Using only the periodic table, predict the most stable ion for Na, Mg, Al, S, \(\mathrm{Cl}, \mathrm{K}\) , Ca, and Ga. Arrange these from largest to smallest radius, and explain why the radius varies as it does. Compare your predictions with Fig. \(8.8 .\)

To determine the most stable ions for each element, we need to consider their electron configurations and the nearest noble gas configuration. Elements prefer to lose or gain electrons to achieve the noble gas electron configuration, as it is more stable. Here are the most stable ions for each element: 1. Na (Sodium): Na has the electron configuration [Ne] 3s1. To achieve the noble gas configuration of Ne (Neon), it can lose one electron. Thus, the most stable ion for Na is Na\(^+\). 2. Mg (Magnesium): Mg has the electron configuration [Ne] 3s2. To achieve the noble gas configuration of Ne (Neon), it can lose two electrons. Thus, the most stable ion for Mg is Mg\(^{2+}\). 3. Al (Aluminum): Al has the electron configuration [Ne] 3s2 3p1. To achieve the noble gas configuration of Ne (Neon), it can lose three electrons. Thus, the most stable ion for Al is Al\(^{3+}\). 4. S (Sulfur): S has the electron configuration [Ne] 3s2 3p4. To achieve the noble gas configuration of Ar (Argon), it can gain two electrons. Thus, the most stable ion for S is S\(^{2-}\). 5. Cl (Chlorine): Cl has the electron configuration [Ne] 3s2 3p5. To achieve the noble gas configuration of Ar (Argon), it can gain one electron. Thus, the most stable ion for Cl is Cl\(^-\). 6. K (Potassium): K has the electron configuration [Ar] 4s1. To achieve the noble gas configuration of Ar (Argon), it can lose one electron. Thus, the most stable ion for K is K\(^+\). 7. Ca (Calcium): Ca has the electron configuration [Ar] 4s2. To achieve the noble gas configuration of Ar (Argon), it can lose two electrons. Thus, the most stable ion for Ca is Ca\(^{2+}\). 8. Ga (Gallium): Ga has the electron configuration [Ar] 3d10 4s2 4p1. To achieve the noble gas configuration of Ar (Argon), it can lose three electrons. Thus, the most stable ion for Ga is Ga\(^{3+}\).

Now that we have determined the most stable ions for each element, we can arrange them in order of size from largest to smallest by considering the atomic and ionic radii trends. The order of the ions from largest to smallest radius will be: K\(^+\), Na\(^+\), Ca\(^{2+}\), Mg\(^{2+}\), S\(^{2-}\), Cl\(^-\), Al\(^{3+}\), Ga\(^{3+}\).

Several factors influence the size of ions: 1. Effective Nuclear Charge: Going from left to right across a period, the number of protons in the nucleus increases, as does the effective nuclear charge. This increased pull from the nucleus causes the size of the ions to decrease. 2. Electron Shielding: As we move down a group, the number of filled energy levels (electron shells) increases, resulting in more electron shielding. The electrons in the outermost energy level experience a weaker electrostatic attraction, which results in larger atomic and ionic radii. 3. Ionization State: Cations are smaller than their parent atoms as they have lost electrons and have a higher effective nuclear charge. Anions are larger than their parent atoms as they have gained electrons, increasing electron-electron repulsion. These factors affect the size of ions as they move across and down the periodic table. From the given order, it can be observed that as we move from left to right across a period, the size of the ions decreases due to an increased effective nuclear charge. As we move down the group, the size of ions increases due to electron shielding. Finally, the ionization state causes the ions to be either larger or smaller than their parent atoms.