List the following ions in order of increasing ionic radius: \(\mathrm{N}^{3-}, \mathrm{Na}^{+}, \mathrm{F}^{-}, \mathrm{Mg}^{2+}, \mathrm{O}^{2-}\)

Understanding the periodic trends in ion size is essential to grasp why ions differ in size. As you go across a period in the periodic table, the number of protons increases, pulling electrons closer to the nucleus and resulting in smaller atomic and ionic radii. This trend, however, resets at each new period where additional electron shells are added, making ions larger due to increased electron shell count. For example, when comparing ions from period 2 to those from period 3, it's crucial to acknowledge that the additional electron shell in period 3 ions results in larger sizes despite similar or higher positive charges.

In the exercise provided, ions from periods 2 and 3 are compared. Period 2 ions like \(\mathrm{N}^{3-}\), \(\mathrm{O}^{2-}\), and \(\mathrm{F}^{-}\) will each be smaller than the period 3 ions \(\mathrm{Na}^{+}\) and \(\mathrm{Mg}^{2+}\) due to the vital influence of that additional shell in period 3, despite variation in their charges.

The ionic charge plays a significant role in determining the size of an ion. Cations (positively charged ions) are generally smaller than their neutral atoms because the loss of electrons results in a reduced electron cloud while the nucleus maintains the same pull on the remaining electrons. Conversely, anions (negatively charged ions) are larger than their neutral atoms because the addition of extra electrons leads to electron-electron repulsion and an enlarged electron cloud.

When comparing ions with the same electron configuration, the ion with the higher positive charge will be the smallest due to stronger nuclear pull per electron. Similarly, among anions with the same configuration, the one with the higher negative charge will be larger due to increased repulsion in the electron cloud. The exercise solution applies this principle, showing \(\mathrm{Mg}^{2+}\) as smaller than \(\mathrm{Na}^{+}\) and \(\mathrm{N}^{3-}\) as larger than both \(\mathrm{O}^{2-}\) and \(\mathrm{F}^{-}\).

When comparing ionic radii, one must consider both the period trend and the charge of ions. As shown in the exercise solution, ions with higher negative or lower positive charges will have larger radii within a given period. However, when comparing ions from different periods, the period's electron shell count can override the effects of charge. To accurately compare, start by examining ions within the same period, ranking them by charge effect on size, and then place the different period groups relative to each other.

For instance, within period 2 anions, \(\mathrm{N}^{3-}\) is larger than \(\mathrm{O}^{2-}\) because of its extra negative charge; \(\mathrm{O}^{2-}\) is larger than \(\mathrm{F}^{-}\) for the same reason. However, when compared to period 3 ions, even the smallest of period 3, \(\mathrm{Mg}^{2+}\), is larger than the biggest of period 2, \(\mathrm{N}^{3-}\), due to the additional electron shell in period 3 ions.