes dipped inside the electrolytic solution. The relation with k and c can be explained as:
$
  cell{\text{ constant = }}\dfrac{L}{A} \\
  cell\,{\text{constant}} \times {\text{c = k}} \\
  {\text{ }}
 $
Finally coming to the Molar conductance, it is the conductance offered by 1 mole of an electrolyte which is placed between two electrodes separated by a distance of $1cm$. Molar conductivity can be given by the formula where K is the conductivity and M is molarity and it is represented by ${\lambda _m}$:
${\lambda _m} = \dfrac{{k \times 1000}}{M}$
Also we should know that when the electrolyte concentration reaches to zero the molar conductivity becomes limiting molar conductivity and it increases when the concentration is decreased as the volume containing 1 mole of electrolytes increases.

Note:
We can also remember the relation between equivalent conductance and conductivity which is basically the conductance offered by 1 equivalent of an electrolyte placed between two electrodes separated by a distance of $1cm$from each other. The formula can be given as:
${\lambda _{eq}} = \dfrac{{k \times 1000}}{N}$ where N is the normality and k is the conductance.