Problem 188 - A Complete Resource Book in Chemistry for JEE Main

Question

The \(E\left(\mathrm{M}^{3+} / \mathrm{M}^{2+}\right)\) values for \(\mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}\) and \(\mathrm{Co}\) are \(-0.41,+1.57,+0.77\) and \(+1.97 \mathrm{~V}\) respectively. For which one of these metals the change in oxidation state form \(+2\) to \(+3\) is easiest? \(\quad\) [2004] (a) \(\mathrm{Cr}\) (b) \(\mathrm{Mn}\) (c) \(\mathrm{Fe}\) (d) \(\mathrm{Co}\)

Step-by-Step Solution

Answer

Chromium (Cr) changes from +2 to +3 most easily.

Step 1: Understanding the Context

The problem provides the standard electrode potentials for the change from the divalent state \(\mathrm{M^{2+}}\) to the trivalent state \(\mathrm{M^{3+}}\) for four metals: Chromium (Cr), Manganese (Mn), Iron (Fe), and Cobalt (Co). The task is to determine which metal most easily changes from \(\mathrm{M^{2+}}\) to \(\mathrm{M^{3+}}\).

Step 2: Electrode Potential Significance

The standard electrode potential \(E(\mathrm{M}^{3+} / \mathrm{M}^{2+})\) indicates how likely a substance will undergo oxidation. A more positive electrode potential implies a greater tendency for the species to be reduced (opposite reaction viewed here for oxidation). Thus, a more negative value implies an easier oxidation from \(\mathrm{M^{2+}}\) to \(\mathrm{M^{3+}}\).

Step 3: Comparing Electrode Potentials

Compare the given electrode potentials: - \(\mathrm{Cr}: -0.41\ \mathrm{V}\) - \(\mathrm{Mn}: +1.57\ \mathrm{V}\) - \(\mathrm{Fe}: +0.77\ \mathrm{V}\) - \(\mathrm{Co}: +1.97\ \mathrm{V}\) The most negative value is \(-0.41\ \mathrm{V}\) for Chromium (Cr). This indicates that Cr has the greatest tendency for the oxidation process \(\mathrm{M^{2+}} \rightarrow \mathrm{M^{3+}}\).

Step 4: Conclusion

Based on the comparisons, Chromium (Cr) with a potential of \(-0.41\ \mathrm{V}\) will most easily change from \(+2\) to \(+3\) oxidation state because it has the lowest electrode potential value.

Key Concepts

Oxidation States

Oxidation states are an important concept in chemistry that help us understand how electrons are distributed in a chemical compound. They represent the charge an atom would have if all bonds were ionic. Each atom in a molecule can have a different oxidation state, depending on its electron arrangement and the elements to which it is bonded.
The oxidation state is indicated by a number. For transition metals like Chromium (Cr), Manganese (Mn), Iron (Fe), and Cobalt (Co), these states often change depending on the reactions they undergo. This is particularly relevant in oxidation-reduction reactions, where electrons are transferred between atoms.
In the context of this exercise, understanding oxidation states helps to explain the tendency and ease for these metals to change from a +2 oxidation state to a +3 state. This knowledge allows us to predict and compare their chemical behavior effectively. Transition metals often exhibit multiple oxidation states due to their electron configurations, leading to varied chemical reactivity and bonding.

Standard Electrode Potential

The standard electrode potential, often symbolized as E°, is a measure of the tendency of a chemical species to be reduced. It is measured under "standard" conditions: 1 M concentration, 1 atm pressure, and 25°C. Values of standard electrode potentials can be found in electrochemical series.
The potential is measured in volts (V) and indicates how easily an element will gain electrons (reduction). In the case of transition metals transitioning from \(M^{2+}\) to \(M^{3+}\), this potential helps us understand their likelihood to lose electrons, completing the oxidation process.
A negative electrode potential indicates a greater tendency for oxidation rather than reduction. Therefore, in our exercise, the transition metal with the most negative potential would more easily oxidize from \(M^{2+}\) to \(M^{3+}\). This is precisely why Chromium (Cr), with its \(-0.41\ \mathrm{V}\) value, finds it easiest to undergo this change.

Transition Metals Chemistry

Transition metals are known for their diverse chemistry, often displaying multiple oxidation states and forming a wide range of coordination compounds. They are found in the center of the periodic table and include elements like iron, manganese, cobalt, and chromium.
One of the most notable characteristics of these metals is their ability to change oxidation states. This property makes them highly versatile and valuable in catalysis and many industrial applications. The unique d-orbital configurations allow them to form complex ions and participate in redox reactions effectively.
In our exercise, the variation in standard electrode potentials among \(Cr\), \(Mn\), \(Fe\), and \(Co\) can be attributed to their specific electronic structures and bonding capabilities. Understanding these differences provides us with deeper insight into why certain metals react more readily in redox processes, influencing their practical applications in chemistry and technology.