Problem 2 - A Complete Resource Book in Chemistry for JEE Main

Question

What is the mass of \(0.5\) moles of \(\mathrm{O}_{3}\) molecules? (a) \(16 \mathrm{gm}\) (b) \(20 \mathrm{gm}\) (c) \(40 \mathrm{gm}\) (d) \(24 \mathrm{gm}\)

Step-by-Step Solution

Answer

The mass of 0.5 moles of \(\mathrm{O}_{3}\) is 24 grams (d).

Step 1: Understand the Problem

We need to find the mass of 0.5 moles of ozone (\(\mathrm{O}_{3}\)). The mass of one mole of a compound is its molar mass, given in grams per mole (\(\text{g/mol}\)). First, we must find the molar mass of ozone.

Step 2: Calculate Molar Mass of Ozone

Ozone is composed of three oxygen atoms. The atomic mass of oxygen is approximately \(16 \text{ g/mol}\). Calculate the molar mass of ozone by multiplying the atomic mass of oxygen by the number of atoms in an ozone molecule: \[3 \times 16\text{ g/mol} = 48 \text{ g/mol}\].

Step 3: Calculate Mass of 0.5 Moles of Ozone

To find the mass of 0.5 moles of ozone, use the formula:\[\text{Mass} = \text{moles} \times \text{molar mass}\].Substitute the known values:\[0.5 \text{ moles} \times 48 \text{ g/mol} = 24 \text{ grams}\].

Step 4: Choose the Correct Answer

The calculated mass of 0.5 moles of ozone is \(24 \text{ grams}\). Thus, among the given options, option (d) \(24 \text{ gm}\) is the correct answer.

Key Concepts

Mole Concept

The mole concept is a fundamental idea in chemistry that helps us count and measure atoms, molecules, and ions through converting between the mass of a sample and the number of particles it contains. It's like a bridge between the microscopic world of atoms and molecules and our macroscopic world. This concept revolves around the quantity known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\). Avogadro's number represents the number of particles in one mole of any substance.

Understanding moles allows chemists to discuss and manipulate chemical formulas and reactions in a practical way. When we say we have one mole of a substance, we are talking about having \(6.022 \times 10^{23}\) of whatever particles make up that substance (atoms, molecules, or ions). This simplifies calculations and helps us relate the mass of a substance to an amount of substance in terms of number of atoms or molecules.

Chemical Calculations

Chemical calculations involve a variety of methods to determine quantities of substances involved in chemical reactions and processes. Molar mass plays a critical role in these calculations. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule. This concept is crucial for predicting how substances will react and the amounts needed or produced.

For example, if you want to find the mass of 0.5 moles of ozone (\(\mathrm{O}_3\)), you first need its molar mass. You calculate this by multiplying the atomic mass of oxygen (16 g/mol) by the three atoms in \(\mathrm{O}_3\), resulting in a molar mass of 48 g/mol. With this information, you can then use the formula:

• \( \text{Mass} = \text{moles} \times \text{molar mass} \)

Using this formula, \(0.5\) moles times \(48\) g/mol equals \(24\) grams, helping you determine the mass of 0.5 moles of ozone easily.

Ozone Molecule

The ozone molecule is a triatomic form of oxygen, signified by its chemical formula \(\mathrm{O}_3\). Ozone is known for its natural presence in the Earth's stratosphere, forming the ozone layer, which is crucial for shielding the planet from harmful ultraviolet radiation.

At the molecular level, an ozone molecule contains three oxygen atoms, making it different from the standard diatomic oxygen (\(\mathrm{O}_2\)) we commonly interact with. Each oxygen atom in ozone contributes an atomic mass of approximately 16 g/mol. Therefore, when calculating the molar mass of ozone, we multiply the atomic mass (16 g/mol) by three. Understanding the structure and mass of the ozone molecule is vital for various practical applications. From environmental science, where it's studied for its effects and importance in our atmosphere, to medical fields where its reactive properties are considered for sanitation and treatment processes, the understanding of ozone is multi-faceted and essential.