JEE Main 2024 — Electrochemistry Question with Solution

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:

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

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:

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

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.