Problem 42 - Chemistry The Central Science

Question

(a) What is the trend in first ionization energies as one proceeds down the group 7 A elements? Explain how this trend relates to the variation in atomic radii. (b) What is the trend in first ionization energies as one moves across the fourthperiod from \(\mathrm{K}\) to \(\mathrm{Kr}\) ? How does this trend compare with the trend in atomic radii?

Step-by-Step Solution

Answer

As one proceeds down the group 7A elements, the ionization energy generally decreases due to an increase in atomic radius and shielding effect. However, when moving across the fourth period from \(\mathrm{K}\) to \(\mathrm{Kr}\), the ionization energy increases because of a decrease in atomic radius and an increase in effective nuclear charge.

Step 1: Trends in Ionization Energy in Group 7A Elements

As one proceeds down the group 7A elements, the ionization energy generally decreases. We will explain this trend by considering the changes in atomic radius.

Step 2: Relationship between Atomic Radius and Ionization Energy in Group 7A Elements

When moving down the group 7A elements, the atomic radius increases. This is because additional electron shells are added as we move down the group. This leads to an increase in the shielding effect, causing a decreased hold of the nucleus on the valence electrons. As the atomic radius increases, the distance between the valence electron and the nucleus also increases, causing the electrostatic attraction between the electron and nucleus to decrease. As a result, the ionization energy decreases because less energy is required to remove the valence electron.

Step 3: Trends in Ionization Energy across the Fourth Period from \(\mathrm{K}\) to \(\mathrm{Kr}\)

As one moves across the fourth period from \(\mathrm{K}\) (potassium) to \(\mathrm{Kr}\) (krypton), the ionization energy generally increases.

Step 4: Relationship between Atomic Radius and Ionization Energy across the Fourth Period

When moving across the fourth period, the atomic radius generally decreases. This is due to an increase in the effective nuclear charge experienced by the valence electrons. The shielding effects remain relatively constant, which means that the increasing nuclear charge results in stronger binding of valence electrons to the nucleus. The decreasing atomic radius means that the valence electrons are closer to the nucleus, resulting in stronger electrostatic attraction between the electrons and the nucleus. Consequently, the ionization energy increases across the period because more energy is required to remove the valence electron. In conclusion, when moving down the group 7A elements, the ionization energy decreases due to an increase in atomic radius and shielding effect. When moving across the fourth period from \(\mathrm{K}\) to \(\mathrm{Kr}\), the ionization energy increases because of a decrease in atomic radius and an increase in effective nuclear charge.

Key Concepts

Atomic Radius

The atomic radius refers to the size of an atom. It is the distance from the nucleus of an atom to the outermost electron shell, where the valence electrons reside. Understanding atomic radius changes helps to predict chemical properties of elements.

• Moving down a group (like group 7A), atomic radius increases. This is due to the addition of extra electron shells.
• Moving across a period from left to right, atomic radius decreases because electrons are added to the same shell while the nuclear charge increases.

A larger atomic radius implies a greater distance between the nucleus and the outer electrons, which impacts the ease with which these electrons can be removed.

Group 7A Elements

Group 7A elements, also known as the halogens, include elements like fluorine, chlorine, bromine, iodine, and astatine. These elements are highly reactive nonmetals known for forming salts when combined with metals.

The elements in group 7A show decreasing ionization energies as one moves down the group. This is due to:

• An increase in atomic radius as more electron shells are added.
• Greater electron shielding, which reduces the effective nuclear charge felt by outer electrons.

Thus, as you move down the group, it becomes easier to remove the outermost electron.

Fourth Period Elements

The fourth period in the periodic table extends from potassium (K) to krypton (Kr). As you move across this period, several trends can be observed:

• Ionization Energy: This generally increases. As more protons are added to the nucleus, the nuclear charge increases, resulting in a stronger attraction to the electrons.
• Atomic Radius: It decreases as the effective nuclear charge pulls valence electrons closer to the nucleus.

These trends show the periodic nature of the elements where properties of elements change predictably across the periodic table.

Effective Nuclear Charge

Effective nuclear charge ( Z_ ext{eff} ) describes the net positive charge experienced by valence electrons. It highlights the inner shell electron shielding effects and helps in understanding many chemical properties:

• Increases across a period: More protons are added to the nucleus, and despite the same shell electrons, more are present to repel each other minimally.
• Stays relatively constant down a group: More inner shells buffer the valence electrons from the increased number of protons.

Effective nuclear charge is crucial in explaining why atoms become smaller across a period and highlights the significant need for more energy to remove electrons as atomic number rises.