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. \(3-5\).

: 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.

: 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⁻

: 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.