Problem 197 - Introductory Chemistry Atoms First

Question

Arrange the following sets of atoms in order of increasing atomic size: (a) \(\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}\) (b) \(\mathrm{Mg}\), \(\mathrm{Na}, \mathrm{S}, \mathrm{Al}\) (c) \(\mathrm{Al}, \mathrm{Si}, \mathrm{Ge}, \mathrm{Te}\)

Step-by-Step Solution

Answer

In order of increasing atomic size, we have: (a) \(\mathrm{F} < \mathrm{Cl} < \mathrm{Br} < \mathrm{I}\) (b) \(\mathrm{Na} < \mathrm{Mg} < \mathrm{Al} < \mathrm{S}\) (c) \(\mathrm{Al} < \mathrm{Si} < \mathrm{Ge} < \mathrm{Te}\)

Step 1: (a) Given atoms: F, Cl, Br, I

These elements belong to the halogen group and are in the same group (Group 17) in the periodic table. As we go down in a group, the atomic size increases, so the order will be: \(\mathrm{F} < \mathrm{Cl} < \mathrm{Br} < \mathrm{I}\)

Step 2: (b) Given atoms: Mg, Na, S, Al

These elements belong to different groups and are in the same period (Period 3) in the periodic table. As we move from left to right across a period, the atomic size generally decreases, so the order will be: \(\mathrm{Na} < \mathrm{Mg} < \mathrm{Al} < \mathrm{S}\)

Step 3: (c) Given atoms: Al, Si, Ge, Te

First, let us identify their positions on the periodic table. Al and Si are in Group 13 and 14, respectively, and are in the same period (Period 3). Ge and Te are in Group 14 and 16, respectively, and are in the same period (Period 4). Now we need to consider two factors - the effect of moving across a period and the effect of moving down a group. To do this, we'll compare and arrange the elements diagonally. Since the atomic radii increase as we move down a group, we have the following comparison: \(\mathrm{Al} < \mathrm{Ge}\) Similarly, since the atomic radii decrease as we move from left to right across a period, we have the following comparison: \(\mathrm{Al} < \mathrm{Si}\) and \(\mathrm{Ge} < \mathrm{Te}\) Putting everything together, the final order of the elements based on increasing atomic size is as follows: \(\mathrm{Al} < \mathrm{Si} < \mathrm{Ge} < \mathrm{Te}\)

Key Concepts

Periodic Table

The periodic table is an organized chart that displays all known chemical elements in a systematic way. It is structured based on their atomic number, electron configuration, and recurring chemical properties. This structure helps easily identify various trends and patterns among the elements, such as atomic size, valence electrons, and electronegativity.

The periodic table is arranged in rows called periods and columns known as groups. Elements in the same group often share similar properties because they have the same number of valence electrons. For example, all the elements in Group 17 are halogens, which include fluorine (F), chlorine (Cl), bromine (Br), and iodine (I).

• Groups: Vertical columns on the table, indicating elements with similar chemical properties.
• Periods: Horizontal rows showing elements with the same electron shell count.

The periodic table is essential in understanding trends such as atomic radii and helps predict the behavior of elements during chemical reactions.

Halogen Group

Halogens are a group of elements located in Group 17 of the periodic table. These elements include fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At). Halogens are known for their high reactivity, especially with alkali and alkaline earth metals, forming ionic compounds.

Halogens have some unique properties:

• High electronegativity: They attract electrons strongly, making them highly reactive.
• Diatomic molecules: In their elemental form, halogens exist as pairs of atoms (e.g., F₂, Cl₂).
• Varied states: They appear in different states at room temperature, with F and Cl as gases and Br as a liquid, while I is a solid.

The atomic size of halogens increases as you move down the group due to the addition of electron shells. This increase in size contributes to their chemical reactivity and other properties.

Atomic Radii

Atomic radii refer to the size of an atom, typically measured from the nucleus to the outermost electron shell. It is a crucial factor in determining the properties of elements, such as how they bond and react with other elements.

The atomic radius tends to vary across the periodic table:

• Across a period: The atomic radius decreases from left to right. This happens because additional protons in the nucleus attract the electron cloud more strongly, pulling electrons closer.
• Down a group: The atomic radius increases as more electron shells are added, expanding the size of the atom.

Understanding atomic radii helps explain the arrangement of atoms in compounds and how the size affects the element's reactivity.

Trends in Atomic Size

Trends in atomic size help us understand how atoms change in size across the periodic table. These trends arise from the arrangement of the periodic table, allowing predictions of atomic behavior in chemical reactions.

Two general trends can be observed:

• Moving across a period: Atomic size decreases. This is because, with each step to the right, a proton is added to the nucleus, increasing the positive charge, thus pulling electrons closer to the nucleus.
• Moving down a group: Atomic size increases. Adding shells leads to a greater distance between the nucleus and the outermost electrons.

These trends are why the halogen group displays increasing atomic size from fluorine to iodine. Similarly, across Period 3 (which includes Na, Mg, Al, and S), atomic sizes decrease. Understanding these trends aids in predicting which atoms will be larger and which will be smaller, influencing their chemical properties.