Problem 154 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following arrangements, the order is not according to the property indicated against it? \([\mathbf{2 0 0 5}]\) (a) \(\quad 1<\mathrm{Br}<\mathrm{F}<\mathrm{Cl}\) increasing electron gain enthalpy (b) \(\quad \mathrm{Li}<\mathrm{Na}<\mathrm{K}<\mathrm{Rb}\) increasing metallic radius (c) \(\quad \mathrm{B}<\mathrm{C}<\mathrm{N}<\mathrm{O}\) increasing first ionization energy (d) \(\mathrm{Al}^{3+}<\mathrm{Mg}^{2+}<\mathrm{Na}^{+}<\mathrm{F}\) increasing ionic size

Step-by-Step Solution

Answer

Option (a) is incorrect for electron gain enthalpy.

Step 1: Understand the Properties

This exercise tests your understanding of the periodic trends: electron gain enthalpy, metallic radius, first ionization energy, and ionic size. Each option matches a sequence of elements with a claimed trend. We need to analyze if the sequences conform to these trends.

Step 2: Evaluate Electron Gain Enthalpy

Electron gain enthalpy refers to the energy change when an electron is added to a neutral atom. For halogens, generally, the trend is \[ \text{F} > \text{Cl} > \text{Br} > \text{I} \]due to their position in the periodic table. Option (a) claims \[ 1 < \text{Br} < \text{F} < \text{Cl} \]which is not correct because \( \text{F} \) should have the highest electron gain enthalpy.

Step 3: Examine Metallic Radius

Metallic radius increases as you move down a group in the periodic table. Option (b) lists \[ \text{Li} < \text{Na} < \text{K} < \text{Rb} \]which is correct because the metallic radius increases from top to bottom in the alkali metal group.

Step 4: Investigate First Ionization Energy

First ionization energy generally increases across a period due to increasing nuclear charge. Option (c) \[ \text{B} < \text{C} < \text{N} < \text{O} \]is generally correct because ionization energy increases from \(\text{B} \) to \( \text{O} \) across the period.

Step 5: Assess Ionic Size

Ionic size for isoelectronic species decreases with increasing nuclear charge. In option (d):\[ \text{Al}^{3+} < \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^- \]The correct order for increasing ionic size considering increasing nuclear charge is indeed correct.

Step 6: Identify the Incorrect Sequence

Reviewing all the options, the incorrect sequence is in option (a) because the order for electron gain enthalpy should be \( \text{F} > \text{Cl} > \text{Br} > \text{I} \), not \( \text{1} < \text{Br} < \text{F} < \text{Cl} \).

Key Concepts

Electron Gain Enthalpy

Electron Gain Enthalpy refers to the energy change that occurs when an electron is added to a neutral atom in the gaseous state to form a negative ion. It is a key concept when evaluating the reactivity of elements, especially nonmetals. Typically, elements with high negative electron gain enthalpy values are more eager to gain electrons. For halogens, the trend generally follows that

• fluorine (F) has the greatest electron gain enthalpy,
• followed by chlorine (Cl),
• then bromine (Br), and
• finally iodine (I).

Halogens possess a strong desire to gain electrons to achieve a stable electron configuration similar to noble gases. However, note that the trend may vary due to atomic size and electron-electron repulsion in the outer shell, impacting the expected sequence in some cases. In the original exercise, the order presented was not consistent with this periodic trend.

Metallic Radius

The Metallic Radius is defined as half the distance between the nuclei of two atoms of the same element in a metallic lattice. When comparing elements vertically within a group in the periodic table, the metallic radius increases as you move down the group. This happens because:

• New electron shells are added, resulting in increased atomic size.
• Therefore, the outermost electrons are farther from the nucleus.

For example, in the group of alkali metals, the sequence from Lithium (\( ext{Li} \)) to Rubidium (\( ext{Rb} \)) shows a clear increase in metallic radius: \( ext{Li} < ext{Na} < ext{K} < ext{Rb} \). Due to decreasing effective nuclear charge influence over the added shells, atoms tend to become larger down a group.

First Ionization Energy

First Ionization Energy is the amount of energy required to remove the outermost electron from an isolated atom in its gaseous state. As a fundamental property, it reflects an element's propensity to lose electrons. Across a period from left to right in the periodic table, first ionization energy generally increases because:

• The atomic number increases, leading to a higher nuclear charge.
• This higher charge attracts the electrons more strongly.
• Therefore, more energy is needed to remove an electron.

This can be seen in the progression from Boron (\( ext{B} \)) to Oxygen (\( ext{O} \)). Here, the elements generally follow the trend: \( ext{B} < ext{C} < ext{N} < ext{O} \), except for some exceptions due to electron pairing in orbitals, which can affect removal energy.

Ionic Size

Ionic Size refers to the effective size of an ion in a crystal lattice. It is influenced by the ion's charge, the number of electrons, and the atomic structure. When considering isoelectronic species, those ions or atoms with the same number of electrons, the size is impacted by their nuclear charge. An isoelectronic series like \( ext{Al}^{3+} < ext{Mg}^{2+} < ext{Na}^{+} < ext{F}^- \) reflects the fact that:

• Ions with a greater positive charge have a smaller size because the same number of electrons are drawn closer to the nucleus by a stronger positive charge.
• Conversely, adding electrons or having fewer protons per electron generally results in larger ionic sizes.

Understanding these trends helps to predict ion behavior in ionic compounds. Therefore, analyzing ionic sizes requires consideration of both the electron count and the nuclear charge for accurate comparisons.