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

Option (d): \(N^{3-}

Step 1: Analyze the Ionic Radii Concept

Ionic radius refers to the radius of an ion in a crystal lattice. When an atom gains extra electrons and turns into an anion, its radius typically increases due to the increased electron-electron repulsion, which leads to the electron cloud expanding.

Step 2: Consider Isoelectronic Species

The given species \( O^{2-} \), \( S^{2-} \), \( N^{3-} \), \( P^{3-} \) are all isoelectronic, which means they have the same number of electrons but different nuclei. Isoelectronic species have ionic radii depending on nuclear charge - the more protons in the nucleus, the smaller the ionic radius due to a stronger attraction between the protons and the electron cloud.

Step 3: Determine the Effective Nuclear Charge

For isoelectronic species, the effective nuclear charge increases as you move across a period in the periodic table because the number of protons increases. This means for the isoelectronic series:- \( N^{3-} \) has the least protons- \( O^{2-} \) has more protons- \( S^{2-} \) has even more- \( P^{3-} \) has the most protonsTherefore, \( P^{3-} \) has the smallest ionic radius, followed by \( S^{2-} \), then \( O^{2-} \), and finally \( N^{3-} \) with the largest.

Step 4: Arrange Ionic Radii in Increasing Order

Based on the effective nuclear charge, arrange the species in increasing order of their ionic radii: \( P^{3-} < S^{2-} < O^{2-} < N^{3-} \).

Key Concepts

Ionic Radius Trend

Ionic radius is a fascinating concept that revolves around how the size of an ion changes when an atom gains or loses electrons. When an atom becomes an anion by gaining electrons, its ionic radius typically increases. This is due to additional electron-electron repulsion among the added electrons. The electron cloud, therefore, expands, leading to a larger ionic radius.
Consider the ionic radii trend as you move across a period or down a group in the periodic table. Across a period, adding electrons into the same outer shell can cause a decrease in ionic size due to the increased nuclear charge if no additional electrons are also added. However, if we compare ions with similar electron configurations (like in isoelectronic series), the ionic size trend is majorly governed by the nuclear charge.
It’s important to note that:

• Larger anions have more electrons, leading to increased repulsion.
• Greater nuclear charge can pull the electron cloud closer to the nucleus, reducing the ionic radius.

Isoelectronic Species

Isoelectronic species are interesting because they possess the same number of electrons but have different elements acting as their core. This causes them to exhibit subtle differences in their properties, such as ionic radii.
Imagine you have different ions all carrying the same number of electrons. What sets them apart is the number of protons in the nucleus of each ion. The species mentioned in the exercise, such as \( O^{2-} \), \( S^{2-} \), \( N^{3-} \), \( P^{3-} \), are all isoelectronic, yet they differ in their ionic radii because they have distinct nuclear charges.
Points to remember:

• Although these species have a similar electron count, their ionic size is dictated by their proton count.
• The more protons present, the stronger the pull on the electron cloud, generally resulting in a smaller ionic radius.
• This makes the concept of isoelectronic species highly significant in predicting the behavior and characteristics of ions.

Effective Nuclear Charge

The concept of effective nuclear charge (often denoted as \( Z_{eff} \)) is crucial to understanding why different ions with the same electron configuration have different sizes. This charge refers to the net positive charge experienced by the electrons in an ion.
In a set of isoelectronic species, the effective nuclear charge becomes a major determinant of ionic size. As the number of protons in the nucleus increases, the electrons are attracted more strongly, resulting in a smaller radius.
Considerations include:

• The effective nuclear charge increases with an increase in protons.
• For the series \( N^{3-} \), \( O^{2-} \), \( S^{2-} \), \( P^{3-} \), each ion has progressively more protons, therefore increasing \( Z_{eff} \).
• This trend explains why \( N^{3-} \) is the largest among these ions, and \( P^{3-} \) is the smallest.

Electron-electron Repulsion

Electron-electron repulsion plays a vital role in defining the size and shape of anions. When additional electrons are added to an atom, making it an anion, these electrons repel each other due to having the same negative charge. This repulsion causes the electron cloud around the nucleus to expand.
As more electrons are added, the repulsion among them increases even if the nuclear attraction also increases due to a greater positive charge in the nucleus. This is why anions typically have larger ionic radii than their parent atoms.
Key points about electron-electron repulsion:

• More electrons mean more repulsion, resulting in a larger ion.
• Greater repulsion spread among electrons increases the space they occupy.
• Balancing the electron repulsion and the attraction from protons is what eventually defines the ionic radius in anions.

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Problem 160

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Problem 162

Other exercises in this chapter

Problem 159

The increasing order of the ionic radii of the given isoelectronic species is: (a) \(\mathrm{Ca}^{2+}, \mathrm{K}^{+}, \mathrm{Cl}^{-}, \mathrm{S}^{2-}\) (b) \(

View solution

Problem 160

The first ionisation potential of \(\mathrm{Na}\) is \(5.1 \mathrm{ev}\). The value of electron gain enthalpy of \(\mathrm{Na}^{+}\)will be? (a) \(-2.55 \mathrm

View solution

Problem 162

The Ionic radii (in \(\mathrm{A}\) ) of \(\mathrm{N}^{-3}, \mathrm{O}^{-2}, \mathrm{~F}^{-}\)are respectively? [2015] (a) \(1.36,1.4\) and \(1.71\) (b) \(1.36,1

View solution

Problem 158

The correct sequence which shows decreasing order of the ionic radii of the elements is (a) \(\mathrm{Al}^{3+}>\mathrm{Mg}^{2+}>\mathrm{Na}^{+}>\mathrm{F}^{-}>\

View solution

Key Concepts

Ionic Radius Trend

Ionic radius is a fascinating concept that revolves around how the size of an ion changes when an atom gains or loses electrons. When an atom becomes an anion by gaining electrons, its ionic radius typically increases. This is due to additional electron-electron repulsion among the added electrons. The electron cloud, therefore, expands, leading to a larger ionic radius.
Consider the ionic radii trend as you move across a period or down a group in the periodic table. Across a period, adding electrons into the same outer shell can cause a decrease in ionic size due to the increased nuclear charge if no additional electrons are also added. However, if we compare ions with similar electron configurations (like in isoelectronic series), the ionic size trend is majorly governed by the nuclear charge.
It’s important to note that:

• Larger anions have more electrons, leading to increased repulsion.
• Greater nuclear charge can pull the electron cloud closer to the nucleus, reducing the ionic radius.

Isoelectronic Species

Isoelectronic species are interesting because they possess the same number of electrons but have different elements acting as their core. This causes them to exhibit subtle differences in their properties, such as ionic radii.
Imagine you have different ions all carrying the same number of electrons. What sets them apart is the number of protons in the nucleus of each ion. The species mentioned in the exercise, such as \( O^{2-} \), \( S^{2-} \), \( N^{3-} \), \( P^{3-} \), are all isoelectronic, yet they differ in their ionic radii because they have distinct nuclear charges.
Points to remember:

• Although these species have a similar electron count, their ionic size is dictated by their proton count.
• The more protons present, the stronger the pull on the electron cloud, generally resulting in a smaller ionic radius.
• This makes the concept of isoelectronic species highly significant in predicting the behavior and characteristics of ions.

Effective Nuclear Charge

The concept of effective nuclear charge (often denoted as \( Z_{eff} \)) is crucial to understanding why different ions with the same electron configuration have different sizes. This charge refers to the net positive charge experienced by the electrons in an ion.
In a set of isoelectronic species, the effective nuclear charge becomes a major determinant of ionic size. As the number of protons in the nucleus increases, the electrons are attracted more strongly, resulting in a smaller radius.
Considerations include:

• The effective nuclear charge increases with an increase in protons.
• For the series \( N^{3-} \), \( O^{2-} \), \( S^{2-} \), \( P^{3-} \), each ion has progressively more protons, therefore increasing \( Z_{eff} \).
• This trend explains why \( N^{3-} \) is the largest among these ions, and \( P^{3-} \) is the smallest.

Electron-electron Repulsion

Electron-electron repulsion plays a vital role in defining the size and shape of anions. When additional electrons are added to an atom, making it an anion, these electrons repel each other due to having the same negative charge. This repulsion causes the electron cloud around the nucleus to expand.
As more electrons are added, the repulsion among them increases even if the nuclear attraction also increases due to a greater positive charge in the nucleus. This is why anions typically have larger ionic radii than their parent atoms.
Key points about electron-electron repulsion:

• More electrons mean more repulsion, resulting in a larger ion.
• Greater repulsion spread among electrons increases the space they occupy.
• Balancing the electron repulsion and the attraction from protons is what eventually defines the ionic radius in anions.