Problem 131 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of gram molecules of oxygen in \(6.02 \times\) \(10^{24}\) CO molecules is (a) \(10 \mathrm{~g}\) molecules (b) \(5 \mathrm{~g}\) molecules (c) l g molecules (d) \(0.5 \mathrm{~g}\) molecules

Step-by-Step Solution

Answer

(a) 10 g molecules

Step 1: Understanding Gram Molecules

A gram molecule, also known as a mole, is the amount of a substance that contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). In this context, gram molecules refer to moles.

Step 2: Relating CO molecules to Oxygen Atoms

Each CO molecule contains one oxygen atom. Thus, the number of oxygen atoms is equal to the number of CO molecules.

Step 3: Calculate Moles of Oxygen Atoms

Divide the given number of CO molecules by Avogadro's number to find the number of moles of oxygen atoms: \[\frac{6.02 \times 10^{24}}{6.022 \times 10^{23}} = 10 \text{ moles}\]

Step 4: Conclusion from Calculations

Since we have calculated that there are 10 moles (gram molecules) of oxygen atoms, the answer that corresponds to this result is option (a) \(10 \mathrm{~g}\) molecules.

Key Concepts

Mole Concept

The concept of a "mole" is central to understanding quantities in chemistry. A mole is a unit of measurement that helps chemists quantify large numbers of small entities, such as atoms or molecules, just as the dozen does for eggs. One mole of any substance contains exactly Avogadro's number of entities, which is essential for chemical calculations.

This number provides a link between the atomic scale and the macroscopic scale. In the context of the given exercise, we deal with moles of oxygen in carbon monoxide (CO) molecules.

Each CO molecule includes one oxygen atom. To determine how many moles of oxygen are present in a large number of CO molecules, you use Avogadro's number to convert those molecules into moles.

Avogadro's Number

Avogadro's number is a key part of stoichiometry, providing the basis for converting between atomic-scale measurements and more manageable units. This is a fixed number, precisely defined as the number of atoms, molecules, ions, or other entities in a mole, which is approximately \(6.022 \times 10^{23}\). This immense number helps chemists scale up the atomic world to laboratory scale.

When we count entities like molecules in a given sample, Avogadro's number becomes a useful tool for expressing the quantity in moles. In the given exercise, converting \(6.02 \times 10^{24}\) CO molecules into moles of oxygen atoms is achieved by dividing by Avogadro's number.

This division converts the large number of molecules into a more manageable number representing moles, illustrating the practicality of using Avogadro's concept in chemical calculations.

Chemical Calculations

Chemical calculations often involve translating between different units and scales. In our exercise, these calculations transform molecular counts into moles. This process is vital in practical chemistry, allowing us to quantify substances based on their molecular or atomic compositions.

By using the number of CO molecules, we can calculate the number of moles of oxygen atoms. This is achieved through the relation that each CO molecule contains one oxygen atom.

The calculation \[\frac{6.02 \times 10^{24}}{6.022 \times 10^{23}} = 10\]yields 10 moles of oxygen atoms, equating to 10 gram molecules. This example shows how chemical calculations enable the practical application of theoretical concepts, bridging the gap between microscopic particles and measurable quantities.