Question

Using only the periodic table, predict the most stable ion for \(\mathrm{Na}, \mathrm{Mg}, \mathrm{Al}, \mathrm{S}, \mathrm{Cl}, \mathrm{K}, \mathrm{Ca},\) and \(\mathrm{Ga} .\) Arrange these elements from largest to smallest radius and explain why the radius varies as it does.

Short answer

The most stable ions for the given elements are: Na\(^+\), Mg\(^{2+}\), Al\(^{3+}\), S\(^{2-}\), Cl\(^-\), K\(^+\), Ca\(^{2+}\), and Ga\(^{3+}\). The elements arranged from largest to smallest atomic radius are: K > Na > Ca > Mg > Ga > Al > Cl > S. This variation in atomic radius occurs because the atomic radius increases down a group due to the addition of electron shells and decreases across a period from left to right due to increased effective nuclear charge pulling electrons closer to the nucleus.

Step-by-step solution

Identify the group number of each element

Using the periodic table, identify the group number (column) for each element: - Na (Sodium) - Group 1 - Mg (Magnesium) - Group 2 - Al (Aluminum) - Group 13 - S (Sulfur) - Group 16 - Cl (Chlorine) - Group 17 - K (Potassium) - Group 1 - Ca (Calcium) - Group 2 - Ga (Gallium) - Group 13

Predict the most stable ion for each element

Using the group number, we can predict the most stable ion for each element based on the electron configuration: - Na is in Group 1 and it will lose 1 electron to achieve a stable noble gas configuration. The most stable ion for Na will be Na\(^+\). - Mg is in Group 2 and it will lose 2 electrons to achieve a stable noble gas configuration. The most stable ion for Mg will be Mg\(^{2+}\). - Al is in Group 13 and it will lose 3 electrons to achieve a stable noble gas configuration. The most stable ion for Al will be Al\(^{3+}\). - S is in Group 16 and it will gain 2 electrons to achieve a stable noble gas configuration. The most stable ion for S will be S\(^{2-}\). - Cl is in Group 17 and it will gain 1 electron to achieve a stable noble gas configuration. The most stable ion for Cl will be Cl\(^-\). - K is in Group 1 and it will lose 1 electron to achieve a stable noble gas configuration. The most stable ion for K will be K\(^+\). - Ca is in Group 2 and it will lose 2 electrons to achieve a stable noble gas configuration. The most stable ion for Ca will be Ca\(^{2+}\). - Ga is in Group 13 and it will lose 3 electrons to achieve a stable noble gas configuration. The most stable ion for Ga will be Ga\(^{3+}\).

Arrange the elements from largest to smallest radius and explain why the radius varies

To arrange the elements according to their atomic radii, we need first to understand the trends in atomic radii across groups and periods in the periodic table. Generally, atomic radii increase down a group and decrease across a period from left to right. Using this trend, we can arrange the given elements from largest to smallest atomic radius as follows: K > Na > Ca > Mg > Ga > Al > Cl > S Here's the explanation for the variations in the radius: - As we move down a group, atomic radius increases due to the addition of electron shells, increased electron shielding and decreased effective nuclear charge. - As we move across a period from left to right, atomic radius decreases due to increased effective nuclear charge and the increasing number of protons in the nucleus which pull the electrons closer to the nucleus.

Key concepts

Ion Formation

Understanding ion formation is essential in chemistry because it explains how elements achieve stable electron configurations. Atoms naturally seek to achieve a complete outer electron shell, often resembling that of the nearest noble gas. This process leads to the formation of ions:

• In Group 1, elements like sodium (Na) and potassium (K) lose one electron. This results in positively charged ions such as Na\(^+\) and K\(^+\).
• Group 2 elements, such as magnesium (Mg) and calcium (Ca), lose two electrons, forming ions like Mg\(^{2+}\) and Ca\(^{2+}\).
• Conversely, Group 13 elements, like aluminum (Al) and gallium (Ga), lose three electrons to form Al\(^{3+}\) and Ga\(^{3+}\) ions.
• In Group 16, elements such as sulfur (S) gain two electrons resulting in S\(^{2-}\) ions.
• Group 17 elements, like chlorine (Cl), gain one electron to form Cl\(^-\) ions.

This pattern of ion formation is related to the position of each element on the periodic table and their electron configurations. Elements closer to the noble gases tend to gain electrons to complete their outer shell. Meanwhile, elements on the opposite side often lose electrons to achieve a similar stable configuration.

Atomic Radius

Atomic radius is a key concept when studying the periodic table, explaining how sizes of atoms vary based on their position in the table. Atomic radius generally increases as you move down a group because of the addition of extra electron shells. Here’s what happens:

• When you move from top to bottom in a group, such as from Na to K, there is an increase in atomic radius due to additional electron shells that create greater distance between the nucleus and the outermost electrons.
• Within the same period, as you move from left to right like from Na to Cl, the atomic radius decreases. This is because more protons are added to the nucleus, increasing the effective nuclear charge, drawing electrons closer to the nucleus, and reducing the radius.

Therefore, in terms of size, potassium (K) is larger than sodium (Na), which is larger than calcium (Ca), and so forth.
Understanding atomic radius is crucial for predicting how elements behave in chemical reactions and how they bond with each other.

Electron Configuration

Electron configuration details how electrons are distributed in an atom's orbitals. This distribution affects not only ion formation but also the chemical behavior and properties of elements.

• Each element's position on the periodic table is directly related to its electron configuration, which follows the order of filling orbitals.
• Elements will fill their electron shells according to the Aufbau principle, Hund's Rule, and Pauli Exclusion Principle, occupying lower energy orbitals first.
• For instance, sodium (Na) has an electron configuration of \(1s^2 2s^2 2p^6 3s^1\). By losing one electron from the 3s orbital, it forms a Na\(^+\) ion with a stable configuration similar to neon.
• In contrast, chlorine (Cl) with an electron configuration of \(1s^2 2s^2 2p^6 3s^2 3p^5\), gains an electron to fill the 3p orbital and form a Cl\(^-\) ion, achieving a configuration like argon.

Thus, understanding electron configurations helps explain why elements form specific ions and how these ions influence chemical reactions.