QJEEM24Chbca7: JEE Main 2024 Chemistry - Class 12 JEEM24Chbca7 Solution: The standard reduction potentials at for the following half…

To determine the number of metals that will be oxidized by $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ in aqueous solution, we need to compare their standard reduction potentials with that of the given reduction potential of $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ .

The reduction reaction for $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ is:

$\mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow 2\mathrm{Cr}^{3+}+7\mathrm{H}_2\mathrm{O}, \quad \mathrm{E}^{\circ}=1.33 \mathrm{~V}$

This means that $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ has a strong tendency to get reduced (due to its high reduction potential of 1.33 V). Thus, any metal with a lower standard reduction potential than 1.33 V has the potential to be oxidized by $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ .

Given the standard reduction potentials:

$\begin{array}{ll} \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe} & \mathrm{E}^{\circ}=-0.04 \mathrm{~V} \\ \mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ni} & \mathrm{E}^{\circ}=-0.25 \mathrm{~V} \\ \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Ag} & \mathrm{E}^{\circ}=0.80 \mathrm{~V} \\ \mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Au} & \mathrm{E}^{\circ}=1.40 \mathrm{~V} \end{array}$

Now we compare these reduction potentials with that of $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ :

• For $\mathrm{Fe}^{3+}/\mathrm{Fe}$ , $\mathrm{E}^{\circ}=-0.04 \mathrm{~V}$ (lower than 1.33 V)
• For $\mathrm{Ni}^{2+}/\mathrm{Ni}$ , $\mathrm{E}^{\circ}=-0.25 \mathrm{~V}$ (lower than 1.33 V)
• For $\mathrm{Ag}^{+}/\mathrm{Ag}$ , $\mathrm{E}^{\circ}=0.80 \mathrm{~V}$ (lower than 1.33 V)
• For $\mathrm{Au}^{3+}/\mathrm{Au}$ , $\mathrm{E}^{\circ}=1.40 \mathrm{~V}$ (higher than 1.33 V)

From the comparison, we see that $\mathrm{Fe}$ , $\mathrm{Ni}$ , and $\mathrm{Ag}$ have standard reduction potentials lower than 1.33 V, meaning these metals can be oxidized by $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ , but $\mathrm{Au}$ cannot.

Therefore, the number of metals that will be oxidized by $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ in aqueous solution is: 3.