Problem 6 - A Complete Resource Book in Chemistry for JEE Main

Question

Given \(E^{\circ}\left(\mathrm{Fe}^{2+} / \mathrm{Fe}\right)=-0.44 \mathrm{~V}\) and \(E^{\circ}\left(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\right)=\) \(0.77 \mathrm{~V}\) \(\mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}\) and \(\mathrm{Fe}\) are placed together then (a) \(\mathrm{Fe}^{3+}\) increases (b) \(\mathrm{Fe}^{3+}\) decreases (c) \(\left[\mathrm{Fe}^{3}\right] /\left[\mathrm{Fe}^{2+}\right]\) remains unchanged (d) \(\mathrm{Fe}^{2+}\) decreases

Step-by-Step Solution

Answer

(b) \(\text{Fe}^{3+}\) decreases.

Step 1: Identify the Reactions

We have two half-reactions involving iron:1. \(\text{Fe}^{2+} + 2e^- \rightarrow \text{Fe}\) with \(E^{\circ} = -0.44 \, \text{V}\)2. \(\text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}\) with \(E^{\circ} = 0.77 \, \text{V}\)

Step 2: Determine Spontaneity of Each Reaction

A spontaneous reaction occurs in the direction where the standard potential is more positive. Here, the reduction of \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) has a positive potential \(\left(0.77 \, \text{V}\right)\), suggesting that this reaction will occur spontaneously.

Step 3: Predict the Change in Concentration

Since the reduction of \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) is spontaneous, \(\text{Fe}^{3+}\) will be consumed while \(\text{Fe}^{2+}\) will be generated. Therefore, the concentration of \(\text{Fe}^{3+}\) will decrease.

Key Concepts

Standard Electrode Potential

The standard electrode potential, represented as \(E^{\circ}\), is a measure of the tendency of a chemical species to be reduced. It is measured in volts (V) and provides insight into the strength of a reductant. Standard conditions assume all solutions are at 1 M concentration and gases at 1 atm pressure at 25°C.

In our exercise, we encounter two different potentials: \(E^{\circ}(\text{Fe}^{2+}/\text{Fe}) = -0.44 \ \text{V}\) and \(E^{\circ}(\text{Fe}^{3+}/\text{Fe}^{2+}) = 0.77 \ \text{V}\).

• A negative \(E^{\circ}\), like that for \(\text{Fe}^{2+}/\text{Fe}\), implies that the reduction of \(\text{Fe}^{2+}\) to \(\text{Fe}\) is less favorable compared to the hydrogen standard electrode.
• Conversely, a positive \(E^{\circ}\), such as \(0.77 \ \text{V}\), indicates a strong tendency for \(\text{Fe}^{3+}\) to be reduced to \(\text{Fe}^{2+}\).

These potentials help predict the spontaneity of redox processes under standard conditions, which leads us to understand the flow of electrons in electrochemistry.

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, involve the transfer of electrons between two chemical species. The substance that gains electrons is reduced, while the one that loses electrons is oxidized.

In our example:

• The reduction process is \(\text{Fe}^{3+} + e^- \rightarrow \text{Fe}^{2+}\), where \(\text{Fe}^{3+}\) gains an electron and is reduced.
• Oxidation would occur if \(\text{Fe}^{2+}\) lost electrons to become \(\text{Fe}^{3+}\), although this is not favored based on the electrode potentials given.

Understanding which component is reduced or oxidized helps predict the direction in which a reaction proceeds. In the exercise, due to the positive potential of \(0.77 \ \text{V}\), the reduction of \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) is spontaneous.

Iron Reduction

Iron reduction specifically deals with the transformation of iron ions into different oxidation states. In the context given:

- The transition from \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) signifies a reduction process since it involves the gain of electrons by \(\text{Fe}^{3+}\).
- Conversely, any transformation leading to \(\text{Fe}^{3+}\) from \(\text{Fe}^{2+}\) would be an oxidation.

In our scenario, the availability of a high \(E^{\circ}\) value \((0.77 \ \text{V})\) for the reduction of \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\) suggests the steel will predominantly convert \(\text{Fe}^{3+}\) to \(\text{Fe}^{2+}\). This decreases the concentration of \(\text{Fe}^{3+}\) over time, aligning with the prediction that the concentration of \(\text{Fe}^{3+}\) will decrease in a spontaneous reaction.