Problem 63 - A Complete Resource Book in Chemistry for JEE Main

Question

Enthalpy change in the following process is \(\mathrm{M}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{-}, \Delta \mathrm{H}=\mathrm{X} \mathrm{kJ} \mathrm{mole}^{-1}\) Which of the following process have enthalpy change \(=\mathrm{X} \mathrm{kJ} \mathrm{mole}^{-1} ?\) (a) \(\mathrm{M}-\mathrm{M}+\mathrm{e}^{-}\) (b) \(\mathrm{M}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}\) (c) \(\mathrm{M}^{2+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{+}\) (d) \(\mathrm{M}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{-}\)

Step-by-Step Solution

Answer

Option (d) has the enthalpy change of \( X \text{ kJ mol}^{-1} \).

Step 1: Understanding the Given Reaction

The given reaction is \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \) with an enthalpy change of \( X \text{ kJ mol}^{-1} \). This describes the gain of an electron by a neutral atom \( \mathrm{M} \) to form a negatively charged ion \( \mathrm{M}^{-} \).

Step 2: Comparison with Option A

Option (a) \( \mathrm{M} - \mathrm{M} + \mathrm{e}^{-} \) is not a valid chemical equation, as it seems to suggest breaking \( \mathrm{M} \) into parts and then adding an electron, which doesn't correspond to typical electron attachment processes.

Step 3: Comparison with Option B

Option (b) \( \mathrm{M}^{+} + \mathrm{e}^{-} \longrightarrow \mathrm{M} \) involves the gain of an electron by a singly positive ion to form a neutral atom. This is the reverse of the ionization process but does not match the original given reaction, where the starting material is a neutral atom.

Step 4: Comparison with Option C

Option (c) \( \mathrm{M}^{2+} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{+} \) involves the gain of an electron by a doubly positive ion to form a singly positive ion. This is not the same as the given reaction, which involves a neutral atom becoming a negative ion.

Step 5: Comparison with Option D

Option (d) \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \) is identical to the given reaction. Therefore, its enthalpy change is the same as the original process, which is \( X \text{ kJ mol}^{-1} \).

Step 6: Conclusion

The only process which has an enthalpy change of \( X \text{ kJ mol}^{-1} \) is option (d) because it directly matches the given reaction.

Key Concepts

Electron Affinity

Electron affinity refers to the energy change that occurs when an electron is added to a neutral atom in the gaseous state, resulting in the formation of a negative ion. It is an important concept in thermochemistry. This addition of an electron generally releases energy, which means that the electron affinity is usually a negative value.

• When an electron is added to a neutral atom, the increased repulsion between electrons might make further addition challenging, which means some elements have positive electron affinity values.
• Electron affinity provides insight into the reactivity of an element. Elements with a high negative electron affinity tend to gain electrons easily, which is a key property of nonmetals.

To understand the prediction of electron affinity trends in the periodic table:

• Electron affinity generally increases across a period from left to right due to an increase in nuclear charge, which more strongly attracts additional electrons.
• Conversely, electron affinity tends to decrease down a group as additional electron shells are added, which increases the distance between the nucleus and the valence electrons, weakening the nuclear attraction.

Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom in the gaseous state, forming a cation. It is one of the fundamental concepts in the study of electronic structure and reactivity.

• The first ionization energy is the energy required to remove the first electron, while successive ionization energies refer to the removal of additional electrons.
• As you remove more electrons, ionization energy increases, as you are removing electrons from an increasingly positive ion.

Understanding the trends in ionization energy across the periodic table involves:

• Ionization energy typically increases across a period as electrons are added to the same energy level while the nuclear charge increases, pulling electrons closer and requiring more energy to remove them.
• It decreases down a group because the outer electrons are farther from the nucleus due to additional energy levels, leading to a weaker attraction and, thus, less energy required for removal.

Thermochemistry

Thermochemistry is a branch of chemistry focused on studying energy changes, particularly the enthalpy change that accompanies chemical reactions and physical transformations. This field helps quantify various phenomena in chemical systems.

• Enthalpy (\( \Delta H \)) reflects the heat absorbed or released under constant pressure during a reaction.
• If \( \Delta H \) is negative, the process is exothermic, meaning it releases heat, while a positive \( \Delta H \) represents an endothermic process, where heat is absorbed.

In response to reactions and transformations, thermochemistry analyzes changes such as:

• Phase changes, where energy changes occur when a substance goes from solid to liquid to gas, or vice versa.
• Chemical reactions, where breaking and forming bonds involves energy changes that can be measured and predicted.

Understanding enthalpy changes is critical for predicting the behavior of chemical systems, designing reactions, and harnessing energy from chemical processes for practical applications.