Problem 83 - 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) \(-10.2 \mathrm{eV}\) (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 \( abla^+\) is \\-5.1 \\mathrm{eV}\.

Step 1: Understand Ionisation Potential

Ionisation potential is the energy required to remove an electron from an atom or ion in its gaseous state. For sodium (Na), the first ionisation potential is the energy needed to remove one electron to form a sodium cation (Na⁺). This is given as 5.1 eV.

Step 2: Define Electron Gain Enthalpy

Electron gain enthalpy is the energy change when an electron is added to an atom or ion in the gaseous state. It's often considered equivalent in magnitude but opposite in sign to the ionisation potential for the formation of the same ion.

Step 3: Calculate the Electron Gain Enthalpy

Since the electron gain enthalpy is the energy change when an electron is added to \(abla^+\), it will have the same magnitude as the ionisation potential but an opposite sign. Thus, the electron gain enthalpy for Na⁺ will be \-5.1 \mathrm{eV}\.

Key Concepts

Ionisation Potential

Understanding ionisation potential is crucial in the study of atomic structures and reactions. Ionisation potential refers to the amount of energy required to remove an electron from an atom or ion, especially when it's in its gaseous state. For example, with sodium (Na), the first ionisation potential indicates the energy necessary to detach a single electron from a neutral sodium atom, thereby forming a positively charged sodium ion (\( \text{Na}^+\)). In this context, the first ionisation potential of sodium is measured as 5.1 electron volts (eV).

This concept helps predict the reactivity of an element.

• High ionisation potential implies that the element does not easily lose electrons, often resulting in lower reactivity.
• Conversely, a low ionisation potential means the element loses electrons more readily, thus exhibiting higher reactivity.

The ease or difficulty of removing an electron from an atom is a fundamental concept in understanding chemical bonding and reactions.

Sodium Ion

The formation of a sodium ion involves the loss of an electron from a neutral sodium atom. When sodium loses one electron, it transforms from a neutral state (\( \text{Na} \)) to a positively charged ion (\( \text{Na}^+\)). This transformation is central to the chemical properties of sodium.

Here's how it works:

• Initially, a neutral sodium atom has 11 electrons and 11 protons.
• By losing one electron, it attains a stable electron configuration similar to the noble gases, which has a significant impact on its reactivity and formation of compounds.
• The resulting sodium ion has 11 protons and 10 electrons, which leads to a net positive charge.

The behavior of sodium ion is particularly important in various chemical reactions where ionic compounds are formed, such as in common table salt, (\(\text{NaCl}\)). Its ability to form these ions is a key part of its chemical identity.

Energy Change

Energy change is a concept vital to understanding various physical and chemical processes. It refers to the transformation of energy from one form to another or from one state to another. In the context of electron gain and ionisation processes, energy change is central.

When discussing electron gain enthalpy, it is essentially the energy change that occurs when an electron is added to an ion or atom. This concept often mirrors the ionisation potential in magnitude but differs in sign:

• In sodium, removing an electron requires 5.1 eV, which is the ionisation potential.
• Addition of an electron (electron gain enthalpy) reverses this effect, with the same energy magnitude but an opposite sign, hence -5.1 eV.

Understanding energy change helps predict how an atom behaves when it interacts with others, providing insights into the stability of ions and molecules formed. This balance between energy added and removed is crucial for anticipating the behavior during chemical reactions.