Question

For each of the following groups, place the atoms and/or ions in order of decreasing size. a. \(\mathrm{V}, \mathrm{V}^{2+}, \mathrm{V}^{3+}, \mathrm{V}^{5+}\) b. \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Cs}^{+}\) c. \(\mathrm{Te}^{2-}, \mathrm{I}^{-}, \mathrm{Cs}^{+}, \mathrm{Ba}^{2+}\) d. \(P, P, P^{2}, P^{3}\) e. \(\mathrm{O}^{2-}, \mathrm{S}^{2-}, \mathrm{Se}^{2-}, \mathrm{Te}^{2-}\)

Short answer

a. \(\mathrm{V} > \mathrm{V}^{2+} > \mathrm{V}^{3+} > \mathrm{V}^{5+}\) b. \(\mathrm{Cs}^{+} > \mathrm{Rb}^{+} > \mathrm{K}^{+} > \mathrm{Na}^{+}\) c. \(\mathrm{Te}^{2-} > \mathrm{I}^{-} > \mathrm{Cs}^{+} > \mathrm{Ba}^{2+}\) d. \(P^{3}>P^{2}>P=P\) e. \(\mathrm{Te}^{2-} > \mathrm{Se}^{2-} > \mathrm{S}^{2-} > \mathrm{O}^{2-}\)

Step-by-step solution

Compare Charges

First, we should compare the charges of the given ions. In general, higher positive charges lead to smaller ionic radii, as the greater pull from the protons in the nucleus results in less shielding between the nucleus and the electrons, making the ion smaller. The order so far: \(\mathrm{V} > \mathrm{V}^{2+} > \mathrm{V}^{3+} > \mathrm{V}^{5+}\) b. \(\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Cs}^{+}\)

Compare Groups \

All ions have the same charge (+1), so we need to consider their positions in the periodic table. As mentioned earlier, atomic/ionic size generally increases going down a group. Since all these elements belong to Group 1, we can use this trend to order them by size. The order from largest to smallest is: \(\mathrm{Cs}^{+} > \mathrm{Rb}^{+} > \mathrm{K}^{+} > \mathrm{Na}^{+}\) c. \(\mathrm{Te}^{2-}, \mathrm{I}^{-}, \mathrm{Cs}^{+}, \mathrm{Ba}^{2+}\)

Compare Charges

We should start by comparing the charges of the ions. We know that cations (negative charges) are generally larger than anions (positive charges) since the cations have more electrons and less proton attraction. So far, we have: \(\mathrm{Te}^{2-} > \mathrm{I}^{-} > \mathrm{Cs}^{+} > \mathrm{Ba}^{2+}\) d. \(P, P, P^{2}, P^{3}\)

Recognize Same Element

We can notice two neutral phosphorus atoms and two phosphorus anions. The neutral atoms have the same size, so we only need to compare the neutral phosphorus with the anions.

Compare Charges

The neutral phosphorus atom has no extra electrons, making it smaller than the anions. Therefore, the order of decreasing size is: \(P^{3}>P^{2}>P=P\) e. \(\mathrm{O}^{2-}, \mathrm{S}^{2-}, \mathrm{Se}^{2-}, \mathrm{Te}^{2-}\)

Compare Groups \

All ions have the same charge (-2), so we need to consider their positions in the periodic table. All these elements are from Group 16, so we can use the trend that atomic/ionic size generally increases going down a group to order them by size. The order from largest to smallest is: \(\mathrm{Te}^{2-} > \mathrm{Se}^{2-} > \mathrm{S}^{2-} > \mathrm{O}^{2-}\)

Key concepts

Periodic Trends

Understanding how atomic and ionic sizes vary in the periodic table is essential for comprehending the relationships between different elements and ions. The size of an atom or ion is influenced by two main factors: the number of electron shells and the effective nuclear charge. As you move across a period from left to right, the addition of protons to the nucleus and electrons to the same shell leads to an increase in the effective nuclear charge. This increment pulls the electron shell closer, resulting in smaller atomic or ionic radii.

Conversely, as you travel down a group, each element has an additional electron shell compared to the one above it. This greater distance from the nucleus, even with the increase in nuclear charge, means there's more shielding, which typically results in larger atomic and ionic sizes. Keep in mind, this explanation simplifies a complex interaction of forces; the periodic trends serve as a good general rule but there are exceptions influenced by the specifics of electron configuration and other factors.

It is also worth noting these trends help us predict the relative sizes of different ions, which is crucial for understanding the physical and chemical properties of compounds. For instance, in a crystal lattice, the size of the ions can affect the structure and stability of the material.

Cation and Anion Size Comparison

Comparing the sizes of cations and anions, there's an important rule to remember: cations are generally smaller than their parent atoms, while anions are larger. For a cation, the loss of one or more electrons, which decreases electron-electron repulsion, together with an unchanged or only slightly increased nuclear charge, means that the remaining electrons are pulled closer to the nucleus.

In contrast, when an atom gains electrons to become an anion, the increased electron-electron repulsion within the same or similar energy level causes the ionic radius to expand beyond that of the neutral atom. Moreover, different charges between ions can drastically affect their size. For instance, a V⁵⁺ ion has lost five electrons, resulting in a much smaller size compared to a V²⁺ ion or a neutral vanadium (V) atom.

In exercises like the one provided, scrutinizing the charge allows students to rank ions correctly. Remember, as the magnitude of positive charge increases, the ionic radius decreases, while the opposite is true for negative charges. This understanding is fundamental when predicting the behavior of ions in chemical reactions, bonding, and interaction with electromagnetic fields.

Periodic Table Groups

Groups in the periodic table are the columns that run from top to bottom. Elements in the same group share similar properties, including trends in their atomic and ionic radii. We commonly use these groups to organize elements by their valence electron configuration, which impacts their chemical reactivity.

A pertinent example can be seen in Group 1, which contains the alkali metals. These elements have a single valence electron and, following the previously mentioned trend, increase in size from top (Lithium) to bottom (Francium). As for ionic sizes, ions in the same group can also differ due to their different initial atomic sizes. For ions with the same charge, generally, the atomic size increases down a group, as seen with the order from largest to smallest in the Group 1 cations in the exercise: Cs⁺, Rb⁺, K⁺, Na⁺.

Since ions in the same group have the same number of electrons, differences in ionic radii within a group are mainly due to the number of electron shells. Students can apply this knowledge to predict properties like ionic mobility, which is important for understanding phenomena such as electrical conductivity in ionic solutions.