Question

Given $E_{{\text{A}}{{\text{g}}^ \oplus }|{\text{Ag}}}^ \oplus = 0.80{\text{ V }}E_{{{\text{H}}^ \oplus }|{{\text{H}}_{\text{2}}}\left( {{\text{Pt}}} \right)}^ \oplus = 0.00{\text{ V }}$
Assertion: $1.0{\text{ M }}{{\text{H}}^ \oplus }$ solution under ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ at $1.0{\text{ bar}}\left( { \approx 1.0{\text{ atm}}} \right)$ is capable of oxidising silver metal in the presence of $1.0{\text{ M A}}{{\text{g}}^ \oplus }$ ion.
Reason: $E_{cell}^ \oplus$ is positive.
A. Both assertion and reason are true and the reason is the correct explanation of assertion.
B. Both assertion and reason are true and the reason is not the correct explanation of assertion.
C. Assertion is true but reason is false.
D. Assertion is false but reason is true.
E. Both assertion and reason are false.

Answer 1

To solve this we will first calculate the overall cell potential. If the cell potential is positive the reaction will be spontaneous. A spontaneous reaction means that the $1.0{\text{ M }}{{\text{H}}^ \oplus }$ solution under ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ at $1.0{\text{ bar}}\left( { \approx 1.0{\text{ atm}}} \right)$ is capable of oxidising silver metal in the presence of $1.0{\text{ M A}}{{\text{g}}^ \oplus }$ ion.

Complete answer:
The reaction in which electrons are gained by one species involved in the reaction is known as the reduction reaction. Thus, the reduction reaction is as follows:
$2{{\text{H}}^ + } + 2{\text{e}} \to {{\text{H}}_2}$
The reaction in which electrons are lost by one species involved in the reaction is known as the oxidation reaction. Thus, the oxidation reaction is as follows:
$2{\text{Ag}} \to 2{\text{A}}{{\text{g}}^ + } + {\rm{2e^-}}$
Calculate the overall cell potential is calculated using the equation as follows:
$E_{cell}^ \oplus = E_{reduction}^ \oplus - E_{oxidation}^ \oplus$
Thus,
$\Rightarrow E_{cell}^ \oplus = E_{{{\text{H}}^ \oplus }|{{\text{H}}_{\text{2}}}\left( {{\text{Pt}}} \right)}^ \oplus - E_{{\text{A}}{{\text{g}}^ \oplus }|{\text{Ag}}}^ \oplus$
We are given $E_{{\text{A}}{{\text{g}}^ \oplus }|{\text{Ag}}}^ \oplus = 0.80{\text{ V}}$ and $E_{{{\text{H}}^ \oplus }|{{\text{H}}_{\text{2}}}\left( {{\text{Pt}}} \right)}^ \oplus = 0.00{\text{ V }}$. Thus,
$\Rightarrow E_{cell}^ \oplus = \left( {0.00 - 0.80} \right){\text{V}}$
$\Rightarrow E_{cell}^ \oplus = - 0.80{\text{ V}}$
Thus, the overall cell potential is $- 0.80{\text{ V}}$. Thus, the cell potential $E_{cell}^ \oplus$ is negative.
Thus, the reason is false.
As the cell potential is negative, the reaction is nonspontaneous. And thus, $1.0{\text{ M }}{{\text{H}}^ \oplus }$ solution under ${{\text{H}}_{\text{2}}}{\text{S}}{{\text{O}}_{\text{4}}}$ at $1.0{\text{ bar}}\left( { \approx 1.0{\text{ atm}}} \right)$ is not capable of oxidising silver metal in the presence of $1.0{\text{ M A}}{{\text{g}}^ \oplus }$ ion.
Thus, the assertion is false.
Thus, both assertion and reason are false.

**Thus, the correct option is (E) both assertion and reason are false.

Note:**
The given reaction requires an external source to occur because it is a non-spontaneous reaction. The negative value of $E_{cell}^ \oplus$ indicates that the cell is not feasible.