Question

The standard reduction potentials at 298 K for the following half cells are given below:
\[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{e}^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}, \, E^\circ = 1.33 \, \text{V} \]
\[ \text{Fe}^{3+} (\text{aq}) + \text{3e}^- \rightarrow \text{Fe}, \, E^\circ = -0.04 \, \text{V} \]
\[ \text{Ni}^{2+} (\text{aq}) + 2\text{e}^- \rightarrow \text{Ni}, \, E^\circ = -0.25 \, \text{V} \]
\[ \text{Ag}^+ (\text{aq}) + \text{e}^- \rightarrow \text{Ag}, \, E^\circ = 0.80 \, \text{V} \]
\[ \text{Au}^{3+} (\text{aq}) + 3\text{e}^- \rightarrow \text{Au}, \, E^\circ = 1.40 \, \text{V} \]
Consider the given electrochemical reactions, the number of metal(s) which will be oxidized by \(\text{Cr}_2\text{O}_7^{2-}\) in aqueous solution is ____.

Answer 1

Correct Answer: 3

The given problem involves determining which metals will be oxidized by the dichromate ion, \(\text{Cr}_2\text{O}_7^{2-}\). The dichromate ion reduction potential is \(E^\circ = 1.33 \, \text{V}\). To determine if a metal will be oxidized, compare its standard reduction potential to that of the dichromate ion. A metal with a lower (more negative) reduction potential will be oxidized by the dichromate ion.

Let's analyze each half-reaction:
 

• \(\text{Fe}^{3+} + 3e^- \rightarrow \text{Fe}, \, E^\circ = -0.04 \, \text{V}\)

Since \(-0.04 \, \text{V} < 1.33 \, \text{V}\), \(\text{Fe}\) can be oxidized.
 

• \(\text{Ni}^{2+} + 2e^- \rightarrow \text{Ni}, \, E^\circ = -0.25 \, \text{V}\)

Since \(-0.25 \, \text{V} < 1.33 \, \text{V}\), \(\text{Ni}\) can be oxidized.
 

• \(\text{Ag}^+ + e^- \rightarrow \text{Ag}, \, E^\circ = 0.80 \, \text{V}\)

Since \(0.80 \, \text{V} < 1.33 \, \text{V}\), \(\text{Ag}\) can be oxidized.
 

• \(\text{Au}^{3+} + 3e^- \rightarrow \text{Au}, \, E^\circ = 1.40 \, \text{V}\)

Since \(1.40 \, \text{V} > 1.33 \, \text{V}\), \(\text{Au}\) cannot be oxidized.

Thus, three metals—\(\text{Fe}\), \(\text{Ni}\), and \(\text{Ag}\)—will be oxidized by \(\text{Cr}_2\text{O}_7^{2-}\). The result, 3, confirms that the solution falls within the provided range (3,3).

Answer 2

Metals with lower standard reduction potentials (E^o) compared to Cr₂O₇²⁻ (E^o = 1.33 V) will be oxidized. These are:

• Fe (E^o = −0.04 V),
• Ni (E^o = −0.25 V),
• Ag (E^o = 0.80 V).

Thus, the number of metals oxidized is 3.

Final Answer: (3)