CBSE 2022 · Region 1 · Set 3 · Q9 · 3 marks
(a)The standard Gibbs energy $\displaystyle \left(\Delta \mathrm{r} \mathrm{G}^{\circ}\right)$ for the following cell reaction is $\displaystyle -300 \mathrm{~kJ} \mathrm{~mol}^{-1}$ : \[\mathrm{Zn}(\mathrm{~s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{~s}) \] Calculate $\displaystyle \mathrm{E}_{\text {cell }}^{\mathrm{o}}$ for the reaction. (Given: $\displaystyle 1 \mathrm{~F}=96500 \mathrm{~mol}^{-1}$ )(b)Calculate $\displaystyle \lambda_{\mathrm{m}}^{\mathrm{o}}$ for $\displaystyle \mathrm{MgCl}_{2}$ if $\displaystyle \lambda^{\mathrm{o}}$ values for $\displaystyle \mathrm{Mg}^{2+}$ ion and $\displaystyle \mathrm{Cl}^{-}$ion are $\displaystyle 106 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ and $\displaystyle 76.3 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ respectively. \[\]
(a)
The standard Gibbs energy $\displaystyle \left(\Delta \mathrm{r} \mathrm{G}^{\circ}\right)$ for the following cell reaction is $\displaystyle -300 \mathrm{~kJ} \mathrm{~mol}^{-1}$ : \[\mathrm{Zn}(\mathrm{~s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{~s}) \] Calculate $\displaystyle \mathrm{E}_{\text {cell }}^{\mathrm{o}}$ for the reaction. (Given: $\displaystyle 1 \mathrm{~F}=96500 \mathrm{~mol}^{-1}$ )
(b)
Calculate $\displaystyle \lambda_{\mathrm{m}}^{\mathrm{o}}$ for $\displaystyle \mathrm{MgCl}_{2}$ if $\displaystyle \lambda^{\mathrm{o}}$ values for $\displaystyle \mathrm{Mg}^{2+}$ ion and $\displaystyle \mathrm{Cl}^{-}$ion are $\displaystyle 106 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ and $\displaystyle 76.3 \mathrm{~S} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}$ respectively. \[\]
Marking-scheme solution
(a)
\[\begin{aligned}
\Delta_{\mathrm{r}} G^{\circ} & =-n F E_{\text {cell }}^{\circ} \\
& =+300 \times 10^{3} \mathrm{~J} \mathrm{~mol}^{-1}=+2 \times 96500 \mathrm{C} \mathrm{~mol}^{-1} \times E_{\text {cell }}^{\circ} \\
E_{\text {cell }}^{\circ} & =\frac{300 \times 10^{3}}{2 \times 96500} \mathrm{~V} \\
E_{\text {cell }}^{\circ} & =1.55 \mathrm{~V}
\end{aligned}
\]
(b)
\[\begin{aligned}
\mathbf{\Lambda}_{\mathrm{m}}^{\circ} & =\lambda_{\mathrm{Mg}^{2+}}^{\circ}+2 \lambda_{\mathrm{Cl}^{-}}^{\circ} \\
\mathbf{\Lambda}_{\mathrm{m}}^{\circ} & =(106+2 \times 76.3)\ \mathrm{S}\ \mathrm{cm}^{2}\ \mathrm{mol}^{-1} \\
\mathbf{\Lambda}_{\mathrm{m}}^{\circ} & =(106+152.6)\ \mathrm{S}\ \mathrm{cm}^{2}\ \mathrm{mol}^{-1} \\
\mathbf{\Lambda}_{\mathrm{m}}^{\circ} & =258.6\ \mathrm{S}\ \mathrm{cm}^{2}\ \mathrm{mol}^{-1}
\end{aligned}
\]
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CBSE Class 12 Chemistry past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.