Question

(a)Following reactions occur at cathode during electrolysis of silver chloride solution:
${\text{A}}{{\text{g}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to {\text{Ag}}\left( {\text{s}} \right){\text{ }}{{\text{E}}^ \circ } = + .80{\text{ V}}$
${{\text{H}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to \frac{1}{2}{{\text{H}}_2}\left( {\text{g}} \right){\text{ }}{{\text{E}}^ \circ } = 0.00{\text{ V}}$
On the basis of their standard reduction electrode potential $\left( {{{\text{E}}^{\text{o}}}} \right)$ values, which reaction is feasible at the cathode and why?
(b)Define limiting molar conductivity. Why conductivity of an electrolyte solution decrease with decrease in concentration

Answer 1

Hint: The reactions having more positive value of the standard reduction potential are feasible at cathode. The conductance due to the ions present in a unit volume of a solution is known as the conductivity of an electrolyte solution.

Complete step by step solution:
(a) We are given two reactions as follows:
${\text{A}}{{\text{g}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to {\text{Ag}}\left( {\text{s}} \right){\text{ }}{{\text{E}}^ \circ } = + .80{\text{ V}}$
${{\text{H}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to \frac{1}{2}{{\text{H}}_2}\left( {\text{g}} \right){\text{ }}{{\text{E}}^ \circ } = 0.00{\text{ V}}$
The equation that gives the relationship between the standard free energy change and the emf of a cell reaction is,
$\Delta {G^ \circ } = - nFE_{{\text{cell}}}^ \circ $
Where, $\Delta {G^ \circ }$ is the standard free energy change,
$n$ is the number of moles of electrons involved in the reaction,
$F$ is the Faraday’s constant,
$E_{{\text{cell}}}^ \circ $ is the emf of a cell reaction.
From the equation, we can say that the more positive the standard reduction potential of the reaction, the more negative is the standard free energy change of the reaction. The reaction is more feasible when the standard free energy change of the reaction is more negative.
The ${{\text{E}}^ \circ }$ value for the reaction ${\text{A}}{{\text{g}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to {\text{Ag}}\left( {\text{s}} \right)$ is more positive. Thus, the reaction ${\text{A}}{{\text{g}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to {\text{Ag}}\left( {\text{s}} \right)$ is feasible at cathode.
Thus, the reaction feasible at the cathode is ${\text{A}}{{\text{g}}^ + }\left( {{\text{aq}}} \right) + {{\text{e}}^ - } \to {\text{Ag}}\left( {\text{s}} \right)$ because it has more positive standard reduction electrode potential $\left( {{{\text{E}}^{\text{o}}}} \right)$ value.

(b)The molar conductivity of an electrolyte when the concentration of the electrolyte in the solution becomes zero is known as the limiting molar conductivity.
The conductance due to the ions present in a unit volume of a solution is known as the conductivity of an electrolyte solution.
As the concentration of an electrolyte decreases, the number of ions that conduct decreases.
Thus, the conductivity of the electrolyte solution decreases as the number of ions decreases.
Thus, the conductivity of an electrolyte solution decreases with decrease in concentration.

Note: The ions in an electrolyte solution are responsible for carrying the current and are the reason for the conducting nature of an electrolyte solution. As the dilution of the electrolyte solution increases, its conductivity decreases.