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) \(2: 2: 3: 4\)

Short answer

The ratio of the number of molecules is \(1: 1: 1: 1\).

Step-by-step solution

- Understand the Conditions

The problem states that the four gases are contained in one-liter flasks under the same conditions. These conditions imply that the temperature and pressure for the gases are the same.

- Apply Avogadro's Law

According to Avogadro's Law, equal volumes of gases, under the same temperature and pressure, contain the same number of molecules. This means that in one-liter flasks, regardless of the type of gas, they each contain the same number of molecules.

- Analyze the Ratios

Given that each gas is in a one-liter flask under identical conditions, the number of molecules in each gas must be the same. Therefore, the ratio of the number of molecules must be equal for all gases.

- Choose the Correct Answer

Since each gas has the same number of molecules due to Avogadro's Law, the ratio is equal for all gases. Hence, the correct answer is option b: \(1: 1: 1: 1\).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry. It describes the behavior of an ideal gas. The law is usually stated as \[ PV = nRT \] where:

• \( P \) is the pressure of the gas.
• \( V \) is the volume of the gas.
• \( n \) is the number of moles of the gas.
• \( R \) is the universal gas constant.
• \( T \) is the temperature in Kelvin.

This formula helps us comprehend how the volume, pressure, and temperature of a gas relate to its quantity.
By altering one of these variables, the others adjust to maintain the balance described by the equation.
Although this equation assumes a perfect scenario, it is a useful tool to understand the general behavior of gases.

Molecular Ratios

Molecular ratios are essential when discussing gases under identical conditions. When you have the same volume of different gases at the same temperature and pressure, they contain an equal number of molecules.
This concept is based on Avogadro's Law. Therefore, the molecular ratio becomes simple; it is determined by the count of molecules.
For example, if you are comparing four distinct gases each in the same volume of one-liter under equivalent conditions, their molecular ratio should be 1:1:1:1.
This implies that despite the chemical nature or mass of the gas, under these specific conditions, the number of molecules remains identical, leading to an equal molecular ratio.

Gas Properties

Gases possess unique properties that distinguish them from liquids and solids. These properties help explain their behavior under various conditions.

• Compressibility: Gases can be compressed more easily than liquids and solids because their molecules are far apart.
• Expansion: They expand to fill the shape and volume of their container completely.
• Low Density: Compared to other states of matter, gases are less dense, which is why they float.
• Diffusion: The molecules of gases can move freely and mix thoroughly with other gases.

These properties play a critical role in understanding behaviors observed in the lab and everyday life, such as balloon inflation or the way perfume spreads through a room.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating quantities in chemical reactions. It is often used to determine the relationships between reactants and products in a chemical equation.
For gases, stoichiometry uses principles from the Ideal Gas Law to relate volume, pressure, and temperature conditions to the amounts of reactants or products.
When dealing with gas reactions, you may need to use molar ratios to convert between units.
For example, if a reaction between gases produces a certain amount of product, stoichiometry helps calculate how much of each reactant is needed.
It involves balancing chemical equations to ensure mass and energy are conserved, guiding practical applications in labs and industrial processes.
In the context of gases, stoichiometry can help predict the volume of gas produced or needed in a reaction under certain conditions.