Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following arrangement represents the increasing order of Ionic radii of the given species \(0^{-2}\), \(\mathrm{S}^{-2}, \mathrm{~N}^{-3}, \mathrm{P}^{-3}\) (a) \(\mathrm{S}^{-2}<\mathrm{P}^{-3}<\mathrm{N}^{-3}<0^{-2}\) (b) \(0^{-2}<\mathrm{N}^{-3}<\mathrm{S}^{-2}<\mathrm{P}^{-3}\) (c) \(0^{-2}<\mathrm{P}^{3-}<\mathrm{N}^{3-}<\mathrm{S}^{-2}\) (d) \(\mathrm{N}^{-3}<\mathrm{S}^{-2}<0^{-2}<\mathrm{P}^{-3}\)

Step-by-Step Solution

Answer

(b) \(O^{2-}<\mathrm{N}^{-3}<\mathrm{S}^{-2}<\mathrm{P}^{-3}\).

Step 1: Understanding Ionic Radii

The ionic radius of an ion is the measure of its size, which generally increases with an increase in negative charge (i.e., more electrons are added without an increase in nuclear charge). For isoelectronic species, the ion with the greater negative charge will have a larger ionic radius.

Step 2: Identifying Isoelectronic Species

In this case, the species given are \[O^{2-}, S^{2-}, N^{3-}, P^{3-}\]They all fall under the same period and group trends which means we can compare their radii based on their position in the periodic table and their respective charges.

Step 3: Analyzing from the Periodic Table

Elements in the same group on the periodic table generally have larger radii as you go down the group. Thus, for elements having similar charge, \[S^{2-} > O^{2-}\]and \[P^{3-} > N^{3-}\]since sulfur is below oxygen and phosphorus is below nitrogen.

Step 4: Comparing Isostructural Ion Sizes

In a given period where species have a similar arrangement, increased electron count means larger size due to increased electron-electron repulsion with the same nuclear charge. A higher negative charge generally implies larger size:\[N^{3-} > O^{2-}\], and \[P^{3-} > S^{2-}\].

Step 5: Ordering the Ionic Radii

By comparing the ions based on previous analysis: - For \[2-\] charged: \[S^{2-} > O^{2-}\], - For \[3-\] charged, \[P^{3-} > N^{3-}\],Therefore, the increasing order of ionic radii is \[O^{2-} < N^{3-} < S^{2-} < P^{3-}\].

Step 6: Selecting the Correct Option

Upon evaluation, the correct answer which aligns with our findings is:(b) \[O^{2-} < N^{3-} < S^{2-} < P^{3-}\].

Key Concepts

Isoelectronic Species

Isoelectronic species are ions or atoms with the same number of electrons. This usually happens when elements lose or gain electrons to achieve a stable electronic configuration, often mimicking the noble gases. For instance, in the exercise given,

• Both \[O^{2-}\] and \[N^{3-}\] are isoelectronic as each has \[10\] electrons, just like neon.
• Similarly, \[S^{2-}\] and \[P^{3-}\] are also isoelectronic, with \[18\] electrons, similar to argon.

Understanding this concept helps in comparing sizes since these species, having identical electron configurations, can then be compared based on nuclear charge. The number of protons in the nucleus determines the effective nuclear charge experienced by the electron cloud.If two ions are isoelectronic, the one with the greater negative charge (due to added electrons) typically has a larger ionic radius. This is because added electrons increase repulsion among them without an increase in positive charge from the nucleus to stabilize the cloud.

Periodic Table Trends

The periodic table is an invaluable tool for predicting atomic and ionic behaviors. Trends such as atomic size, ionization energy, and electronegativity play crucial roles in understanding chemical behaviors. Generally, as you move from left to right across a period, the ionic size decreases due to increased nuclear charge attracting the electron cloud closer to the nucleus.However, going down a group, we witness an increase in size. This is because additional electron shells are added, making the electron cloud larger despite increased nuclear charge. In the given case:

• Sulfur \[ (S^{2-}) \] and oxygen \[ (O^{2-}) \] fall in the same group, making it clear that sulfur would have a larger radius.
• Similarly, phosphorus \[ (P^{3-}) \] would have a larger ionic radius compared to nitrogen \[ (N^{3-}) \] for the same reason.

These trends reflect how the periodic table's structure influences ion sizes, helping in arranging ions in order of increasing or decreasing radii effectively.

Charge and Ionic Size

The relation between charge and ionic size is pivotal in chemistry. A larger negative charge generally indicates a larger ionic size among isoelectronic species. This phenomenon occurs as more electrons increase electron-electron repulsion in the same electron shell, causing the ion to expand.

• For example, \[N^{3-}\] has more electrons compared to \[O^{2-}\], causing \[N^{3-}\] to have a larger ionic radius.
• Similarly, \[P^{3-}\] has a more negative charge and thus a larger radius than \[S^{2-}\].

With no increase in nuclear charge to counter more electrons, the effective nuclear charge felt by each electron decreases, allowing them to spread out more. Thus, in an isoelectronic series, we usually find that ionic size increases with increasing negative charge: ions possessing higher negative charges become noticeably larger. By understanding this principle, we can effortlessly deduce the order of ionic sizes when comparing such ions.