This question aims to find the **balanced equation** and **standard emf** with the value of **G** and equilibrium constant **K** of the given reactions.

The quotient of the **concentration of products** and the **concentration of reactants** is expressed by equilibrium constant K while $\Delta G°$ represents the **free energy** during the reaction. $\Delta G°$ and K are related by the equation:

\[\Delta G° = -RT lnk\]

Where $\Delta G°$ shows the standard state of all reactants and products.

## Expert Answer

To find the balanced equation, we have to write the **half-cell reactions**:

\[2I^{-1} (aq) \longrightarrow I _ 2 (s) + 2e^ {-2}\]

\[Hg^ {2+} _ {2} (aq) + 2e {-1} \longrightarrow 2 Hg (l)\]

To write a balanced equation:

\[2 I ^ {-1} (aq) + Hg^ {2+} _ {2} (aq) \longrightarrow I _ 2 (s) + 2 Hg (l)\]

The term **standard cell potential** refers to the difference between the **standard reduction potential** of the cathode reaction $E ° _ {red} (cathode)$ and the standard reduction potential of the anode $E ° _ {red} (anode)$.

To find the standard cell potential:

\[E °_ {cell} = E °_ {red} (cathode) – anode E °_ {red} (anode)\]

\[E °_ {cell} = 0.789 V – 0.536\]

\[E °_ {cell} = 0.253 V\]

To determine the **Gibbs free energy** of the reaction:

\[\Delta G° = – nFE°\]

The symbol **n** represents the **moles of the electrons** that are transferred during the reaction while **F** represents **Faraday’s constant.**

By putting values:

\[\Delta G° = – 2 mol \times 96,485( J/mol) V \times (0.253 V)\]

\[\Delta G° = – 48.83 kJ\]

To determine the **equilibrium constant**, we will use the equation:

\[ \Delta G° = -RT lnk \]

Rearranging the equation:

\[ lnK = \frac { – \Delta G °} { RT}\]

\[lnK = \frac { – 48830} { 8.314 (J/mol) K \times 298 K}\]

\[lnK = 19.71\]

\[K= e^19.71\]

\[K= 3.6 \times 10^8\]

## Numerical Results

The answer of the balanced equation is $2 I ^ {-1} (aq) + Hg^ {2+} _ {2} (aq) \longrightarrow I _ 2 (s) + 2 Hg (l)$ and standard emf is $0.253V$ with value of G that is $-48.83 kJ$ and equilibrium constant K $3.6 \times 10^8$ of the given reactions.

## Example

To find the **equilibrium constant K** for the reaction of $O_2$ with $N_2$ to give **NO** at **423K**.

The balanced equation is:

\[ N _ 2 ( g ) + O _ 2 ( g ) \rightleftharpoons 2 N O (g) \]

$ \Delta G °$ for this reaction is **+ 22.7 kJ /mol** for $ N_2 $.

To determine the equilibrium constant, we will use the equation:

\[ \Delta G° = -RT lnk \]

Rearranging the equation:

\[ lnK = \frac { – \Delta G °} { RT}\]

\[lnK = \frac { (- 22 . 7 kJ) ( 1000 J / kJ )} { 8.314 (J/mol) K \times 298 K}\]

\[ lnK = – 6. 45 \]

\[ K= e^ – 6 . 45 \]

\[ K= 1.6 \times 10^{-3}\]

*Image/Mathematical drawings are created in Geogebra**.*