Problem 16 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

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) \(+2.55 \mathrm{eV}\)

Step-by-Step Solution

Answer

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

Step 1: Understanding Ionization Potential

Ionization potential is the energy required to remove an electron from an atom in the gaseous state. For sodium (Na), this is given as 5.1 eV, meaning that it takes 5.1 eV to remove one electron from a neutral sodium atom to form a Na⁺ ion.

Step 2: Defining Electron Gain Enthalpy

Electron gain enthalpy is the energy change when an electron is added to an atom in the gaseous state. For an already positively charged ion like Na⁺, adding an electron would release energy because you're essentially going in the reverse direction of ionization.

Step 3: Relating Ionization Potential to Electron Gain Enthalpy

The electron gain enthalpy of Na⁺ will be equal in magnitude but opposite in sign to the ionization potential of Na. This is because adding an electron to Na⁺ (to form Na) is the reverse process of removing an electron from Na.

Step 4: Calculating Electron Gain Enthalpy

Since the ionization potential of Na is 5.1 eV, the electron gain enthalpy for Na⁺ will be \(-5.1\) eV, as it releases energy when an electron is added back to form neutral Na.

Key Concepts

Electron Gain Enthalpy

Electron gain enthalpy is a fascinating concept that deals with the energy change when an electron is added to an atom or ion in the gaseous state. This process can either release or absorb energy depending on the nature of the atom or ion. For elements that are keen on accepting an electron, this energy change is usually negative, indicating that energy is released.

• When an electron is added to a neutral atom, the atom forms an anion (negatively charged ion).
• The more stable anion configurations usually yield greater energy release.

In the case of \( ext{Na}^+\), the electron gain enthalpy is actually the energy released when an electron is added to form neutral sodium. This is essentially the reverse process of ionization where an electron is removed. Therefore, the electron gain enthalpy of \( ext{Na}^+\) is \(-5.1\) eV, due to the release of energy during this process. It is crucial to remember that the value is negative, signifying an exothermic reaction.

Energy Change in Gaseous State

Energy changes in the gaseous state are significant because atoms or ions are isolated from other interactions. These changes are essential for understanding how elements form ions or revert back to neutral atoms. In the gaseous state:

• Atoms behave independently, allowing for isolated energy measurements.
• Both ionization energy and electron gain enthalpy provide insights into this energy dynamic.

Feel the freedom of gaseous atoms as they gain or lose electrons. Ionization involves energy input, while electron gain typically releases energy. The gaseous state eliminates external influences, allowing for pure measurements critical for theoretical calculations and practical applications. The study of these energies helps us understand chemical reactivity and bonding behavior.

Sodium Ionization Energy

Ionization energy is the energy needed to strip an electron from an atom, turning it into a positive ion. For sodium, this process involves removing one electron to form \( ext{Na}^+\) from \( ext{Na}\).

Ionization energies highlight the ease with which an element can form cations:

• The lower the ionization energy, the easier it is for the atom to lose an electron.
• Sodium has a relatively low first ionization energy (5.1 eV), meaning it's comparatively easy to remove one electron.

This low energy requirement is why sodium readily forms \( ext{Na}^+\) ions, becoming stable in many compounds. Understanding the ionization energy of sodium helps explain its high reactivity and role in forming ionic compounds. It sheds light on why sodium is active in reactions, contributing to its frequent use in tests and syntheses.