Problem 62 - A Complete Resource Book in Chemistry for JEE Main

Question

If \(\mathrm{N}_{\mathrm{A}}\) is Avogadro's number then number of valence electrons in \(4.2 \mathrm{~g}\) of nitride ions \(\left(\mathrm{N}^{3}\right)\) is (a) \(3.2 \mathrm{~N}_{\mathrm{A}}\) (b) \(1.6 \mathrm{~N}_{\mathrm{A}}\) (c) \(2.4 \mathrm{~N}_{\mathrm{A}}\) (d) \(1.2 \mathrm{~N}_{\mathrm{A}}\)

Step-by-Step Solution

Answer

The correct answer is (c) \(2.4\, \text{N}_{\text{A}}\).

Step 1: Understanding the Ion

First, we need to understand what a nitride ion \( \text{N}^{3-} \) is. A nitride ion is a nitrogen atom that has gained 3 extra electrons. In its neutral state, nitrogen has 5 valence electrons (it's in Group 15 of the periodic table). Upon gaining 3 electrons, a nitride ion will have a total of \( 5 + 3 = 8 \) valence electrons.

Step 2: Calculate Moles of Nitride Ions

Let's find the number of moles of nitride ions in \( 4.2 \, \text{g} \) of \( \text{N}^{3-} \). The atomic mass of nitrogen is approximately \( 14 \, \text{g/mol} \). Therefore, the number of moles is given by:\[ \text{Moles of } \text{N}^{3-} = \frac{4.2 \text{ g}}{14 \text{ g/mol}} = 0.3 \text{ moles}. \]

Step 3: Find Total Number of Valence Electrons

Each nitride ion \( \text{N}^{3-} \) has 8 valence electrons, as calculated earlier. To find the total number of valence electrons, multiply the number of moles by Avogadro's number \( \text{N}_{\text{A}} \) and then multiply by the number of valence electrons per ion:\[ 0.3 \text{ moles} \times \text{N}_{\text{A}} \times 8 \text{ valence electrons/mole} = 2.4 \text{N}_{\text{A}} \text{ valence electrons}. \]

Step 4: Complete the Answer

Based on the calculation, the total number of valence electrons in \( 4.2 \, \text{g} \) of nitride ions is \( 2.4 \, \text{N}_{\text{A}} \). Comparing this to the given options, it matches option (c).

Key Concepts

Nitride Ion

A nitride ion is derived from a nitrogen atom, which is an element famously known for being crucial in both biology and atmospheric science. In its neutral state, nitrogen, located in Group 15 of the periodic table, possesses five valence electrons. However, when it gains three electrons, it forms the nitride ion, represented as \( \text{N}^{3-} \). This gain of electrons is critical as it fills its outer electron shell, leading to a stable configuration. The gaining of these electrons results in the nitride ion having a total of eight valence electrons. This is important because the valence electrons are the ones that participate in interactions with other atoms and ions. Understanding the concept of a nitride ion is foundational for exploring its chemical behavior and properties, especially in various compounds.

Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom. These electrons are vital since they determine how an atom interacts with others, playing a crucial role in the formation of chemical bonds. In the case of the nitrogen atom, it has five valence electrons in its neutral state. However, when nitrogen forms a nitride ion, it gains three additional electrons. This results in a total of eight valence electrons for the nitride ion. As a rule of thumb, elements aim to fill their outer electron shell to achieve stability, often following the octet rule, meaning they prefer to have eight electrons in their valence shell. This rule is significant in understanding the chemical behavior of elements, especially non-metals like nitrogen, as they tend to gain or share electrons during reactions to achieve such stability.

Moles Calculation

Calculating moles is fundamental in chemistry as it allows us to quantitatively understand the amount of a substance. The concept of moles connects the microscopic world of atoms and molecules to the macroscopic world we interact with. For nitrogen, with an atomic mass of approximately \( 14 \, \text{g/mol} \), we calculate moles by dividing the mass of the substance by its molar mass. In the example exercise, 4.2 grams of nitride ions are provided. To find the moles of \( \text{N}^{3-} \), the formula used is: \[ \text{Moles of } \text{N}^{3-} = \frac{4.2 \, \text{g}}{14 \, \text{g/mol}} = 0.3 \, \text{moles}. \] This result tells us that there are 0.3 moles of nitride ions in the sample. Understanding how to perform these calculations is essential when working with chemical equations and reactions.

Periodic Table

The periodic table is a remarkable tool used by chemists as it organizes all the known elements according to their atomic number, electron configurations, and recurring chemical properties. Nitrogen, the precursor to the nitride ion, is found in Group 15. This group is characterized by having five valence electrons, a key aspect in defining their chemical behavior. Elements in the same group often exhibit similar chemical properties. Therefore, learning to navigate the periodic table not only helps in determining the properties of an element like nitrogen but also in predicting how it might behave in chemical reactions. The periodic trends, such as electronegativity, atomic size, and ionization energy, further aid in understanding the nature of elements like nitrogen and its ions.