Problem 64 - A Complete Resource Book in Chemistry for JEE Main

Question

The formation of \(\mathrm{O}^{2-}(\mathrm{g})\) starting from \(\mathrm{O}(\mathrm{g})\) is endothermic by \(603 \mathrm{~kJ} \mathrm{~mol}^{-1}\). If electron affinity of \(\mathrm{O}(\mathrm{g}\) ) is \(-141 \mathrm{~kJ} \mathrm{~mol}^{-1}\), the second electron affinity of oxygen would be (a) \(+744 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(-744 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (c) \(+462 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(-462 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Step-by-Step Solution

Answer

The second electron affinity of oxygen is \(+744 \mathrm{~kJ} \mathrm{~mol}^{-1}\). (a) is correct.

Step 1: Problem Introduction

We need to find the second electron affinity of oxygen given that the formation of \( \mathrm{O}^{2-}(\mathrm{g}) \) from \( \mathrm{O}(\mathrm{g}) \) is endothermic by \( 603 \mathrm{~kJ} \mathrm{~mol}^{-1} \), and the first electron affinity of \( \mathrm{O}(\mathrm{g}) \) is \( -141 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

Step 2: First Electron Gain Process

The first electron affinity is the energy change when an oxygen atom gains one electron to form \( \mathrm{O}^{-}(\mathrm{g}) \). This is given as \( \Delta E_1 = -141 \mathrm{~kJ} \mathrm{~mol}^{-1} \).

Step 3: Calculate Second Electron Affinity

The total energy required to form \( \mathrm{O}^{2-}(\mathrm{g}) \) from \( \mathrm{O}(\mathrm{g}) \) is \( 603 \mathrm{~kJ} \mathrm{~mol}^{-1} \), which includes both the first and second electron affinities. The second electron affinity is the energy change for \( \mathrm{O}^{-}(\mathrm{g}) \) gaining another electron to form \( \mathrm{O}^{2-}(\mathrm{g}) \), calculated as follows: \[ \Delta E_2 = \Delta E_{\mathrm{total}} - \Delta E_1 = 603 \mathrm{~kJ/mol} - (-141 \mathrm{~kJ/mol}) = 603 + 141 = 744 \mathrm{~kJ/mol} \].

Step 4: Choose the Correct Answer

The calculated second electron affinity is \( +744 \mathrm{~kJ/mol} \), which matches choice (a).

Key Concepts

Endothermic Process

An endothermic process occurs when a system absorbs energy from the surroundings. This energy absorption typically happens in the form of heat. By nature, endothermic reactions require energy input to proceed. They are characterized by a positive heat flow into the system.

In the context of forming oxygen anions, the transition from an oxygen atom, \( \mathrm{O}(\mathrm{g}) \), to an \( \mathrm{O}^{2-}(\mathrm{g}) \) anion is endothermic by 603 kJ/mol. This means it requires 603 kJ of energy per mole to add two electrons to an oxygen atom. The first electron addition might release some energy, but the second electron addition demands more energy due to increased electron-electron repulsion.

It's crucial to recognize that endothermic processes are common in nature and play vital roles in many chemical reactions. Understanding them helps grasp how and why certain substances change when energy is absorbed.

Electron Affinity Calculation

The term 'electron affinity' refers to the amount of energy change that occurs when an atom in the gas phase gains an electron. It is typically measured in kilojoules per mole (kJ/mol). Electron affinity can either be positive or negative:

• Negative electron affinity indicates an exothermic process, where energy is released as an electron is added.
• Positive electron affinity means that what happens is endothermic, requiring energy input for the electron to attach to an atom.

When calculating the second electron affinity, we essentially determine the energy change as an already negatively charged oxygen ion, \( \mathrm{O}^{-}(\mathrm{g}) \), gains another electron to become \( \mathrm{O}^{2-}(\mathrm{g}) \). This involves both the first electron affinity and the total energy change for the process.

Given that the total endothermic process requires 603 kJ/mol and that the first electron affinity is \(-141\) kJ/mol, we find the second electron affinity:\[\Delta E_2 = 603 \mathrm{~kJ/mol} - (-141 \mathrm{~kJ/mol}) = 744 \mathrm{~kJ/mol}.\]

Oxygen Anions

Oxygen anions refer to oxygen atoms that have gained one or more electrons, thereby acquiring a negative charge. The simplest anion of oxygen is the single negative charge \( \mathrm{O}^{-} \). When it receives another electron, it becomes \( \mathrm{O}^{2-} \).

Forming oxygen anions involves overcoming several inherent challenges, especially due to the electron-electron repulsions in \( \mathrm{O}^{2-} \). Electrons are negatively charged and repel each other, making the acquisition of additional electrons energy-intensive. This results in the second electron affinity being endothermic.

Understanding the formation of \( \mathrm{O}^{2-} \) is vital across various scientific fields. Whereas single-electron processes are relatively straightforward, the addition of a second electron shows the intricacies of atomic and molecular physics. The energy considerations play critical roles in chemistry and materials science, where control over the charge state of ions can influence chemical reactions and properties of compounds.