Question

Rank the ions in each set in order of decreasing size, and explain your ranking: (a) \(\mathrm{Se}^{2-}, \mathrm{S}^{2-}, \mathrm{O}^{2-}\) (b) \(\mathrm{Te}^{2-}, \mathrm{Cs}^{+}, \mathrm{I}^{-}\) (c) \(\mathrm{Sr}^{2+}, \mathrm{Ba}^{2+}, \mathrm{Cs}^{+}\)

Short answer

(a) \(\text{Se}^{2-} > \text{S}^{2-} > \text{O}^{2-}\) (b) \(\text{Te}^{2-} > \text{I}^{-} > \text{Cs}^{+}\) (c) \(\text{Ba}^{2+} > \text{Cs}^{+} > \text{Sr}^{2+}\)

Step-by-step solution

Understanding the Concept

The size of ions is affected by their positions in the periodic table and their charges. Within a group, as you move down the table, the ionic size increases due to the addition of electron shells. For ions with the same charge, the ionic size increases with increasing atomic number.

Ranking the Ions (a)

For the ions a) \(\text{Se}^{2-}, \text{S}^{2-}, \text{O}^{2-}\)1. All have a \(2-\)charge, and belong to group 16. 2. Moving down the group, the order is \(\text{O}, \text{S}, \text{Se}\)\.Hence, \(\text{Se}^{2-}\) is largest and \(\text{O}^{2-}\) is smallest. 3. Order of size: \(\text{Se}^{2-} > \text{S}^{2-} > \text{O}^{2-}\).

Ranking the Ions (b)

For the ions b) \(\text{Te}^{2-}, \text{Cs}^{+}, \text{I}^{-}\)1. Comparing \(\text{Te}^{2-}\) and \(\text{I}^{-}\): Te is below I in group 16, making \(\text{Te}^{2-}\) larger than \(\text{I}^{-}\).2. The \(\text{Cs}^{+}\) ion, being a cation with one less electron shell, is smaller than both anions.3. Order of size: \(\text{Te}^{2-} > \text{I}^{-} > \text{Cs}^{+}\).

Ranking the Ions (c)

For the ions c) \(\text{Sr}^{2+}, \text{Ba}^{2+}, \text{Cs}^{+}\)1. Both \(\text{Sr}^{2+}\) and \(\text{Ba}^{2+}\) are from group 2. Ba, being below Sr, is larger.2. \(\text{Cs}^{+}\) ion size is larger than \(\text{Sr}^{2+}\) but smaller than \(\text{Ba}^{2+}\) due to the lower charge impact of losing just one electron.3. Order of size: \(\text{Ba}^{2+} > \text{Cs}^{+} > \text{Sr}^{2+}\).

Key concepts

Periodic Table Trends

Understanding periodic table trends is crucial for predicting the sizes of ions. In general, as you move down a group, the ionic size increases. This happens because each row adds a new electron shell, making the atom larger. Similarly, as you move from left to right across a period, the ionic size generally decreases due to increased nuclear charge pulling electrons closer. These trends help in predicting and comparing the sizes of ions within different groups and periods.

Ionic Size

Ionic size refers to the radius of an ion. The size of an ion is influenced by the number of electron shells and the effective nuclear charge. For example, an anion (negatively charged ion) is typically larger than its neutral atom because the extra electron increases repulsion among electrons. On the other hand, a cation (positively charged ion) is usually smaller than its neutral atom because losing electrons results in fewer electron-electron repulsions and a greater effective nuclear charge per remaining electron. Thus, ions of the same element can have different sizes depending on their charges.

Ion Charge Effects

The charge of an ion significantly affects its size. Anions, which gain electrons, are larger than their parent atoms due to increased electron-electron repulsion. Cations, which lose electrons, are smaller because the loss of an electron reduces repulsion and allows the remaining electrons to be pulled closer to the nucleus. For isoelectronic species—ions with the same number of electrons—the ion with the greater positive charge will be smaller due to increased attraction between the electrons and the nucleus. For example, \(\text{Ca}^{2+}\) is smaller than \(\text{K}^{+}\) even though both have the same number of electrons.

Group and Period Trends

Group and period trends play a vital role in determining ionic sizes. Within a group, moving from top to bottom, ionic size increases due to the addition of electron shells. Within a period, moving from left to right, ionic size decreases despite the addition of electrons because the increase in nuclear charge pulls electrons closer to the nucleus. When comparing ions in different groups or periods, these trends help in predicting which ion will be larger or smaller. For instance, within the same group, \(\text{Ba}^{2+}\) is larger than \(\text{Sr}^{2+}\) as it is lower in the group and has more electron shells.