Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

The electron gain enthalpy of Na⁺ is -5.1 eV, answer: (d).

Step 1: Understanding Ionisation Potential

The ionisation potential is the energy required to remove an electron from an atom in its gaseous state. For Na, the first ionisation potential is given as 5.1 eV, which means 5.1 eV is needed to remove an electron from a neutral Na atom.

Step 2: Understanding Electron Gain Enthalpy

Electron gain enthalpy is the energy change when an electron is added to an atom or ion. In this case, it represents the energy change when an electron is added to Na extsuperscript{+} to form a neutral Na atom.

Step 3: Relating Ionisation Potential to Electron Gain Enthalpy

The electron gain enthalpy is numerically equal and opposite in sign to the ionisation potential for the same atom transitioning between the same states. Therefore, the electron gain enthalpy for converting Na extsuperscript{+} to Na is ext{-5.1 eV}.

Step 4: Identifying The Correct Answer

Among the given options, the electron gain enthalpy of Na extsuperscript{+} is ext{-5.1 eV}, which corresponds to option (d).

Key Concepts

Ionisation Potential

Ionisation potential, sometimes referred to as ionisation energy, is a crucial concept in chemistry because it describes the energy needed to remove an electron from an atom or molecule in a gaseous state. This particular energy metric helps us understand the reactivity of elements. The higher the ionisation potential, the more energy you need to remove an electron, making the atom less likely to lose an electron easily.
In the specific case of sodium (Na), the first ionisation potential is 5.1 electron volts (eV). This means that 5.1 eV of energy is required to remove one electron from a neutral sodium atom, creating a sodium ion (Na⁺). This process is vital in understanding chemical behavior because it dictates how sodium interacts with other atoms, especially in forming ionic bonds.

Sodium Ion

When a sodium atom loses an electron, it becomes a sodium ion, denoted as Na⁺. This positively charged ion occurs because the removal of one negatively charged electron leaves behind a predominance of protons in the nucleus, which are positively charged.
Unlike its neutral counterpart, the sodium ion has different chemical properties due to its ionic nature. For example:

• It is more likely to participate in electrostatic interactions with negatively charged species.
• Its ionic state makes sodium ions highly soluble in water, aiding in biological processes and various chemical reactions.

Friends from biology and chemistry classes will remember that sodium ions play pivotal roles in nerve function and fluid balance in living organisms, further emphasizing their importance.

Energy Change

Energy change in the context of electron gain or loss is important for understanding chemical reactions and processes. Specifically, when an atom or ion gains an electron, the process is marked by an energy change known as electron gain enthalpy.
Here’s what happens:

• For Na⁺ to become a neutral sodium atom again, an electron must be added, and this process involves an energy change.
• This change is the opposite of the ionisation potential in terms of energy magnitude but with a negative sign since energy is released when an electron is gained.

Consequently, for sodium, where the ionisation potential was 5.1 eV, the electron gain enthalpy will be -5.1 eV. This understanding helps chemists predict the stability and likelihood of substances forming in chemical reactions.