Problem 66 - A Complete Resource Book in Chemistry for JEE Main

Question

Number of atoms in \(4.25 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) is approximately (a) \(6 \times 10^{23}\) (b) \(15 \times 10^{23}\) (c) \(1.5 \times 10^{23}\) (d) \(2.5 \times 10^{23}\)

Step-by-Step Solution

Answer

The number of atoms in 4.25 g of NH3 is approximately \(6 \times 10^{23}\).

Step 1: Find Molar Mass of Ammonia

Ammonia (NH) consists of 1 nitrogen and 3 hydrogen atoms. The atomic mass of nitrogen (N) is approximately 14.01 u and that of hydrogen (H) is about 1.01 u. Thus, the molar mass of ammonia is calculated as follows:\[ \text{Molar mass of } \mathrm{NH}_3 = (1 \times 14.01) + (3 \times 1.01) = 14.01 + 3.03 = 17.04 \, \text{g/mol} \]

Step 2: Calculate Moles of Ammonia

To find the number of moles of ammonia in 4.25 g, use the formula:\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]\[ \text{moles of } \mathrm{NH}_3 = \frac{4.25}{17.04} \approx 0.249 \text{ mol} \]

Step 3: Compute Number of Molecules

Utilize Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole, to find the total number of ammonia molecules:\[ \text{number of molecules} = 0.249 \times 6.022 \times 10^{23} \approx 1.50 \times 10^{23} \text{ molecules} \]

Step 4: Calculate Number of Atoms

Since each molecule of ammonia (\(\mathrm{NH}_3\)) contains 4 atoms (1 nitrogen + 3 hydrogen), the total number of atoms present is:\[ 1.50 \times 10^{23} \times 4 = 6.0 \times 10^{23} \text{ atoms} \]

Key Concepts

Molar Mass

When considering chemical substances, the molar mass is a fundamental concept to understand. Molar mass is the mass of one mole of a given substance, typically expressed in grams per mole (g/mol). To find the molar mass of a compound like ammonia (NH extsubscript{3}), you must sum the atomic masses of all atoms present in the molecule.
For ammonia, it contains one nitrogen atom and three hydrogen atoms. The atomic mass of nitrogen is approximately 14.01 atomic mass units (u), and each hydrogen atom is about 1.01 u. Thus, the molar mass of NH extsubscript{3} can be calculated as:

• 14.01 (from N) + 3 × 1.01 (from H) = 17.04 g/mol.

This value is crucial for determining how many moles of ammonia are present in a given amount of mass, such as 4.25 grams.

Moles Calculation

Once you know the molar mass of a compound, you can calculate the number of moles present in a sample. The calculation connects the mass of the substance to the number of moles.
To find the moles of ammonia in a 4.25 gram sample, use the formula:

• \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \)

For NH extsubscript{3}, the moles calculation is:

• \( \text{moles of NH}_3 = \frac{4.25}{17.04} \approx 0.249 \text{ mol} \)

This tells us that the sample contains approximately 0.249 moles of ammonia molecules.

Ammonia Molecules

The number of individual molecules in a substance can be determined by using Avogadro's number. Avogadro's number is a constant that defines how many entities (usually atoms or molecules) are in one mole of a substance, approximately \(6.022 \times 10^{23}\) molecules per mole.
Knowing there are about 0.249 moles of ammonia in the sample, we calculate the number of molecules:

• \( \text{number of molecules} = 0.249 \times 6.022 \times 10^{23} \approx 1.50 \times 10^{23} \text{ molecules} \)

This result helps us understand the vast number of ammonia molecules present even in a small sample, showcasing the significance of Avogadro's number.

Number of Atoms

Each molecule of ammonia (NH extsubscript{3}) is made up of one nitrogen atom and three hydrogen atoms, totaling four atoms per molecule. To find the total number of atoms in a sample, multiply the number of molecules by the number of atoms per molecule.
Given that the number of ammonia molecules is approximately \(1.50 \times 10^{23}\), we calculate the total number of atoms:

• \( 1.50 \times 10^{23} \times 4 = 6.0 \times 10^{23} \text{ atoms} \)

This demonstrates how a seemingly small sample mass can contain an enormous number of atoms, emphasizing the scale at which chemical reactions and molecular interactions occur.