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) \(2.4 \mathrm{~N}_{\Lambda}\) (d) \(1.2 \mathrm{~N}_{\mathrm{A}}\)

Step-by-Step Solution

Answer

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

Step 1: Find the molar mass of nitride ion

The nitride ion is represented as \( \text{N}^{3-} \), which is essentially a nitrogen atom with three additional electrons. The atomic mass of a nitrogen atom is approximately 14 g/mol.

Step 2: Calculate the number of moles of nitride ions

To find the number of moles, use the formula \( \text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} \). For 4.2 g of \( \text{N}^{3-} \), the calculation is: \[ \text{Moles of } \text{N}^{3-} = \frac{4.2}{14} = 0.3 \text{ moles} \]

Step 3: Determine the total number of nitride ions

Multiply the number of moles by Avogadro's number \( \mathrm{N}_{\mathrm{A}} = 6.022 \times 10^{23} \text{ ions/mol} \). Thus, the total number of nitride ions is: \[ 0.3 \times \mathrm{N}_{\mathrm{A}} \]

Step 4: Calculate number of valence electrons in nitride ions

Each \( \text{N}^{3-} \) ion has 8 electrons (5 in the valence shell normally for nitrogen, plus 3 added for \( \text{N}^{3-} \)). Thus, the number of valence electrons in all ions is: \[ (0.3 \times \mathrm{N}_{\mathrm{A}}) \times 8 \] which simplifies to \( 2.4 \mathrm{N}_{\mathrm{A}} \).

Key Concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry. It refers to the mass of one mole of a substance, commonly expressed in grams per mole (g/mol). For elements, the molar mass is the atomic mass expressed in g/mol.
For compounds, it's the sum of the atomic masses of its constituent elements, also indicated in g/mol.
This value is crucial for converting between the mass of a substance and its amount in moles.

• Example: The molar mass of nitrogen (N) is approximately 14 g/mol.
• For a compound, like water (H₂O), it's calculated by adding twice the atomic mass of hydrogen (approximately 1 g/mol) and the atomic mass of oxygen (approximately 16 g/mol), resulting in 18 g/mol.

Exploring the Nitride Ion

The nitride ion, represented as \( \text{N}^{3-} \), is derived from a nitrogen atom that has gained three electrons.
This gaining of electrons occurs because nitrogen originally has five electrons in its valence shell, and by gaining three more, it reaches a stable electronic configuration similar to that of neon.

• The extra electrons give it a negative charge of 3-, hence the notation \( \text{N}^{3-} \).
• It is important to note that ions like \( \text{N}^{3-} \) are commonly found in ionic compounds, where they pair with positive ions to form a stable structure.

Counting Valence Electrons

Valence electrons play a key role in chemical bonding and reactions. They are the outermost electrons of an atom and determine how an atom will interact with others.
Nitrogen, in its neutral form, has five valence electrons.

• For \( \text{N}^{3-} \), there are five valence electrons from nitrogen plus three additional electrons, making a total of eight valence electrons.
• This configuration allows \( \text{N}^{3-} \) to have a full outer shell, which is a desirable state in terms of stability.
• Understanding the count of valence electrons is essential for predicting and explaining chemical bonding and reactivity.

Mastering Moles Calculation

The mole is a standard unit for amount of substance in chemistry. One mole contains exactly Avogadro's number of particles, which is approximately \( 6.022 \times 10^{23} \) particles.
To convert between mass and moles, the equation \( \text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} \) is used.

• Step-by-step: For 4.2 g of \( \text{N}^{3-} \), given its molar mass is 14 g/mol, the moles calculation is \( \frac{4.2}{14} \), resulting in 0.3 moles.
• This calculation is crucial for further determining the number of ions or atoms present by multiplying the moles by Avogadro's number.

Calculating moles is an essential skill for solving many chemical problems.