Ionization And Electron Gain Enthalpy

Ionization And Electron Gain Enthalpy

Shivani PooniaUpdated on 02 Jul 2025, 06:30 PM IST

Ionization enthalpy, also called ionization energy, is defined as the energy associated with removing an electron in a gaseous neutral atom to form a cation. This is called an endothermic process, which means it needs energy to be put in. The energy required for the removal of the first electron is called the first ionization energy; successive ionization energies are required for the removal of succeeding electrons. The factors that come into play in ionization energy are the size of the atom, nuclear charge, and the effect of shielding the electrons. In general, the trend of ionization energy increases down a group because of the increase in the size of the atom, and it decreases down a group owing to a decrease in nuclear charge.

This Story also Contains

  1. Ionization Energy And Electron Affinity
  2. Some Solved Examples
  3. Summary
Ionization And Electron Gain Enthalpy
Ionization And Electron Gain Enthalpy

Ionization Energy And Electron Affinity

Ionization energy and electron affinity are defined at absolute zero. At any other temperature, heat capacities for the reactants and the products have to be taken into account.

$\begin{aligned} & \mathrm{M}(\mathrm{g}) \rightarrow \mathrm{M}^{+}(\mathrm{g})+\mathrm{e}^{-}(\text {for ionization }) \\ & \mathrm{M}(\mathrm{g})+\mathrm{e}^{-} \rightarrow \mathrm{M}^{-}(\mathrm{g}) \text { (for electron gain) }\end{aligned}$

at temperature, T is

$\Delta_r H^{\ominus}(T)=\Delta_r H^{\ominus}(0)+\int_0^T \Delta_r C_p^{\ominus} d T$

The value of Cp for each species in the above reaction is 5/2 R (CV = 3/2R)

So, $\Delta_r C_p^{\ominus}=+5 / 2 \mathrm{R}$ (for ionization) $\Delta_I C_p^{\ominus}=-5 / 2 \mathrm{R}$ (for electron gain)

Therefore,

$\begin{aligned} & \Delta_r H^{\ominus}(\text { ionization enthalpy })=E_0(\text { ionization energy })+5 / 2 \mathrm{RT} \\ & \Delta_r H^{\ominus}(\text { electron gain enthalpy })=-\mathrm{A}(\text { electron affinity })-5 / 2 \mathrm{RT}\end{aligned}$

Recommended topic video on ( Ionization And Electron Gain Enthalpy)


Some Solved Examples

Example 1: The first and second ionization enthalpies of metal are 496 and $4560 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. How many moles of HCl and $\mathrm{H}_2 \mathrm{SO}_4$, respectively, will be needed to react completely with 1 mole of the metal hydroxide?
1)1 and 2

2) 1 and 0.5

3)1 and 1

4)2 and 0.5

Solution

According to the given data of I.E., this element must belong to group 1, and thus it is monovalent and forms a hydroxide of the type M(OH).

$\mathrm{MOH}+\mathrm{HCl} \longrightarrow \mathrm{MCl}+\mathrm{H}_2 \mathrm{O}$

$2 \mathrm{MOH}+\mathrm{H}_2 \mathrm{SO}_4 \longrightarrow \mathrm{M}_2 \mathrm{SO}_4+2 \mathrm{H}_2 \mathrm{O}$

Thus, from the reaction stoichiometry, it is clear that 1 mole of the metal hydroxide requires 1 mole and 0.5 moles of HCl and H2SO4 respectively for complete neutralization.

Example 2: The absolute value of the electron gain enthalpy of halogens satisfies :
1) Cl> F > Br > I

2)F >Cl> Br > I

3)Cl> Br > F > I

4)I > Br >Cl> F

Solution

The absolute value of the electron gain enthalpy of halogens satisfies:

Cl > F > Br > I

Chlorine has a higher electron gain enthalpy than fluorine due to less electron density.

Example 3: The enthalpy change for the conversion of $\frac{1}{2} \mathrm{Cl}_2(\mathrm{~g})$ to $\mathrm{Cl}^{-}(\mathrm{aq})$ is $(-) \mathrm{kJmol}^{-1}$ (Nearest integer) Given :$\Delta_{\mathrm{dis}} \mathrm{H}_{\mathrm{Cl}_{2(\mathrm{~g})}^{\ominus}}^{\ominus}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{eg}} \mathrm{H}_{\mathrm{Cl}(\mathrm{g})}^{\ominus}=-350 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{hyd}} \mathrm{H}_{\mathrm{Cl}_{(\mathrm{g})}^{-}}^{\ominus}=310 \mathrm{~kJ} \mathrm{~mol}^{-1}$

1) 610

2)510

3)400

4)256

Solution


$\begin{aligned} \Delta \mathrm{H}_\gamma^{\circ} & =\frac{1}{2} \times \mathrm{BE}+\Delta \mathrm{H}_{\mathrm{eg}}+\Delta \mathrm{H}_{\mathrm{Hyd}} \\ & =\frac{1}{2} \times 240+(-350)+(-380) \\ & \Rightarrow 120-350-380 \\ & \Rightarrow-610\end{aligned}$

Example 4: For electron gain enthalpies of the elements denoted as $\Delta_{\mathrm{eg}} H$, the incorrect option is :

1)$\Delta_{\mathrm{eg}} \mathrm{H}(\mathrm{Te})<\Delta_{\mathrm{eg}} \mathrm{H}(\mathrm{PO})$

2) $2 . \Delta_{\text {eg }} H(\mathrm{Se})<\Delta_{\text {eg }} H(\mathrm{~S})$

3)$\Delta_{\text {eg }} H(\mathrm{Cl})<\Delta_{\text {eg }} H(\mathrm{~F})$

4)$\Delta_{\text {eg }} H(\mathrm{I})<\Delta_{\text {eg }} H(\mathrm{At})$

Solution

Electron gain enthalpies $\rightarrow$
$\begin{aligned} & \rightarrow \mathrm{S}>\mathrm{Se}>\mathrm{Te}>\mathrm{O} \\ & \rightarrow \mathrm{Cl}>\mathrm{F}>\mathrm{Br}>\mathrm{I}\end{aligned}$

Summary

Ionization enthalpy and electron gain enthalpy are some of the important concepts in understanding the chemical behavior by an element. Ionization enthalpy measures the energy requirement necessary to pull electrons away from an atom. It generally increases across a period due to stronger nuclear attraction. It decreases down a group due to increased atomic size and electron shielding. Electron gain enthalpy, on the other hand, measures the energy change for the addition of an electron to a neutral atom. It could be exothermic or endothermic, reflecting an element's tendency to gain electrons. Nonmetals always have negative electron gain enthalpies, which imply that energy is released when an electron is added.

Frequently Asked Questions (FAQs)

Q: Why is there often a significant jump in ionization enthalpy when removing electrons from a noble gas configuration?
A:
There's often a significant jump in ionization enthalpy when removing electrons from a noble gas configuration because these configurations are exceptionally stable. Noble gas configurations have completely filled shells, which provide maximum stability due to electron-electron repulsion being minimized and electron-nuclear attraction being optimized. Removing an electron from this stable state requires breaking into a new, much higher energy level, resulting in a large increase in ionization enthalpy.
Q: How do ionization enthalpy and electron gain enthalpy contribute to the concept of chemical hardness?
A:
Chemical hardness, a concept in hard and soft acid-base (HSAB) theory, is related to the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). This gap can be approximated by the difference between the ionization enthalpy and the electron gain enthalpy. Elements with a large gap (high ionization enthalpy and low electron affinity) are considered "hard," while those with a small gap are "soft." This concept helps predict reactivity and stability in chemical reactions.
Q: What is the connection between ionization enthalpy and atomic spectroscopy?
A:
Ionization enthalpy is closely connected to atomic spectroscopy. The energy required to remove an electron from an atom (ionization) corresponds to specific spectral lines in an atom's emission or absorption spectrum. These spectral lines provide direct experimental evidence for the quantized nature of electron energy levels and can be used to measure ionization enthalpies with high precision.
Q: How does the lanthanide contraction affect ionization enthalpies?
A:
The lanthanide contraction, which is the decrease in atomic and ionic radii across the lanthanide series, affects ionization enthalpies. As the atomic radius decreases due to poor shielding by f-electrons, the effective nuclear charge increases. This leads to higher ionization enthalpies than might be expected based on the general trend down a group. This effect also influences the properties of elements following the lanthanides.
Q: How do ionization enthalpy and electron gain enthalpy influence the formation of ionic compounds?
A:
Ionization enthalpy and electron gain enthalpy play crucial roles in the formation of ionic compounds. Elements with low ionization enthalpies (like alkali metals) tend to lose electrons easily, forming cations. Elements with high electron affinities (like halogens) readily gain electrons, forming anions. The energy released when these ions come together to form an ionic compound often compensates for the energy required for ionization, making the overall process energetically favorable.
Q: What is the relationship between ionization enthalpy and the photoelectric effect?
A:
Ionization enthalpy is closely related to the photoelectric effect. The minimum energy of light required to eject an electron from an atom (the threshold frequency in the photoelectric effect) is directly related to the ionization enthalpy. This connection highlights the quantum nature of electron behavior and the discrete energy levels within atoms.
Q: Why is there a larger jump in ionization enthalpy between the second and third periods compared to subsequent periods?
A:
The larger jump in ionization enthalpy between the second and third periods is due to the introduction of the 3d subshell. While this subshell remains unfilled in period 3, its presence increases the effective nuclear charge more significantly than in subsequent periods. This results in a more pronounced increase in ionization enthalpy when moving from period 2 to 3 compared to later period transitions.
Q: How do ionization enthalpy and electron gain enthalpy relate to the concept of electronegativity?
A:
Ionization enthalpy and electron gain enthalpy are both components of electronegativity. Electronegativity, which describes an atom's ability to attract electrons in a chemical bond, is often calculated using a combination of these two properties. Elements with high ionization enthalpies and highly negative electron gain enthalpies tend to have high electronegativity values, as they strongly attract and hold onto electrons.
Q: What is the significance of Koopmans' theorem in relation to ionization enthalpy?
A:
Koopmans' theorem states that the ionization energy of a molecular system is approximately equal to the negative of the orbital energy of the electron being removed. This theorem provides a theoretical basis for interpreting photoelectron spectra and understanding the relationship between electronic structure and ionization energies. It's particularly useful in computational chemistry for estimating ionization enthalpies.
Q: How does the concept of electron affinity differ from electron gain enthalpy?
A:
Electron affinity and electron gain enthalpy are closely related but not identical. Electron affinity specifically refers to the energy released when a neutral atom in its ground state gains an electron. Electron gain enthalpy, on the other hand, includes the energy changes associated with any structural reorganization that might occur when the electron is added. In practice, the values are often very similar, but the distinction is important in precise thermochemical calculations.