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 $△G^{∘}$ 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 $\text{Al}\left(\text{s}\right)  \text{and}  {\text{Cd}}^{\text{+ 2}}\left(\text{aq}\right)$ is given below.

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

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

$$\begin{gathered} \text{2Al}\left(\text{s}\right)→2{\text{Al}}^{\text{+ 3}}\left(\text{aq}\right){\text{+ 6e}}^{\text{-}}                      {\text{E}°}_{\text{anode}}=-1.66 V \\ {\text{3Cd}}^{\text{+ 2}}\left(\text{aq}\right){\text{+ 6e}}^{\text{-}}→2\text{Cd}\left(\text{s}\right)                  {{\text{E}}^{∘Â\pm }}_{\text{cathode}}=-0.40 \text{V} \end{gathered}$$

$$\begin{gathered} {E^{∘}}_{cell}={E^{∘}}_{cathode}-{E^{∘}}_{anode} \\ {E^{∘}}_{cell}=-0.40V-\left(-1.66\right)V \\ {E^{∘}}_{cell}=1.26V \end{gathered}$$

We know that,

$$\begin{gathered} △G^{∘}=-nF{E^{∘}}_{cell} \\ △G^{∘}=-6×96500C/mol×1.26V \\ △G^{∘}=-729.54KJ/mol \end{gathered}$$

Hence$△G^{∘}=-729.54KJ/mol$

The redox reaction taking place between ${\text{l}}_2\left(\text{s}\right)  \text{and}  {\text{Br}}^{\text{-}}\left(\text{aq}\right)$is given below.

${\text{I}}_2(\text{s})+2{\text{Br}}^{-}\left(\text{aq}\right)→2{\text{I}}^{-}\left(\text{aq}\right)+{\text{Br}}_2\left(\text{l}\right)$

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

$$\begin{gathered} {\text{l}}_2\left(\text{s}\right){\text{+ 2e}}^{\text{-}}→{\text{2I}}^{\text{-}}\left(\text{aq}\right)                        {\text{E}°}_{\text{cathode}}=0.53\text{V} \\ {\text{2Br}}^{\text{-}}\left(\text{aq}\right)    →{\text{Br}}_{\text{2}}\left(\text{s}\right){\text{+ 2e}}^{\text{-}}              {\text{E}°}_{\text{anode}}=1.07 \text{V} \end{gathered}$$

$$\begin{gathered} {E^{∘}}_{cell}={E^{∘}}_{cathode}-{E^{∘}}_{anode} \\ {E^{∘}}_{cell}=\left(0.53-1.07\right)V \\ {E^{∘}}_{cell}=-0.54V \end{gathered}$$

We know that,

$$\begin{gathered} △G^{∘}=-nF{E^{∘}}_{cell} \\ △G^{∘}=-2×96500C/mol×-0.54V \\ △G^{∘}=104.22KJ/mol \end{gathered}$$

Hence $△G^{∘}=104.22KJ/mol$.