The standard reduction potentials at $298 \mathrm{~K}$ for the following half cells are given below :

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

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

Consider the given electrochemical reactions,

The number of metal(s) which will be oxidized be $\mathrm{Cr}_2 \mathrm{O}_7^{2-}$, in aqueous solution is _________.

<p>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 $\mathrm{Cr}_2\mathrm{O}_7^{2-}$.</p> <p>The reduction reaction for $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ is:</p> <p>$$\mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow 2\mathrm{Cr}^{3+}+7\mathrm{H}_2\mathrm{O}, \quad \mathrm{E}^{\circ}=1.33 \mathrm{~V}$$</p> <p>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 $\mathrm{Cr}_2\mathrm{O}_7^{2-}$.</p> <p>Given the standard reduction potentials:</p> <p>$$\begin{array}{ll} \mathrm{Fe}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe} & \mathrm{E}^{\circ}=-0.04 \mathrm{~V} \\ \mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ni} & \mathrm{E}^{\circ}=-0.25 \mathrm{~V} \\ \mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Ag} & \mathrm{E}^{\circ}=0.80 \mathrm{~V} \\ \mathrm{Au}^{3+}(\mathrm{aq})+3 \mathrm{e}^{-} \rightarrow \mathrm{Au} & \mathrm{E}^{\circ}=1.40 \mathrm{~V} \end{array}$$</p> <p>Now we compare these reduction potentials with that of $\mathrm{Cr}_2\mathrm{O}_7^{2-}$:</p> <ul> <li>For $\mathrm{Fe}^{3+}/\mathrm{Fe}$, $\mathrm{E}^{\circ}=-0.04 \mathrm{~V}$ (lower than 1.33 V)</li> <li>For $\mathrm{Ni}^{2+}/\mathrm{Ni}$, $\mathrm{E}^{\circ}=-0.25 \mathrm{~V}$ (lower than 1.33 V)</li> <li>For $\mathrm{Ag}^{+}/\mathrm{Ag}$, $\mathrm{E}^{\circ}=0.80 \mathrm{~V}$ (lower than 1.33 V)</li> <li>For $\mathrm{Au}^{3+}/\mathrm{Au}$, $\mathrm{E}^{\circ}=1.40 \mathrm{~V}$ (higher than 1.33 V)</li> </ul> <p>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.</p> <p>Therefore, the number of metals that will be oxidized by $\mathrm{Cr}_2\mathrm{O}_7^{2-}$ in aqueous solution is: <strong>3</strong>.</p>