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Step-by-Step Explanation
Step 1: Understand the Meaning of $E_{M^{3+}/M^{2+}}^0$
The notation $E_{M^{3+}/M^{2+}}^0$ refers to the standard reduction potential for the reaction:
$$
M^{3+} + e^- \rightarrow M^{2+}.
$$
A higher reduction potential means it is more favorable for the $M^{3+}$ ion to be reduced to the $M^{2+}$ ion. Equivalently, the $M^{3+}$ ion is more stable (or more easily formed) if the potential for its conversion to $M^{2+}$ is higher.
Step 2: Identify the Elements and Their Electronic Configurations
The question provides four transition metals from the first row (with their atomic numbers):
Cr (Z = 24)
Mn (Z = 25)
Fe (Z = 26)
Co (Z = 27)
Each has different electronic configurations and, therefore, different stabilities of their $+2$ and $+3$ oxidation states.
Step 3: Compare Stability of the $+2$ and $+3$ Oxidation States
• Chromium (Cr): Typically stable in the $+2$ and $+3$ states, but $Cr^{2+}$ ($3d^4$) can be easily oxidized to $Cr^{3+}$ ($3d^3$).
• Manganese (Mn): Commonly found in $+2$, though $+3$ is less stable compared to $+2$ because of half-filled $d$ configuration in $Mn^{2+}$ ($d^5$).
• Iron (Fe): Frequently exists in $+2$ ($3d^6$) and $+3$ ($3d^5$) forms, with $+3$ especially stable due to the half-filled $3d^5$ configuration.
• Cobalt (Co): Often occurs in $+2$ ($3d^7$) and $+3$ ($3d^6$) oxidation states. Although $+2$ is common, $+3$ can be quite stable in complexes, influencing the reduction potential.
Among these, whether $Co^{3+}$ is more easily reduced to $Co^{2+}$ or not depends on how stable $Co^{3+}$ is. If $Co^{3+}$ is relatively stable (or if $Co^{2+}$ is more difficult to form from $Co^{3+}$), then the reduction potential $E_{Co^{3+}/Co^{2+}}^0$ will be higher.
Step 4: Recognize the Role of Energy and Spin State
Cobalt(III) can often form low-spin complexes due to a relatively large crystal field splitting, making the $+3$ state more stable in such complexes. The stability of $Co^{3+}$ causes its reduction to require more energy, thus resulting in a higher reduction potential.
Step 5: Conclusion
Because cobalt(III) ($Co^{3+}$) is quite stable (especially in complex formation) and it is not as easily reduced to cobalt(II) as some of the other ions, the standard reduction potential $E_{Co^{3+}/Co^{2+}}^0$ is the highest among the listed metals.
Correct Answer: Co (Z = 27)
