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.

Step 1: Understand the Mole Concept

A mole of any substance contains Avogadro's number of molecules, approximately \(6.022 \times 10^{23}\). The mass of one mole of a chemical compound in grams is equal to its molecular weight.

Step 2: Calculate Molecular Weight

The molecular weight of \(\mathrm{O}_3\) (ozone) is the sum of the atomic weights of its constituent atoms. Each oxygen atom has an atomic weight of approximately \(16\) grams/mole. Hence, the molecular weight of \(\mathrm{O}_3\) is \(3 \times 16 = 48\) grams/mole.

Step 3: Find Mass Using Given Moles

We need to find the mass of \(0.5\) moles of \(\mathrm{O}_3\). Using the formula: \( \text{Mass} = \text{Number of moles} \times \text{Molecular weight} \), substitute the values: \( \text{Mass} = 0.5 \times 48 = 24 \text{ grams} \).

Key Concepts

Molecular Weight Calculation

Molecular weight calculation is an essential step in determining the amount of a substance based on its molecular composition. To calculate the molecular weight of a compound, you simply add up the atomic weights of all the atoms that make up that compound. For example, ozone \(\mathrm{O}_{3}\) consists of three oxygen atoms. Each oxygen atom has an atomic weight of approximately 16 grams per mole. Thus, the molecular weight of ozone is calculated as \(3 \times 16 = 48\) grams per mole. Understanding this calculation allows us to link the number of molecules to the corresponding mass in grams easily.

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry, usually represented as \(6.022 \times 10^{23}\). This large number is used to count the number of particles, such as atoms or molecules, in one mole of a substance. The mole concept links microscopic quantities of substances to macroscopic amounts that can be measured directly. Using Avogadro's number helps chemists convert between the number of molecules and the amount in moles, making it easier to work with macroscopic materials. Knowing the number of molecules through Avogadro's number allows us to calculate the mass using the molecular weight of the compound, which is critical in laboratory and industrial settings.

Ozone Molecules

Ozone molecules, denoted as \(\mathrm{O}_{3}\), are made up of three oxygen atoms. This molecule is important in protecting life on Earth by absorbing the majority of the sun's harmful ultraviolet radiation in the stratosphere. When calculating the mass of ozone, one must take into account its structure of three oxygen atoms, leading to its molecular weight of 48 grams per mole. When working with moles of ozone, it becomes easy to determine the mass by multiplying the number of moles by its molecular weight. For instance, for half a mole of ozone, the mass is calculated as \(0.5 \times 48 = 24\) grams, which illustrates the straightforward connection between molecular composition and mass in practical calculations.