Problem 38 - A Complete Resource Book in Chemistry for JEE Main

Question

One mole of \(\mathrm{CH}_{4}\) contains (a) \(4.0 \mathrm{~g}\) atoms of hydrogen (b) \(3.0 \mathrm{~g}\) atom of carbon (c) \(6.02 \times 10^{23}\) atoms of hydrogen (d) \(1.81 \times 10^{23}\) molecules of \(\mathrm{CH}_{4}\)

Step-by-Step Solution

Answer

Option (a) is correct: 4.0 g atoms of hydrogen.

Step 1: Determine the Composition of Methane

First, understand that one molecule of methane (\(\text{CH}_4\)) consists of one carbon atom and four hydrogen atoms. This basic information will help to analyze the quantities given in each option.

Step 2: Calculate Moles of Hydrogen and Carbon Atoms

Since one mole of \(\text{CH}_4\) contains 4 hydrogen atoms, it also contains 1 mole of carbon and 4 moles of hydrogen atoms. Therefore, 1 mole of \(\text{CH}_4\) contains\(4 \times 6.02 \times 10^{23} = 2.408 \times 10^{24}\) hydrogen atoms.

Step 3: Evaluate Option A: 4.0 g Atoms of Hydrogen

1 mole of hydrogen atoms weighs 1 gram, so 4 moles of \(\text{H}\) atoms weigh \(4 \text{ g}\). Hence, option (a) is correct as one mole of \(\text{CH}_4\) does indeed contain 4.0 g atoms of hydrogen.

Step 4: Evaluate Option B: 3.0 g Atoms of Carbon

1 mole of carbon atoms weighs 12 g, not 3 g. Hence, option (b) is incorrect since one mole of \(\text{CH}_4\) contains 1 mole of carbon or 12 g atoms.

Step 5: Evaluate Option C: 6.02 x 10^23 Atoms of Hydrogen

Option (c) is incorrect because one mole of \(\text{CH}_4\) contains \(4 \times 6.02 \times 10^{23}\) hydrogen atoms, which equals\(2.408 \times 10^{24}\) hydrogen atoms.

Step 6: Evaluate Option D: 1.81 x 10^23 Molecules of CH4

Since one mole of any substance contains \(6.02 \times 10^{23}\) molecules, option (d) is incorrect. One mole of \(\text{CH}_4\) contains \(6.02 \times 10^{23}\) molecules, not \\(1.81 \times 10^{23}\).

Key Concepts

Mole Concept

The mole concept is fundamental in chemistry, acting as a bridge between the microscopic world of atoms and molecules and the macroscopic world that we can measure. A mole is a unit that denotes a specific quantity: 6.022 x 10^23 entities, whether they be atoms, molecules, or ions. This number is known as Avogadro's number, serving as a method to quantify atoms and molecules in a way that's understandable and workable. In exercises involving chemical compounds like methane (0CH_41), understanding the mole concept allows us to comprehend how many constituent atoms are present in a single mole. One mole of 0CH_41 contains one mole of carbon atoms and four moles of hydrogen atoms. This means that in a mole of 0CH_41, we find exactly 6.022 x 10^23 carbon atoms and 4 x 6.022 x 10^23 hydrogen atoms. Through this understanding, scientists can easily calculate the mass and number of atoms or molecules in a given sample.

Atomic Mass

Atomic mass is a crucial concept when dealing with chemical calculations, as it provides the mass of an atom. Expressed in atomic mass units (amu), it is generally equivalent to the number of protons and neutrons in an atom since electrons have negligible mass. For chemical reactions, it becomes essential because it helps in understanding the mass relations between different elements involved. Consider carbon, which has an atomic mass of approximately 12 amu. This informs us that one mole of carbon atoms weighs about 12 grams. Similarly, hydrogen has an atomic mass of about 1 amu, so one mole of hydrogen atoms weighs approximately 1 gram. By applying this knowledge in stoichiometry, we can determine the amount of substance necessary for reactions, allowing for the conversion between mass, moles, and number of atoms.

Avogadro's Number

Avogadro's number is a cornerstone of chemical quantification, intrinsically linked to the mole concept. Named after the scientist Amedeo Avogadro, this number—6.022 x 10^23—is the quantity of atoms, molecules, or ions in one mole of a substance, providing a connection between the macroscopic and atomic scales. When working with Avogadro's number, understanding that it applies universally to all substances is key. For example, in the context of the molecule methane (0CH_41), one mole of methane equates to 6.022 x 10^23 molecules of 0CH_41. Each of these molecules contains five total atoms—one carbon and four hydrogens—so multiplying Avogadro's number by the counts of each gives the total number of individual atoms present. By grasping the significance of Avogadro's number and how it facilitates calculations, students can effectively relate molecular formulas to tangible amounts, furthering their understanding of chemical substance quantification.