Problem 53 - A Complete Resource Book in Chemistry for JEE Main

Question

Four one litre flasks are separately filled with the gases \(\mathrm{O}_{2}, \mathrm{~F}_{2}, \mathrm{CH}_{4}\) and \(\mathrm{CO}_{2}\) under same conditions. The ratio of the number of molecules in these gases are (a) \(2: 2: 4: 3\) (b) \(1: 1: 1: 1\) (c) \(1: 2: 3: 4\) (d) \(2: 2: 3: 4\)

Step-by-Step Solution

Answer

(b) 1: 1: 1: 1

Step 1: Understanding the Concept

According to Avogadro's law, equal volumes of gases at the same temperature and pressure contain an equal number of molecules. Therefore, if we have four flasks each with one liter of gas, under the same conditions, each flask should contain the same number of molecules if all other conditions are constant.

Step 2: Applying Avogadro's Law

Since all the flasks are filled with gases under the same conditions (same temperature and pressure), and each flask has the same volume of one liter, by Avogadro's law, each flask will contain the same number of molecules.

Step 3: Identifying the Ratios

Given that each flask contains the same number of molecules, the ratio of the number of molecules in - \mathrm{O}_{2}- \mathrm{F}_{2}- \mathrm{CH}_{4}- \mathrm{CO}_{2}will all be equal. Thus, the ratio is (b) \(1: 1: 1: 1\).

Key Concepts

Molecules in gases

Gases are composed of tiny particles known as molecules. These molecules are always in motion, colliding with each other and the walls of their container. The behavior of gas molecules can be explained by the kinetic molecular theory. According to this theory, gas molecules:

• Move rapidly and randomly.
• Have negligible attractive or repulsive forces between them.
• Exert pressure on their container through collisions.
• Have a distribution of speeds, with some moving faster than others.

Avogadro's Law builds upon these properties to explain how the number of molecules relates to the volume of gas.

Equal volumes of gases

Avogadro's Law states that equal volumes of different gases, at the same temperature and pressure, contain the same number of molecules. This means if you have a specific volume of gas, say one liter, and keep the conditions of temperature and pressure constant, any other gas occupying that same volume will have the same number of molecules:

• Volume is directly proportional to the number of molecules.
• This law helps to compare gases and predict behavior in reactions.
• The concept is integral to understanding molar volume, where one mole of any ideal gas occupies a volume of 22.4 liters at standard temperature and pressure (STP).

Equal number of molecules

When Avogadro's Law is applied, we understand that each gas, regardless of its type, contains an equal number of molecules when the conditions of temperature and pressure are the same. This concept was pivotal in reaching the conclusion in our original exercise, which showed that different gases in equal volumes possessed the same number of molecules. New insights when studying gases include:

• It allows chemists to use gas data to infer other properties of the molecules, such as molar mass.
• Understanding this equality helps in balancing chemical equations involving gases.

This further reinforces the idea of gases behaving predictably under set conditions, allowing for a unified approach in studying reaction stoichiometry.

Gas laws

Gas laws describe how different properties of gases relate to one another, such as pressure, volume, and temperature. They allow us to understand and predict how a gas will behave under varying conditions. Key gas laws include:

• Boyle's Law: Illustrates the inverse relationship between volume and pressure at constant temperature.
• Charles's Law: Details how volume and temperature are directly proportional at constant pressure.
• Avogadro's Law: Discusses the relationship between volume and the number of molecules at constant temperature and pressure.
• Combined Gas Law: Integrates Boyle's, Charles's, and Avogadro's laws into one formula.

Using these laws, we can predict how gases will interact, change, or react under different conditions, thus embodying the core principles of physical chemistry.