Question

Using only the periodic table, predict the most stable ion for Na, Mg. Al, \(\mathrm{S}, \mathrm{Cl}, \mathrm{K}, \mathrm{Ca},\) and Ga. Arrange these from largest to smallest radius, and explain why the radius varies as it does. Compare your predictions with Fig. \(3-5\).

Short answer

The most stable ions for Na, Mg, Al, S, Cl, K, Ca, and Ga are Na⁺, Mg²⁺, Al³⁺, S²⁻, Cl⁻, K⁺, Ca²⁺, and Ga³⁺, respectively. These ions are arranged based on their radii as K⁺ < Na⁺ < Ca²⁺ < Mg²⁺ < Ga³⁺ < Al³⁺ < S²⁻ < Cl⁻. The ionic radii vary due to differences in electron-electron repulsion and effective nuclear charge. This prediction should match the data in Figure 3-5.

Step-by-step solution

Predict the most stable ions

: We'll start by determining the most stable ions for each element based on their electron configurations and their position in the periodic table. 1. Na (Sodium) - Na has an electron configuration of [Ne] 3s1. It can lose 1 electron to achieve a noble gas configuration of [Ne], similar to Ne. Hence, its most stable ion is Na⁺. 2. Mg (Magnesium) - Mg has an electron configuration of [Ne] 3s2. By losing 2 electrons, it achieves the noble gas configuration of [Ne] and forms Mg²⁺ ion. 3. Al (Aluminum) - Al has an electron configuration of [Ne] 3s2 3p1. By losing its 3 valence electrons, it achieves the noble gas configuration of [Ne], and forms Al³⁺ ion. 4. S (Sulfur) - S has an electron configuration of [Ne] 3s2 3p4. It can gain 2 electrons to achieve a noble gas configuration of [Ar], similar to Ar. Hence, its most stable ion is S²⁻. 5. Cl (Chlorine) - Cl has an electron configuration of [Ne] 3s2 3p5. It can gain 1 electron to achieve a noble gas configuration of [Ar], and forms Cl⁻ ion. 6. K (Potassium) - K has an electron configuration of [Ar] 4s1. By losing its 1 valence electron, it achieves the noble gas configuration of [Ar], and forms K⁺ ion. 7. Ca (Calcium) - Ca has an electron configuration of [Ar] 4s2. By losing 2 electrons, it achieves the noble gas configuration of [Ar] and forms Ca²⁺ ion. 8. Ga (Gallium) - Ga has an electron configuration of [Ar] 3d10 4s2 4p1. By losing 3 electrons (2 from s and 1 from p orbital), it achieves the noble gas configuration of [Ar], and forms Ga³⁺ ion.

Arrange the ions based on ionic radii

: To arrange the ions based on their radii, we will consider two factors: the number of electrons in the ions and the effective nuclear charge. More electrons lead to greater electron-electron repulsion, resulting in a larger ion. A higher effective nuclear charge means more attraction between the positively charged nucleus and negatively charged electrons, causing the ion to be smaller. The order of ions based on these factors is: K⁺ < Na⁺ < Ca²⁺ < Mg²⁺ < Ga³⁺ < Al³⁺ < S²⁻ < Cl⁻

Explain variation in ionic radius

: The ionic radius varies for the positive ions (cations) as they lose varying numbers of electrons, resulting in differences in electron-electron repulsion and effective nuclear charge. For instance, K⁺ has more electron-electron repulsion than Na⁺ due to the additional filled 3d orbitals in K, making its ionic radius larger. In addition, Ca²⁺ has a higher effective nuclear charge than Mg²⁺ due to the presence of more protons in its nucleus, making its ionic radius smaller. On the other hand, for negative ions (anions) such as S²⁻ and Cl⁻, the addition of electrons increases electron-electron repulsion, resulting in larger ionic radii. However, Cl⁻ has more protons than S²⁻, leading to a higher effective nuclear charge and smaller ionic radius than S²⁻. Finally, the exercise asks us to compare our predictions with Figure 3-5, which should display all the ions arranged according to their ionic radii. Our prediction should match the data shown in the figure.

Key concepts

Ionic Radius

The ionic radius of an atom is the measure of an ion's size when it is formed from an atom. This size can vary depending on whether the ion is a cation (positively charged) or an anion (negatively charged). The ionic radius is different from the atomic radius because the electron arrangement changes once an ion is formed.

For cations, losing electrons usually results in smaller ionic radii compared to their neutral atom. This reduction in size occurs because there is less electron-electron repulsion in the ion and the remaining electrons are drawn closer to the nucleus, which has the same number of protons.

• For example, when Na loses an electron to become Na⁺, its ionic radius decreases.
• Similarly, Mg becomes Mg²⁺, losing two electrons, which further decreases its size due to the reduced electron-electron repulsion.

In the case of anions, adding electrons increases the ionic radius as the added electrons increase electron-electron repulsion, pushing them further apart within the electron cloud. Hence, anions tend to have larger ionic radii compared to their corresponding neutral atoms.

• For instance, when Cl gains an electron to become Cl⁻, its size expands relative to the neutral chlorine atom.
• This is because the additional electron causes more repulsion among the existing electrons.

Electron Configuration

Electron configuration describes how electrons are arranged within an atom, providing us insights into an atom's stability and reactivity. Electrons fill orbitals starting from the lowest energy levels, following a specific order dictated by principles like the Aufbau principle, Hund’s rule, and the Pauli Exclusion Principle.

When forming ions, atoms aim to achieve a more stable electron configuration, often resembling that of a noble gas, due to its stable, full shell.

• Sodium (Na) with an initial configuration of [Ne] 3s1 loses an electron to match Neon’s configuration, forming Na⁺.
• Magnesium (Mg) follows a similar process: starting at [Ne] 3s2 and losing two electrons to form Mg²⁺, reaching a stable configuration like Neon’s.
• For Chlorine (Cl), starting at [Ne] 3s2 3p5, gaining one electron results in the configuration of Argon, giving Cl⁻ a stable state.

The goal of forming stable ions drives atoms to lose or gain electrons, therefore dictating which electron configuration they would reach leading to their respective stable ions.

Effective Nuclear Charge

The effective nuclear charge (Z_eff) is an important concept for understanding how the positive charge of the nucleus is experienced by an electron in an atom. While the actual nuclear charge is the total positive charge of the nucleus, Z_eff accounts for the shielding effect, where inner shell electrons reduce the pull on the outer shell electrons.

As a result, electrons are not attracted to the full nuclear charge but instead are attracted by this reduced charge, known as Z_eff. This is crucial in explaining variations in atomic and ionic radii across periods and down groups in the periodic table.

• A higher Z_eff means that electrons are pulled closer, often resulting in smaller ionic radii.
• For instance, though both calcium (Ca) and magnesium (Mg) form ions by losing two electrons, Ca²⁺ ends up being smaller because its nucleus has more protons, increasing the Z_eff.
• This is why the effective nuclear charge helps to understand why Mg²⁺ is larger than Ca²⁺, despite both losing two electrons.

Thus, Z_eff is a balancing factor, aiding us in predicting changes in radius and reactivity as seen across the periodic table.

Cations and Anions

When elements form ions, they can become cations or anions, based on whether they lose or gain electrons, respectively. Cations are positive ions formed by losing electrons, whereas anions are negative ions formed by gaining electrons.

Cations:

• These atoms lose electrons to achieve a stable electron configuration, often reducing in size compared to their neutral states.
• Common examples from alkaline and alkaline earth metals are Na⁺ and Ca²⁺, formed when sodium and calcium lose one and two electrons, respectively.
• The reduction to a lower electron energy level often results in a significant decrease in radius for cations.

Anions:

• Anions gain electrons to fulfill their valence shell, increasing their radius due to increased electron-electron repulsion.
• Sulfur typically becomes S²⁻, and chlorine becomes Cl⁻, both achieving stable electrical states by gaining electrons.
• This gain leads to a larger ionic radius because the new electron increases the electron cloud size due to greater repulsion.

Overall, understanding the formation and characteristics of cations and anions is fundamental to predicting ionic behavior and stability in chemical reactions.