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 (b) represents the correct increasing order of ionic radii: \(O^{2-}<\mathrm{N}^{3-}<\mathrm{S}^{2-}<\mathrm{P}^{3-}\).

Step 1: Understand Ionic Radii

Ionic radius refers to the size of an ion and is determined by the number of electrons around the nucleus. More negative charge usually means more electrons and a larger ionic radius due to increased electron-electron repulsion.

Step 2: Analyze the Species

The given ions are: \(O^{2-}\), \(S^{2-}\), \(N^{3-}\), and \(P^{3-}\). These ions are part of groups 15 and 16 and all are isoelectronic with a noble gas. The isoelectronic series follow the principle that within a series, as the nuclear charge increases, the ionic radius decreases.

Step 3: Compare Species Electronically

All ions have the same electron configuration but different numbers of protons. \(N^{3-}\) has the fewest protons and weakest attraction which makes it largest. \(O^{2-}\) has more protons than \(N^{3-}\) but fewer than \(S^{2-}\) and \(P^{3-}\). \(P^{3-}\) has the most protons.

Step 4: Determine Ionic Radii Order

Based on the number of protons, the ionic radii order from smallest to largest should be \(O^{2-} < S^{2-} < N^{3-} < P^{3-}\). More protons mean a smaller ionic radius due to stronger nuclear pull.

Step 5: Match with Given Options

Given the calculated order, compare with the options: (a) \(\mathrm{S}^{2-}<\mathrm{P}^{3-}<\mathrm{N}^{3-}<0^{2-}\), (b) \(O^{2-}<\mathrm{N}^{3-}<\mathrm{S}^{2-}<\mathrm{P}^{3-}\), (c) \(O^{2-}<\mathrm{P}^{3-}<\mathrm{N}^{3-}<\mathrm{S}^{-2}\), (d) \(\mathrm{N}^{3-}<\mathrm{S}^{2-}

Key Concepts

Isoelectronic Species

Isoelectronic species are ions or atoms that have the same number of electrons, and therefore the same electron configuration. Even though they have the same electron count, they differ in the number of protons. For example, in our problem, ions such as \( O^{2-} \), \( S^{2-} \), \( N^{3-} \), and \( P^{3-} \) are all isoelectronic.
Each of these ions has the electron configuration resembling the nearest noble gas configuration, which is \([Ne]\) or \([Ar]\). Isoelectronic species help us understand reactions and properties based on their tendency to gain or lose electrons to achieve a stable arrangement.
In such a series, although the number of electrons remains constant, changes in nuclear charge due to varying numbers of protons can influence their chemical behavior and physical attributes such as ionic radii.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom or ion's atomic orbitals. It determines many chemical properties and interactions. An isoelectronic series, such as the one presented, means that even with different elements, the species share similar electron configurations.
For \( N^{3-} \), \( O^{2-} \), \( S^{2-} \), and \( P^{3-} \), they all attain electronic structures similar to noble gases. \( N^{3-} \) would have the configuration: \( 1s^2 2s^2 2p^6 \). Similarly, \( O^{2-}, S^{2-}, \) and \( P^{3-} \) end up in the configuration equivalent to \([Ne]\) or transition to \([Ar]\).
These consistent electron configurations result in a set of ions that are chemically stable, but their ionic radii differ due to differences in their nuclear charge.

Nuclear Charge Effect

The nuclear charge effect is an intrinsic property of atoms that affects their size and behavior. It involves the positive charge of the nucleus due to protons, which impacts the attraction it can exert on surrounding electrons.
In an isoelectronic series, such as \( N^{3-}, O^{2-}, S^{2-}, \) and \( P^{3-} \), even though their electron configurations are similar, the total number of protons varies. This directly influences their ionic radii. A higher nuclear charge, i.e., more protons, usually exerts a stronger attraction on electrons, pulling them closer and resulting in a smaller ion.

• \( N^{3-} \) has fewer protons, therefore a weaker pull, and hence a larger ionic radius.
• \( P^{3-} \) has more protons, exerting greater pull, which reduces its ionic size compared to others in the series.

Understanding this effect helps in predicting how atoms will interact with each other chemically.

Electron-Electron Repulsion

When negatively charged electrons are present within an atom or ion, they naturally repel each other. This electron-electron repulsion plays a critical role in determining the size of an ion. The more electrons present, the higher the repulsion, which often increases the overall ionic radius.
For isoelectronic species like \( N^{3-}, O^{2-}, S^{2-}, \) and \( P^{3-} \), the number of electrons is constant. However, the differences in nuclear charge bring us back to the interplay of repulsion versus attraction.

• A reduced effective nuclear attraction due to fewer protons, like in \( N^{3-} \), results in less control over electron distribution, causing larger ionic radii.
• In contrast, for \( P^{3-} \), despite the same electron numbers, the increased nuclear charge effectively counteracts electron repulsion, leading to a more compact size.

This delicate balance between electron-electron repulsion and nuclear attraction is vital in shaping the ionic size and, therefore, their chemical properties.

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Problem 159

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Problem 162

Other exercises in this chapter

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

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 162

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

View solution

Problem 157

The set representing the correct order of ionic radius is: \(\quad\) (a) \(\mathrm{Na}^{+}>\mathrm{Li}^{+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (b) \(\mathrm{Li}

View solution

Key Concepts

Isoelectronic Species

Isoelectronic species are ions or atoms that have the same number of electrons, and therefore the same electron configuration. Even though they have the same electron count, they differ in the number of protons. For example, in our problem, ions such as \( O^{2-} \), \( S^{2-} \), \( N^{3-} \), and \( P^{3-} \) are all isoelectronic.
Each of these ions has the electron configuration resembling the nearest noble gas configuration, which is \([Ne]\) or \([Ar]\). Isoelectronic species help us understand reactions and properties based on their tendency to gain or lose electrons to achieve a stable arrangement.
In such a series, although the number of electrons remains constant, changes in nuclear charge due to varying numbers of protons can influence their chemical behavior and physical attributes such as ionic radii.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom or ion's atomic orbitals. It determines many chemical properties and interactions. An isoelectronic series, such as the one presented, means that even with different elements, the species share similar electron configurations.
For \( N^{3-} \), \( O^{2-} \), \( S^{2-} \), and \( P^{3-} \), they all attain electronic structures similar to noble gases. \( N^{3-} \) would have the configuration: \( 1s^2 2s^2 2p^6 \). Similarly, \( O^{2-}, S^{2-}, \) and \( P^{3-} \) end up in the configuration equivalent to \([Ne]\) or transition to \([Ar]\).
These consistent electron configurations result in a set of ions that are chemically stable, but their ionic radii differ due to differences in their nuclear charge.

Nuclear Charge Effect

The nuclear charge effect is an intrinsic property of atoms that affects their size and behavior. It involves the positive charge of the nucleus due to protons, which impacts the attraction it can exert on surrounding electrons.
In an isoelectronic series, such as \( N^{3-}, O^{2-}, S^{2-}, \) and \( P^{3-} \), even though their electron configurations are similar, the total number of protons varies. This directly influences their ionic radii. A higher nuclear charge, i.e., more protons, usually exerts a stronger attraction on electrons, pulling them closer and resulting in a smaller ion.

• \( N^{3-} \) has fewer protons, therefore a weaker pull, and hence a larger ionic radius.
• \( P^{3-} \) has more protons, exerting greater pull, which reduces its ionic size compared to others in the series.

Understanding this effect helps in predicting how atoms will interact with each other chemically.

Electron-Electron Repulsion

When negatively charged electrons are present within an atom or ion, they naturally repel each other. This electron-electron repulsion plays a critical role in determining the size of an ion. The more electrons present, the higher the repulsion, which often increases the overall ionic radius.
For isoelectronic species like \( N^{3-}, O^{2-}, S^{2-}, \) and \( P^{3-} \), the number of electrons is constant. However, the differences in nuclear charge bring us back to the interplay of repulsion versus attraction.

• A reduced effective nuclear attraction due to fewer protons, like in \( N^{3-} \), results in less control over electron distribution, causing larger ionic radii.
• In contrast, for \( P^{3-} \), despite the same electron numbers, the increased nuclear charge effectively counteracts electron repulsion, leading to a more compact size.

This delicate balance between electron-electron repulsion and nuclear attraction is vital in shaping the ionic size and, therefore, their chemical properties.