Problem 42 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) What is the trend in first ionization energies as one proceeds down the group 17 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 fourth period from \(\mathrm{K}\) to \(\mathrm{Kr}\) ? How does this trend compare with the trend in atomic radii?

Step-by-Step Solution

Answer

\( (a) \) The first ionization energies decrease as one proceeds down the group 17 elements, as the atomic radii increase because outermost electrons are less strongly attracted to the nucleus. \( (b) \) As one moves across the fourth period from K to Kr, the first ionization energies increase, contrary to the trend in atomic radii which decrease. This is due to the stronger attraction between the nucleus and the electrons, as the number of protons increases.

Step 1: Ionization Energy and Atomic Radii

Ionization energy is the energy required to remove an electron from an atom (or ion) in the gaseous state. As for atomic radius, it is defined as the distance between the nuclei of two adjacent atoms. Step 2: Analyzing the Trend in First Ionization Energies in Group 17 elements

Step 2: Trend in Group 17 elements

Group 17 elements are also known as halogens. As we move down the group, the atomic radii increase as there are more electron shells present in each successive element. With a larger atomic radius, the electrons in the outermost shell are further away from the nucleus and are less strongly attracted to it. Consequently, less energy is required to remove an electron from the outermost shell. Therefore, the first ionization energies decrease as one proceeds down the group 17 elements. Step 3: Relating the Trend in Ionization Energies with Atomic Radii for Group 17 elements

Step 3: Relation between Ionization Energies and Atomic Radii in Group 17

The trend in first ionization energies in group 17 elements is directly related to the variation in atomic radii. As the atomic radii increase down the group, the first ionization energies decrease due to the outermost electrons being further away from the nucleus and being less strongly attracted to it. Step 4: Analyzing the Trend in First Ionization Energies across the Fourth Period

Step 4: Trend in the Fourth Period

As we move across the fourth period from K (potassium) to Kr (krypton), the atomic number increases which implies that the number of protons in the nucleus increases. Consequently, the positive charge in the nucleus becomes stronger. This results in a stronger attraction between the nucleus and the electrons. This stronger attraction makes it more difficult to remove an electron, meaning the ionization energies increase from left to right across the fourth period. Step 5: Comparing the Trend in Ionization Energies with the Trend in Atomic Radii across the Fourth Period

Step 5: Comparison in Fourth Period

The trend in first ionization energies across the fourth period is contrary to the trend in atomic radii. As we move from K to Kr, the atomic radii decrease because the increasing number of protons in the nucleus pulls the electrons closer to it. However, the ionization energies increase from left to right across the fourth period due to the stronger attraction between the nucleus and the electrons.

Key Concepts

Atomic Radius

The atomic radius is an important concept in chemistry and helps us understand how the size of an atom affects its properties. It refers to the distance between the nucleus of an atom and the boundary of its surrounding electron cloud. When measuring atomic radius, it’s typically taken as half the distance between the nuclei of two atoms of the same element that are touching each other.

Several factors can influence the size of an atomic radius:

• Number of electron shells: More shells mean a larger atomic radius because there is more space taken up by electrons.
• Nuclear charge: An increase in the number of protons creates a greater pull on the electrons, usually resulting in a smaller atomic radius.
• Electron-electron repulsions in higher energy levels: These can sometimes cause anomalies in size as electrons repel each other causing the electron cloud to expand slightly.

Understanding these factors helps explain why atomic radii change when you move across a period or down a group in the periodic table.

Group 17 Elements

Group 17 elements are commonly known as halogens and include elements such as Fluorine (F), Chlorine (Cl), Bromine (Br), and Iodine (I). These non-metals can be very reactive and are known for their distinct trends in properties as you move down the group.

In terms of atomic radius, as you go down the group, the elements have more electron shells. This increase in electron shells results in a larger atomic radius, even though the effective nuclear charge also increases slightly.

• Increasing atomic radius means that the outer electrons are further away from the nucleus.
• With such increased distance, there is a weaker attraction between the outer electrons and the nucleus.
• This results in lower ionization energy because less energy is needed to remove an electron from these larger atoms.

The trend for decreasing ionization energy down the group is a direct consequence of the increasing atomic radii and is a fundamental concept in understanding the reactivity and manipulation of halogens in various chemical reactions.

Fourth Period Trends

Moving across the fourth period of the periodic table from Potassium (K) to Krypton (Kr), we observe some notable trends. One of the key trends is the changing ionization energy, which generally increases as you proceed across the period.

As you move from left to right:

• The atomic number increases, meaning more protons are present in the nucleus. This additional positive charge draws electrons closer to the nucleus, decreasing atomic radii.
• Smaller atomic radii create greater attraction between the nucleus and the electrons, necessitating more energy to remove an electron, thus leading to increasing ionization energy.
• Because electrons are being added to the same valence shell, the extra positive charge pulls them closer without significant increases in shielding effect, intensifying this trend.

Although the atomic radius decreases, the increased effective nuclear charge dominates, resulting in heightened ionization energy which impacts the chemical reactivity and characteristics of elements across the period.