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

Option (a) \(+744 \, \text{kJ/mol}\) is correct.

Step 1: Understand the given data

We are told that the formation of \(\text{O}^{2-}(\text{g})\) from \(\text{O}(\text{g})\) is endothermic by \(603 \, \text{kJ/mol}\). Also, the electron affinity of \(\text{O}(\text{g})\) is \(-141 \, \text{kJ/mol}\). We need to find the second electron affinity of oxygen.

Step 2: Define electron affinity

Electron affinity is the amount of energy released when an electron is added to a neutral atom to form a negative ion. For oxygen, the first electron affinity is given as \(-141 \, \text{kJ/mol}\), indicating energy is released.

Step 3: Setup energy balance equation

The total change in energy for forming \(\text{O}^{2-}(\text{g})\) from \(\text{O}(\text{g})\) can be expressed as the sum of the first electron affinity and the second electron affinity (\(EA_2\)). Since the overall process is endothermic, this means energy is absorbed: \[ \Delta H = EA_1 + EA_2 \] where \( \Delta H = 603 \, \text{kJ/mol} \) and \( EA_1 = -141 \, \text{kJ/mol} \).

Step 4: Substitute and solve for the second electron affinity

Substituting the given values into the energy balance equation: \[ 603 = -141 + EA_2 \] Solving for \(EA_2\), we rearrange the equation to find:\[ EA_2 = 603 + 141 = 744 \, \text{kJ/mol} \].

Step 5: Select the correct option

The calculated second electron affinity of oxygen is \( +744 \, \text{kJ/mol} \). Therefore, the correct answer is option (a) \(+744 \, \text{kJ/mol}\).

Key Concepts

Formation of O2-

In chemistry, the formation of ions from neutral atoms is fundamental for understanding how reactions occur. When oxygen (O) takes in an electron, it forms a negatively charged ion, known as oxide ion (\( \text{O}^- \)). This process releases energy, a behavior typical for many non-metals, including oxygen.
When an additional electron is added to this already negatively charged \( \text{O}^- \) ion, results in the formation of \( \text{O}^{2-} \) ion, completing the two-step electron gain.
In simpler terms, when neutral oxygen gains two electrons, it becomes \( \text{O}^{2-} \). This transformation is not just a rearrangement of matter, but also involves significant energy changes which depend on electron affinity and are conceptually similar to the idea of electron negativity. The first electron is attracted and bound easily, however, the second electron experiences repulsion from the already negatively charged ion, requiring additional energy.

Endothermic Process

When a chemical process absorbs energy, it's known as endothermic. Unlike exothermic processes, where energy is released, endothermic processes require energy input for the reaction to proceed.
In the context of forming \( \text{O}^{2-} \), the process is endothermic due to the energy needed to overcome the repulsion between the negatively charged \( \text{O}^- \) ion and the second electron being added.

• This is because adding an electron to an already negative environment is like adding like charges together, which naturally repel each other.
• Such transitions occur only when energy, such as heat, is absorbed by the system.

In our specific scenario, the reaction remains endothermic by \( 603 \, \text{kJ/mol} \), meaning the energy absorbed is greater than that released through the formation of the ion.

Energy Balance Equation

Energy balance equations in chemistry are vital for calculating how much energy is released or needed during reactions. This equation is essentially a method to quantify and solve for unknown energy values using known ones.
For the conversion of oxygen to \( \text{O}^{2-}(\text{g}) \), the energy balance equation is:\[\Delta H = EA_1 + EA_2\]

• \(\Delta H\) denotes the total energy change, while \( EA_1 \) and \( EA_2 \) stand for the first and second electron affinities, respectively.
• The sum of electron affinities, in this case equaling the endothermic total energy input of \( 603 \, \text{kJ/mol} \).

By plugging in known values, \( EA_1 = -141 \, \text{kJ/mol} \) and \( \Delta H = 603 \, \text{kJ/mol} \), one can solve the equation for \( EA_2 \). Such calculations illustrate how chemists use thermodynamics to understand chemical reaction dynamics, ensuring balanced and accurate energy assessments.