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) \(\mathrm{M}^{-} \longrightarrow \mathrm{M}+\mathrm{e}^{-}\) (b) \(\mathrm{M}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{M}\) (c) \(\mathrm{M}^{2+}+\mathrm{e}^{2} \longrightarrow \mathrm{M}^{+}\) (d) \(\mathrm{M}+\mathrm{e}^{-} \longrightarrow \mathrm{M}^{-}\)

Step-by-Step Solution

Answer

The correct process is (d): \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \).

Step 1: Identify the given reaction

The enthalpy change given in the problem is for the reaction: \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \) with \( \Delta \mathrm{H} = \mathrm{X} \mathrm{kJ} \text{ mole}^{-1} \). Here, a neutral atom \( \mathrm{M} \) gains an electron to become an anion \( \mathrm{M}^{-} \).

Step 2: Analyze each option's reaction

Let's analyze each option:(a) \( \mathrm{M}^{-} \longrightarrow \mathrm{M} + \mathrm{e}^{-} \): This is the reverse reaction of the given process, where an anion loses an electron to form a neutral atom. The enthalpy change for this reaction would be \( -X \mathrm{kJ} \text{ mole}^{-1} \) (opposite in sign because it's the reverse).

Step 3: Determine pairs for Option (b)

(b) \( \mathrm{M}^{+} + \mathrm{e}^{-} \longrightarrow \mathrm{M} \): In this process, a cation gains an electron to form a neutral atom. Typically, this process does not have the same enthalpy change as forming an anion from a neutral atom as described in the given reaction.

Step 4: Examine Option (c)

(c) \( \mathrm{M}^{2+} + \mathrm{e}^{2-} \longrightarrow \mathrm{M}^{+} \): This would involve a doubly charged cation gaining one electron to become a singly charged cation. The stoichiometry does not match, nor does the nature of enthalpy change align with the given reaction \( \Delta \mathrm{H} = X \mathrm{kJ} \text{ mole}^{-1} \).

Step 5: Confirmation of given process (Option (d))

(d) \( \mathrm{M} + \mathrm{e}^{-} \longrightarrow \mathrm{M}^{-} \): This is the same as the original reaction given in the problem. Hence, the enthalpy change for this process is clearly \( X \mathrm{kJ} \text{ mole}^{-1} \), matching the description provided.

Key Concepts

Thermochemistry

Thermochemistry focuses on the heat changes that occur during chemical reactions. It deals with the relationship between chemical reactions and energy changes involving heat. The enthalpy change is a crucial concept in thermochemistry. It's the amount of heat absorbed or released in a reaction at constant pressure. Understanding how different reactions absorb or release energy helps us manipulate reactions for desired results. For example, knowing the enthalpy change helps predict reaction feasibility under given conditions. Key to understanding enthalpy changes is realizing that they can be positive or negative:

• A positive enthalpy change (9H > 0) indicates an endothermic process, where heat is absorbed.
• A negative enthalpy change (9H < 0) indicates an exothermic process, where heat is released.

Ionization Energy

Ionization energy is the energy required to remove an electron from a gaseous atom or ion. It's a fundamental property that measures the tendency of an atom to resist losing an electron. For instance, turning a neutral atom into a cation involves overcoming the attraction between the negatively charged electron and the positively charged nucleus:

• First ionization energy refers to the removal of the first electron.
• Successive ionization energies refer to removing additional electrons, each requiring more energy.

Ionization energies are crucial for understanding the stability of ions and help predict the reactivity of elements. Generally, ionization energy increases across a period and decreases down a group in the periodic table.

Chemical Reactions

Chemical reactions are processes that lead to the transformation of one set of chemical substances to another. They involve breaking and forming bonds between atoms, leading to changes in the composition and energy of substances involved. In reactions:

• Reactants are the starting substances.
• Products are the substances formed as a result.

Each reaction involves changes in energy, usually measured as enthalpy. The nature of these energy changes can dictate whether a reaction is feasible. Reactions where products are at a lower energy state than reactants tend to be spontaneous.

Electron Affinity

Electron affinity measures an atom's tendency to gain an electron, forming a negative ion. It's the energy change when an electron is added to a gaseous atom. Electron affinities vary across the periodic table and provide insights into the chemical properties of elements. A higher electron affinity indicates a greater tendency to accept an electron:

• Most nonmetals have high electron affinities, making them more likely to form anions.
• Typically, electron affinity becomes more negative across a period and less negative down a group.

This property is central to the process of forming anions during chemical reactions, where energy changes are described by the enthalpy of the process.