Problem 160 - A Complete Resource Book in Chemistry for JEE Main

Question

The first ionisation potential of \(\mathrm{Na}\) is \(5.1 \mathrm{ev}\). The value of electron gain enthalpy of \(\mathrm{Na}^{+}\)will be? (a) \(-2.55 \mathrm{ev}\) (b) \(-5.1 \mathrm{ev}\) (c) \(-10.2 \mathrm{ev}\) (d) \(2.25 \mathrm{ev}\)

Step-by-Step Solution

Answer

The electron gain enthalpy of \(\mathrm{Na}^{+}\) is \(-5.1\) eV (option b).

Step 1: Understand Ionization Potential

The ionization potential (or ionization energy) is the energy required to remove an electron from a neutral atom in the gaseous state. For sodium (Na), this is given as 5.1 eV.

Step 2: Understand Electron Gain Enthalpy

The electron gain enthalpy is the energy change when an electron is added to an isolated gaseous atom. When an electron is added to Na\(^{+}\), energy is released, which is the negative of the ionization energy.

Step 3: Relate Ionization Potential to Electron Gain Enthalpy

The process of removing an electron from Na to form Na\(^{+}\) is the opposite of the process of adding an electron to Na\(^{+}\) to form Na. Therefore, the electron gain enthalpy of Na\(^{+}\) is the negative of the ionization potential of Na.

Step 4: Calculate Electron Gain Enthalpy

Since the ionization energy for Na is 5.1 eV, the electron gain enthalpy for Na\(^{+}\) will be \(-5.1\) eV. This is because the addition of an electron to Na\(^{+}\) releases energy equal to the ionization energy.

Key Concepts

Electron Gain Enthalpy

Electron gain enthalpy is an important concept in chemistry, which involves the amount of energy released when an electron is added to a neutral atom in its gaseous state, transforming it into an anion. Understanding electron gain enthalpy helps in predicting the stability and reactivity of atoms. In the case of sodium (\(Na^+\)), its electron gain enthalpy reflects the energy change when an electron is added to a sodium ion, leading to the formation of a neutral sodium atom.

When we talk about electron gain enthalpy:

• It is often represented with a negative value because adding an electron releases energy.
• A more negative electron gain enthalpy means that the atom 'wants' the electron more, indicating greater affinity.

For sodium ions, we interpret a value like \(-5.1 \text{ eV}\) as the amount of energy released when an electron is added to \(Na^+\), highlighting how much energy it takes (or releases) to form a stable as opposed to a neutral sodium atom.

Sodium Atom

Sodium, represented by the symbol \(Na\), is a fundamental element belonging to the alkali metals group. In its neutral atomic form, it is characterized by having 11 electrons, with a notable tendency to lose one, forming a positive ion (\(Na^+\)). This makes sodium an excellent example associated with discussions on ionization processes.

Sodium atoms exhibit distinct properties:

• Sodium is highly reactive, especially when exposed to water, and is often kept in oil to prevent unwanted reactions.
• It tends to lose one electron and form a positive ion, as this leads to a more stable electronic configuration resembling the nearest noble gas (neon).

The transformations of sodium under ionization and electron gain processes illustrate essential concepts in physical chemistry, aiding students in understanding how energy changes are involved in chemical transformations.

Ionization Energy

Ionization energy or ionization potential is essential for understanding atom and molecule behavior during chemical reactions. It is defined as the energy required to remove an electron from a neutral atom in its gaseous state to form a cation. This property is crucial in studying trends across the periodic table and predicting element behavior.

For an element like sodium, the ionization energy explains:

• The tendency of sodium atoms to lose an electron, forming \(Na^+\) ions. Sodium’s first ionization energy is valued at \(5.1 \text{ eV}\).
• Lower ionization energies facilitate electron removal, explaining why sodium, an alkali metal, readily participates in reactions by shedding its outermost electron.

The knowledge of ionization energy enhances the understanding of atomic interactions, guiding the prediction of reactivity and the strength of bonds formed in chemical compounds.