Problem 4 - A Complete Resource Book in Chemistry for JEE Main

Question

A mole of any substance is related to (a) number of particles (b) volume of gaseous substances (c) mass of a substance (d) all of these

Step-by-Step Solution

Answer

A mole relates to (d) all of these: number of particles, volume of gases, and mass.

Step 1: Understanding the Mole Concept

A mole is a fundamental unit in chemistry used to express amounts of a chemical substance. One mole is defined as exactly 6.02214076 × 10²³ elementary entities (atoms, molecules, ions, etc.). This number is known as Avogadro's number.

Step 2: Analyzing each option

We need to determine how a mole relates to particles, volume, and mass: - (a) Number of particles: A mole directly represents a specific number of particles, which is Avogadro's number. - (b) Volume of gaseous substances: One mole of any gas at standard temperature and pressure (STP, 0°C and 1 atm) occupies 22.4 liters; hence, it relates to volume. - (c) Mass of a substance: The mass of one mole of a substance is the molar mass, stated in grams per mole, and relates to the mass of the substance.

Step 3: Drawing a Conclusion

Since a mole relates to all these aspects: number of particles, volume of gases at STP, and the mass of a substance, option (d) 'all of these' is the most comprehensive and accurate choice.

Key Concepts

Avogadro's Number

In chemistry, Avogadro's number is a fundamental constant that represents the number of particles in one mole of a substance. Whether you are dealing with atoms, molecules, ions, or other entities, one mole always contains exactly 6.02214076 × 10²³ of these particles. But why this specific number? It simply links the macroscopic and atomic scales, allowing chemists to work conveniently with ordinary amounts of material.

Avogadro's number allows us to convert between the mass of a substance and the number of atoms or molecules it contains. For example:

• Knowing the number of moles, you can calculate the total number of molecules using Avogadro's number.
• If you know the number of entities, you can find the mole amount by dividing by Avogadro's number.

This concept is central to understanding chemical reactions and stoichiometry, as it bridges measurements at the atomic level to those we measure in the laboratory.

Molar Volume

Molar volume is the volume occupied by one mole of a gas at standard temperature and pressure (STP). At STP, defined as 0°C (273.15 K) and 1 atmosphere of pressure, the molar volume of an ideal gas is 22.4 liters. This means that, regardless of the identity of the gas, one mole will occupy this consistent volume as long as the gas behaves ideally.

This concept is useful, especially in calculations involving gases, because it provides a direct relationship between the amount of gas and its volume.

• Knowing the moles of a gas, you can easily find its volume at STP by multiplying by 22.4 L/mol.
• Conversely, given the volume of a gas, you can find the number of moles by dividing by 22.4 L/mol, if the conditions are at STP.

This principle is integral to gas law calculations in chemistry, simplifying problems and making them more approachable.

Molar Mass

Molar mass is the mass of one mole of a given substance, typically expressed in grams per mole (g/mol). It is essentially a bridge between the macroscopic world we see and measure and the molecular world. Calculating the molar mass involves summing up the atomic masses of all the elements in a molecule. Each atomic mass can be found on the periodic table.

Understanding molar mass helps in:

• Converting between the mass of a substance and the amount in moles.
• Predicting the mass of reagents and products in chemical reactions.

For instance, if you know the molar mass of a compound and you have a certain mass of it, you can calculate how many moles this mass corresponds to by dividing the mass by the molar mass. Similarly, if you know the number of moles, you can find the mass of the substance by multiplying by its molar mass. It's a vital concept to grasp for practical chemistry applications, from laboratory to industry.