Problem 77 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of molecules in \(4.25 \mathrm{~g}\) of ammonia is (a) \(1.5 \times 10^{23}\) (b) \(2.5 \times 10^{23}\) (c) \(3.5 \times 10^{23}\) (d) \(15 \times 10^{23}\)

Step-by-Step Solution

Answer

(a) \(1.5 \times 10^{23}\) molecules.

Step 1: Determine Molar Mass of Ammonia

Ammonia is denoted by the chemical formula \( ext{NH}_3\). Calculate the molar mass by adding the atomic masses of nitrogen (N) and hydrogen (H). The atomic mass of nitrogen is approximately \(14 ext{ g/mol}\) and that of hydrogen is \(1 ext{ g/mol}\). Therefore, the molar mass of ammonia is \(14 + 3 imes 1 = 17 ext{ g/mol}\).

Step 2: Calculate Moles of Ammonia

To determine the moles of ammonia, use the formula \( ext{moles} = \frac{ ext{mass in grams}}{ ext{molar mass}}\). Substitute the known values: \( ext{moles of NH}_3 = \frac{4.25 ext{ g}}{17 ext{ g/mol}} = 0.25 ext{ moles}.\)

Step 3: Use Avogadro's Number

Avogadro's number, \(6.022 imes 10^{23}\), is the number of molecules in one mole of a substance. Multiply the number of moles of ammonia by Avogadro's number to find the number of molecules: \(0.25 imes 6.022 imes 10^{23} = 1.5055 imes 10^{23}\) molecules.

Step 4: Select the Correct Answer

Compare the calculated number of molecules \(1.5055 imes 10^{23}\) with the given options. The closest option is \(1.5 imes 10^{23}\), which corresponds to option (a).

Key Concepts

Molecular Mass Calculation

To find the molecular mass of a compound, you add up the atomic masses of all the atoms in its formula. Let's take ammonia, which is represented by \(\text{NH}_3\). This chemical formula indicates that ammonia consists of one nitrogen atom and three hydrogen atoms.

• Nitrogen (N) has an atomic mass of approximately \(14\, \text{g/mol}\).
• Hydrogen (H) has an atomic mass of about \(1\, \text{g/mol}\), and we have three of them.

Thus, the molecular mass of ammonia is calculated as follows:
\[\text{Molecular mass of } \text{NH}_3 = 14 + 3 \times 1 = 17\, \text{g/mol}.\]
Understanding how to calculate molecular mass is essential, as it allows us to convert between grams and moles, laying the groundwork for further calculations in chemistry.

Mole Concept

The mole concept is a fundamental chemical principle that relates the mass of a substance to the number of entities, such as atoms, molecules, or ions, in that mass. It acts like a bridge between the atomic world and the macroscopic world. Here's how it works:
One mole of any substance contains \(6.022 \times 10^{23}\) entities, and this is known as Avogadro's Number. In calculations, converting between grams and moles involves using the molecular mass of the substance. The formula to find the number of moles is:
\[\text{Moles} = \frac{\text{mass in grams}}{\text{molar mass}}.\]
For example, by using this conversion formula, we determined that \(4.25\) grams of ammonia is equivalent to \(0.25\) moles. Knowing this conversion can greatly simplify solving chemical equations and understanding reactions.

Ammonia Chemistry

Ammonia, \(\text{NH}_3\), is a vital compound in chemistry, agriculture, and industry. It is a colorless gas with a distinctive pungent smell and plays a significant role as a precursor to various fertilizers.

Properties and Uses

Ammonia is composed of one nitrogen atom and three hydrogen atoms, forming a triangular pyramidal shape. It is highly soluble in water, forming ammonium hydroxide, a key reactant in many chemical reactions.

• In agriculture, it is essential for making nitrogen fertilizers.
• In industry, it serves as a refrigerant and in the production of plastics, explosives, and cleaning agents.

Importance in Chemistry

Understanding ammonia's chemistry and molecular structure allows chemists to manipulate it for various applications and create derivatives.
Ammonia also provides an excellent example of applying the mole concept and molecular mass calculation, essential tools in any chemist's toolkit.