91Ó°ÊÓ

For a redox reaction taking place, the standard reduction potential is the difference between the respective cell potential.

${\text{E}}_{\text{cell}}°={\text{E}}_{\text{cathode}}°{\text{- E}}_{\text{anode}}°$

The relation between and the standard electrode potential is given below.

$△G^{∘}=-nF{E_{cell}}^{∘}$

Where,

n = number of electrons involved in the redox reaction

$\text{F} \text{=} \text{96500} \text{C/mol}$

The redox reaction taking place between $\text{Ni}\left(\text{s}\right)  \text{and}  {\text{Ag}}^{\text{+}}\left(\text{aq}\right)$is given below.

$\text{Ni}\left(\text{s}\right)+2{\text{Ag}}^{+}\left(\text{aq}\right)→{\text{Ni}}^{2+}\left(\text{aq}\right)+2\text{Ag}\left(\text{s}\right)$

Now, we have to write down the cathode and anode half-cell reaction along with their respective electrode potential.

$$\begin{gathered} \text{Ni}\left(\text{s}\right)→{\text{Ni}}^{\text{+ 2}}\left(\text{aq}\right){\text{+ 2e}}^{\text{-}}                      {\text{E}°}_{\text{anode}}=-0.25 \text{V} \\ {\text{2Ag}}^{\text{+}}\left(\text{aq}\right){\text{+ 2e}}^{\text{-}}→2\text{Ag}\left(\text{s}\right)              {\text{E}°}_{\text{cathode}}=0.80 \text{V} \end{gathered}$$

$$\begin{gathered} {E^{∘}}_{cell}={E^{∘}}_{cathode}-{E^{∘}}_{anode} \\ {E^{∘}}_{cell}=0.80V-\left(-0.25V\right) \\ {E^{∘}}_{cell}=1.05V \end{gathered}$$

Since two electrons are involved in this redox reaction, n=2.

$$\begin{gathered} △G^{∘}=-nF{E^{∘}}_{cell} \\ △G^{∘}=-2×96500C/mol×1.05V \\ △G^{∘}=-202.65KJ/mol \end{gathered}$$

Hence $△G^{∘}=-202.65KJ/mol$

The redox reaction taking place between $\text{Fe}\left(\text{s}\right)  \text{and}  {\text{Cr}}^{\text{+ 3}}\left(\text{aq}\right)$ is given below.

$3\text{Fe}\left(\text{s}\right)+2{\text{Cr}}^{3+}\left(\text{aq}\right)→3{\text{Fe}}^{2+}\left(\text{aq}\right)+2\text{Cr}\left(\text{s}\right)$

Now, we have to write down the cathode and anode half-cell reaction along with their respective electrode potential.

$$\begin{gathered} \text{3Fe}\left(\text{s}\right)→3{\text{Fe}}^{\text{+ 2}}\left(\text{aq}\right){\text{+ 6e}}^{\text{-}}                      {\text{E}°}_{\text{anode}}=-0.44 \text{V} \\ {\text{2Cr}}^{\text{+ 3}}\left(\text{aq}\right){\text{+ 6e}}^{\text{-}}→2\text{Cr}\left(\text{s}\right)                      {\text{E}°}_{\text{cathode}}=-0.74 \text{V} \end{gathered}$$

$$\begin{gathered} {E^{∘}}_{cell}={E^{∘}}_{cathode}-{E^{∘}}_{anode} \\ {E^{∘}}_{cell}=-0.74V-\left(-0.44V\right) \\ {E^{∘}}_{cell}=-0.30V \end{gathered}$$

Since six electrons are involved in this redox reaction, n=6

$$\begin{gathered} △G^{∘}=-6×96500×\left(-0.30\right) \\ △G^{∘}=173.7KJ/mol \end{gathered}$$

Hence$△G^{∘}=173.7KJ/mol$