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? (a) \(\mathrm{Cr}\) (b) \(\mathrm{Mn}\) (c) \(\mathrm{Fe}\) (d) \(\mathrm{Co}\)

Step-by-Step Solution

Answer

(a) \(\mathrm{Cr}\) because it has the most negative reduction potential.

Step 1: Understanding the Question

We are given the standard reduction potentials \( E \left( \mathrm{M}^{3+}/\mathrm{M}^{2+} \right) \) for metals \( \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe} \), and \( \mathrm{Co} \). We need to determine for which metal the oxidation state change from +2 to +3 is easiest. The ease is determined by the standard reduction potential; the more negative the potential, the easier the oxidation.

Step 2: Analyzing the Reduction Potential

The given values are \(-0.41\, \mathrm{V}\) for \(\mathrm{Cr}\), \(+1.57\, \mathrm{V}\) for \(\mathrm{Mn}\), \(+0.77\, \mathrm{V}\) for \(\mathrm{Fe}\), and \(+1.97\, \mathrm{V}\) for \(\mathrm{Co}\). Since we are looking for the easiest oxidation (from +2 to +3), we need the corresponding reduction potential to be the most negative, which implies the least favorable reduction or the most favorable oxidation.

Step 3: Identifying the Metal with Easiest Oxidation

Among the given potentials, \(-0.41\, \mathrm{V}\) for \(\mathrm{Cr}\) is the most negative. This means \(\mathrm{Cr}^{3+} \rightarrow \mathrm{Cr}^{2+}\) is hardest (least favorable), making the opposite reaction (oxidation from +2 to +3) the easiest. Thus, \(\mathrm{Cr}\) undergoes oxidation from +2 to +3 most easily.

Key Concepts

Standard Reduction Potential

Standard reduction potential is an essential concept in electrochemistry. It helps us understand how easily a substance can be reduced, or in simpler terms, gain electrons. It is denoted by the symbol \( E^0 \) and measured in volts (V).

When examining reactions, a more negative standard reduction potential means the substance prefers to be oxidized rather than reduced. Oxidation involves losing electrons. In the context of the original exercise, for oxidation of metals from +2 to +3 oxidation state, a more negative value indicates easier oxidation.

In the original exercise, we are given the reduction potentials for \( \mathrm{Cr}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Co} \) in their \( +3/+2 \) states. By comparing these values, we can deduce which metal is more inclined to undergo oxidation from +2 to +3.

Oxidation States

Oxidation states, or oxidation numbers, are assigned to elements in a chemical compound to indicate the distribution of electrons among them. This number reflects the degree of oxidation, or loss of electrons, an atom has undergone.

In the exercise, the metals transition from a +2 to a +3 oxidation state. This signifies the loss of one electron per metal atom. Determining the oxidation state can give insight into the electron transfer processes:

• An increase in oxidation state (e.g., +2 to +3) corresponds to oxidation.
• A decrease indicates reduction.

Understanding oxidation states is crucial for balancing redox reactions and predicting how elements will react with others. In transition metals, these states can vary widely, providing diverse chemical behavior.

Transition Metals Chemistry

Transition metals, such as chromium, manganese, iron, and cobalt in the exercise, have unique properties. They can exhibit multiple oxidation states, form various complex ions, and often act as catalysts in chemical reactions. This variability is due to their electron configuration and the interplay of d orbitals.

For instance, transition metals:

• Have variable oxidation states, frequently by changing the number of d electrons.
• Can easily form complex ions and show interesting magnetic properties.
• Exhibit colors in compounds due to d-d transitions among their d orbitals.

Their chemistry is rich and versatile, greatly influencing reactions in both biological and industrial settings. Understanding how transition metals behave in redox reactions, like the oxidation from +2 to +3 states, is vital in fields like electrochemistry and catalysis.