Question

Select the smaller member of each pair. (a) \(\mathrm{P}\) and \(\mathrm{P}^{3-}\) (b) \(\mathrm{V}^{2+}\) and \(\mathrm{V}^{4+}\) (c) \(\mathrm{K}\) and \(\mathrm{K}^{+}\) (d) \(\mathrm{Co}\) and \(\mathrm{Co}^{3+}\)

Short answer

a) P or P^(3-) b) V^(2+) or V^(4+) c) K or K^+ d) Co or Co^(3+) Answer: a) P b) V^(4+) c) K^+ d) Co^(3+)

Step-by-step solution

Pair (a): Comparing P and P^(3-)

For the first pair, we need to compare the sizes of a neutral phosphorus atom (P) and its ion with a charge of -3 (P^(3-)). Recall that an atom will become larger when it forms a negatively charged ion, which happens when it gains electrons. Therefore, P^(3-) must be larger than P. Hence, the smaller member is P.

Pair (b): Comparing V^(2+) and V^(4+)

In this pair, we need to compare the sizes of two positively charged ions of vanadium: V^(2+) and V^(4+). When comparing two cations of the same element, the larger size corresponds to the lower positive charge, as there are more electrons available to repel each other and shield the outer electrons from the nucleus. Thus, V^(2+) is larger than V^(4+), making V^(4+) the smaller member.

Pair (c): Comparing K and K^+

In this pair, we need to compare the size of a neutral potassium atom (K) and its ion with a charge of +1 (K^+). Remember that when an atom loses electrons to form a positively charged ion, the ion's size decreases. In this case, K^+ is smaller than K because K has lost one electron to form the ion. Therefore, the smaller member is K^+.

Pair (d): Comparing Co and Co^(3+)

Finally, for the last pair, we need to compare the sizes of a neutral cobalt atom (Co) and its ion with a charge of +3 (Co^(3+)). Similar to pair (c), a positively charged ion is smaller than its neutral atom counterpart because it has lost electrons. Thus, Co^(3+) is smaller than Co, making Co^(3+) the smaller member.

Key concepts

Comparing Atom and Ion Sizes

When examining the size differences between atoms and their associated ions, it's crucial to understand how electron configurations affect atomic radius. Atoms consist of a nucleus surrounded by electrons arranged in various energy levels or shells. The number of electrons in the outer shell and their distribution greatly influence the size of the atom.

For neutral atoms, the size is largely determined by the number of electron shells; more shells mean a larger atom. However, when atoms transform into ions, either by losing or gaining electrons, the situation changes significantly. Loss of electrons results in a smaller ion, while gain of electrons leads to increased repulsion among the remaining electrons, causing the ion to expand and become larger. Hence, when comparing an atom with its ion, it is essential to consider which process—electron gain or loss—has occurred to predict the change in size.

Cation and Anion Size Differences

The fundamental difference between cations (positively charged ions) and anions (negatively charged ions) is their charge due to loss or gain of electrons, respectively. The size of a cation is smaller than its parent atom since the electron loss leads to reduced electron-electron repulsion and allows the remaining electrons to be pulled closer to the nucleus by its positive charge.

On the other hand, anions are larger than their parent atoms. The additional electrons increase repulsion within the electron cloud, pushing the electrons further apart and resulting in a larger ionic radius. This difference in size based on charge is pivotal in understanding the behavior of ions in different chemical environments, such as in ionic bonding or in the formation of crystal structures.

Electron Gain and Loss Impact on Atomic Size

The impact of electron gain or loss on atomic size is governed by the effective nuclear charge and electron-electron interactions. When an atom loses one or more electrons, becoming a cation, the effective nuclear charge experienced by the remaining electrons increases since there are now fewer electrons being repelled by the same nuclear charge. This results in a smaller atomic radius.

Conversely, when an atom gains electrons and becomes an anion, the addition of negative charge leads to greater electron-electron repulsion, which outweighs the attraction to the nucleus, causing the ion to expand in size. It's helpful to think of it as a balance of forces: the loss of electrons tips the balance towards attraction (shrinking the ion), while the gain of electrons pushes the balance towards repulsion (expanding the ion).