Question

The molar conductance of $ 0.05M $ solution of $ MgC{{l}_{2}} $ is $ 194.5{{\Omega }^{-1}}c{{m}^{2}}mo{{l}^{-1}}~ $ at $ {{25}^{\circ }}C $ A cell with electrodes having $ 1.50c{{m}^{2}}~ $ surface area and $ 0.50cm $ apart is filled with $ 0.05M $ solution $ MgC{{l}_{2}}. $ How much current will flow when the potential difference between the electrodes is $ 5.0V $ ?

Answer 1

Hint: For this we must know the relation between the molar conductivity at infinite solution. Substituting the known values in the formula we will get the molar conductivity of the weak acid. The conductance is the property of the conductor (metallic as well as electrolytic) which facilitates the flow of resistance; the formula for Molar Conductivity $ = $ Specific Conductance / Concentration of electrolyte.

Complete step by step solution:
The molar conductance of a solution is defined as the conductance of all the ions produced by ionization of one gram mole of an electrolyte when present in $ Vml $ of solution.
Molar Conductivity $ = $ Specific Conductance / Concentration of electrolyte.
 $ K=m\times C $
Substituting the value of molar conductivity $ K $ , and Concentration of electrolyte $ C. $
 $ K=194.5\times 0.05 $
 $ \Rightarrow K=9.752 $
Since, one litre is $ 1000c{{m}^{3}} $ , thus $ 1{{L}^{-1}}={{10}^{-3}}c{{m}^{-3}} $
Also we know that $ \dfrac{1}{R}=K\dfrac{A}{l} $ Here $ A $ is area of cross section of cell and $ l $ is length of electrode cell.
 $ \dfrac{1}{R}=9.725\times {{10}^{-3}}\times \dfrac{1.50}{0.50}=0.029 $
Thus value of resistance $ R=34.27 $
The basic equation for ohm's law is $ V=IR $
It can be rewritten as $ I=\dfrac{V}{R}=\dfrac{5}{34.27} $
 $ \Rightarrow I=0.145A $

Additional Information:
At infinite dilution the weak acid also becomes or behaves as strong acid. Infinite solution is a point when conductance of electrolyte gets saturated and at that point the molar conductance is known as limiting molar conductance. The force of attraction due to dilution becomes very less and hence they also dissociate completely at infinite solution. Molar conductivity is the conductance of a solution that contains one mole of electrolyte or simply it is the conductance of one mole of electrolyte. Molar conductivity of both strong and weak electrolytes increases with decrease in concentration. Alpha is the degree of dissociation of an electrolyte which states that the amount of electrolyte dissociates per unit amount of electrolyte that was taken initially.

Note:
Electrolytes are the substance which does not conduct electricity. In the solid state but is an electric conductor in their molten or aqueous state. This happens because of the presence of free ions in electrolyte when they dissociate and the movement of these ions will carry current.