Question

The correct sequence of the ionic radii of the following is: (a) \(\mathrm{I}^{-}>\mathrm{S}^{2-}>\mathrm{Cl}^{-}>\mathrm{O}^{2-}>\mathrm{F}^{-}\) (b) \(\mathrm{S}^{2-}>\mathrm{I}^{-}>\mathrm{O}^{2-}>\mathrm{Cl}^{-}>\mathrm{F}^{-}\) (c) \(\mathrm{I}^{-}>\mathrm{Cl}^{-}>\mathrm{S}^{2-}>\mathrm{O}^{2-}>\mathrm{F}^{-}\) (d) \(\mathrm{I}^{-}>\mathrm{S}^{2-}>\mathrm{Cl}^{-}>\mathrm{F}^{-}>\mathrm{O}^{2-}\)

Short answer

Option (a) \( \mathrm{I}^{-} > \mathrm{S}^{2-} > \mathrm{Cl}^{-} > \mathrm{O}^{2-} > \mathrm{F}^{-} \).

Step-by-step solution

Understanding the Concept of Ionic Radii

Ionic radii are influenced by the number of protons and the overall electron configuration. For atoms in a group, the ionic radius tends to increase down the group due to additional electron shells. For isoelectronic species (those having the same number of electrons), more negative ions have larger radii as they have lesser nuclear charge per electron, causing less effective nuclear attraction.

Comparing Ions Across the Options

The ions given are - \( \mathrm{I}^{-} \) (anions from Group 17, 5th period), - \( \mathrm{S}^{2-} \) (anions from Group 16, 3rd period), - \( \mathrm{Cl}^{-} \) (anions from Group 17, 3rd period), - \( \mathrm{O}^{2-} \) (anions from Group 16, 2nd period), and - \( \mathrm{F}^{-} \) (anions from Group 17, 2nd period). Thus, the sequence of ionic radii should be as follows: 'Ions from the same group have an increase in size moving downwards.' Hence, the sequence should reflect ions ordered by period primarily, then by charge influence.

Establishing the Correct Order

For the given ions, the order of increasing ionic radii should be \( \mathrm{F}^{-} < \mathrm{O}^{2-} < \mathrm{Cl}^{-} < \mathrm{S}^{2-} < \mathrm{I}^{-} \). This reflects both the greater period number contributing to size and considering the isoelectronic context when necessary, thus the correct option is option \( (a) \).

Key concepts

Periodic Trends

In the realm of chemistry, **periodic trends** play a pivotal role in understanding the properties of elements, including ionic radii. The periodic table is structured in such a way that certain patterns emerge as you move across periods or down groups. For ionic radii, a key trend is that as you move down a group, the size of ions generally increases. This is due to each subsequent element having an additional electron shell, resulting in a larger atomic size.

Across a period, however, the trend can be a bit different. Generally, as you move from left to right across a period, ions become smaller. This occurs because more protons are present in the nucleus, increasing the positive charge. This greater charge pulls electrons in more tightly, reducing the ion's radius despite them having the same number of electron shells.

Understanding these periodic trends helps in predicting and explaining the behavior of elements, particularly the comparison of ionic sizes as required in tasks like ordering the ionic radii of various ions.

Isoelectronic Species

**Isoelectronic species** refer to atoms or ions that share the same number of electrons. It's an intriguing concept because despite having the same electron count, these species can have different ionic sizes. The size difference arises from the varying numbers of protons, which lead to differences in nuclear attraction.

For example, take oxygen ion \(O^{2-}\) and fluoride ion \(F^{-}\). They both contain the same number of electrons, making them isoelectronic. However, \(O^{2-}\) has fewer protons compared to \(F^{-}\), resulting in a larger ionic radius for oxygen ion. This is because with fewer protons to attract the same number of electrons, there's less pull on the electron cloud, making the ion larger.

When sorting or comparing ionic radii, especially among isoelectronic species, it’s crucial to consider the number of protons as it greatly affects their sizes.

Nuclear Charge

The term **nuclear charge** refers to the total charge of the nucleus, which is determined largely by the number of protons it contains. It's an important factor in understanding ionic radii and other properties of elements.

As the nuclear charge increases, its positive force grows, attracting electrons more strongly and thereby reducing the size of the electron cloud around the nucleus. For ions, this means that a species with a higher nuclear charge will typically have a smaller radius if the electron count remains constant, because the electrons are pulled in more effectively towards the nucleus.

In the context of isoelectronic species, where multiple ions have the same electron number, the species with the higher nuclear charge will feature a smaller ionic radius. This principle significantly impacts the understanding of atomic and ionic behavior across the periodic table.

Effective Nuclear Attraction

The **effective nuclear attraction** is a key concept that describes how effectively the nucleus can attract and hold onto its electrons, particularly in the valence shell. Two main factors influence this attraction: nuclear charge and electron shielding.

Electron shielding occurs when inner electron shells block the outer electrons from feeling the full force of the nucleus's charge. As the number of inner electrons increases, they create a "screening" effect that reduces the effective nuclear attraction experienced by the outermost electrons.

When dealing with ionic radii, effective nuclear attraction explains why ions with more inner electron shells generally have larger radii despite potentially greater nuclear charges. The reduced attraction caused by shielding means that outer electrons are less tightly held, resulting in a larger ionic size.

• A greater number of electron shells implies stronger electron shielding.
• Stronger shielding leads to less effective nuclear attraction on the outer electrons.
• This results in larger ionic radii as you move down a group in the periodic table.

Understanding effective nuclear attraction is vital for predicting the behavior of elements and ions in various chemical contexts, including the determination of ionic radii.