Question

Calculatefor each of the reactions

$$\begin{gathered} {\mathbf{\text{(a)Ni(s)andAg}}}^{\mathbf{\text{+}}}\mathbf{\text{(aq)}} \\ {\mathbf{\text{(b)Fe(s)andCr}}}^{\mathbf{\text{3 +}}}\mathbf{\text{(aq)}} \end{gathered}$$

Short answer

a. $△G^{\circ }=-202.65KJ/mol$

b. $△G^{\circ }=173.7KJ/mol$

Step-by-step solution

Standard electrode potential and△G∘

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.

$△G^{\circ }=-nF{E_{cell}}^{\circ }$

Where,

n = number of electrons involved in the redox reaction

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

△G∘for Ni(s) and Ag+(aq)

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

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

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

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

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

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

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

Hence $△G^{\circ }=-202.65KJ/mol$

△G∘for Fe(s) and Cr3+(aq)

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.

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

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

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

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

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

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

Hence$△G^{\circ }=173.7KJ/mol$