Question

Rank the ions in each set in order of increasing size, and explain your ranking: (a) \(\mathrm{Li}^{+}, \mathrm{K}^{+}, \mathrm{Na}^{+}\) (b) \(\mathrm{Se}^{2-}, \mathrm{Rb}^{+}, \mathrm{Br}^{-}\) (c) \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{N}^{3-}\)

Short answer

(a) \(\text{Li}^+ < \text{Na}^+ < \text{K}^+\). (b) \(\text{Rb}^+ < \text{Br}^- < \text{Se}^{2-}\). (c) \(\text{F}^- < \text{O}^{2-} < \text{N}^{3-}\)

Step-by-step solution

Understanding Ionic Size

Ionic size depends on the nuclear charge, number of electrons, and the electron configuration. Ions with the same charge typically follow the trend of increasing size down a group in the periodic table.

Rank \(\text{Li}^+, \text{K}^+, \text{Na}^+\)

All ions have a \(+1\) charge. Ionic size increases down the group: \(\text{Li}^+ < \text{Na}^+ < \text{K}^+\)

Rank \(\text{Se}^{2-}, \text{Rb}^+, \text{Br}^-\)

These ions have different charges. Generally, \(\text{Se}^{2-} \) is larger than \(\text{Br}^-\) because adding electrons increases size. \(\text{Rb}^+\) is smaller since it loses an electron. Rank: \(\text{Rb}^+ < \text{Br}^- < \text{Se}^{2-}\)

Rank \(\text{O}^{2-}, \text{F}^-, \text{N}^{3-}\)

All species are isoelectronic, having the same number of electrons. The size increases with more negative charge: \(\text{F}^- < \text{O}^{2-} < \text{N}^{3-}\)

Key concepts

Nuclear Charge

Understanding nuclear charge is important for grasping ionic size. The nuclear charge is the total charge of all the protons in an atom's nucleus. It is denoted by the symbol Z, representing the number of protons. The greater the nuclear charge, the more strongly the nucleus pulls on the electrons.
This pull affects the size of the ion: more nuclear charge usually means a smaller ion since the electrons are pulled closer to the nucleus.
For example, in the set \(\text{Li}^+, \text{K}^+, \text{Na}^+\), all ions have the same charge but different nuclear charges. Lithium has 3 protons, sodium has 11, and potassium has 19. The nuclear charge increases as you go from lithium to potassium, which leads to changes in the ionic sizes.

Periodic Table Trends

Periodic table trends play a crucial role in determining ionic size. As you move down a group in the periodic table, the size of ions increases. This is because ions down a group have more electron shells, making the ions larger despite having the same charge.
For example, in the set \(\text{Li}^+, \text{K}^+, \text{Na}^+\), all ions have a +1 charge. However, Li\textsuperscript{+} < Na\textsuperscript{+} < K\textsuperscript{+} in size because lithium ion is in the second period, sodium ion in the third, and potassium ion in the fourth.
Additionally, when comparing ions across a period, the ions tend to get smaller due to increasing nuclear charge pulling the electrons closer. Always consider both group and period trends to determine ionic size properly.

Isoelectronic Ions

Isoelectronic ions have the same number of electrons but differing numbers of protons. This means they all share the same electron configuration. Despite sharing the same number of electrons, the ionic size will differ due to differences in nuclear charge.
For example, in the set \(\text{O}^{2-}, \text{F}^{-}, \text{N}^{3-}\), all ions have 10 electrons. However, oxygen has 8 protons, fluorine has 9, and nitrogen has 7. Therefore, the nuclear charge is different for each, influencing their sizes. More protons mean a stronger pull on the electrons, decreasing the size: \(\text{N}^{3-} > \text{O}^{2-} > \text{F}^{-}\). Isoelectronic ions show that even with the same number of electrons, nuclear charge significantly impacts the ionic size.

Ionic Charge

The ionic charge is another critical factor in determining the size of an ion. Ions with higher positive charges are usually smaller because the increased nuclear charge pulls electrons closer. Conversely, ions with higher negative charges are larger because added electrons increase repulsion among the existing electrons, expanding the electron cloud.
Take \(\text{Se}^{2-}, \text{Rb}^+, \text{Br}^-\) for example: selenium ion (\text{Se}\(^{2-}\)) has gained two electrons, making it bigger, while rubidium ion (\text{Rb}\(^+\)) has lost one electron, making it smaller. Bromine ion (\text{Br}\(^-\)), which has gained one electron, falls in between. The ionic sizes rank: \(\text{Rb}^+ < \text{Br}^- < \text{Se}^{2-}\).