Understanding the Molecular Ratio in a Gas Mixture of Oxygen and Nitrogen

In this article, we will explore the concept of determining the ratio of the number of molecules in a gaseous mixture that contains oxygen (O?) and nitrogen (N?) in a specific weight ratio. We will start by explaining the fundamental principles and then walk through a detailed step-by-step example to illustrate the process.

Introduction to Molar Mass and Avogadro's Number

To calculate the ratio of the number of molecules in a gas mixture, we need to consider the molar masses of the components and use the concept of Avogadro's number. The molar mass is the mass of one mole of a substance, and Avogadro's number is the number of particles (atoms or molecules) in one mole.

Molar Mass

The molar mass of oxygen (O?) is calculated as:

$$ 2 times 16 , text{g/mol} 32 , text{g/mol} $$

The molar mass of nitrogen (N?) is calculated as:

$$ 2 times 14 , text{g/mol} 28 , text{g/mol} $$

A mole of any gas contains (6.022 times 10^{23}) molecules (Avogadro's number).

Weight Ratio to Mole Ratio

Given a weight ratio of oxygen to nitrogen as 1:4, we can convert these weights to moles to find the corresponding mole ratio.

Step-by-Step Calculation

Step 1: Determine the Molar Mass

The molar mass of O? is 32 g/mol, and the molar mass of N? is 28 g/mol.

Step 2: Establish the Weight Ratio

Let the weight of O? be 1 g, then the weight of N? will be 4 g.

Step 3: Convert Weight to Moles

The number of moles of O? can be calculated as:

$$ text{Moles of O?} frac{text{Weight of O?}}{text{Molar mass of O?}} frac{1 , text{g}}{32 , text{g/mol}} frac{1}{32} , text{mol} $$

The number of moles of N? can be calculated as:

$$ text{Moles of N?} frac{text{Weight of N?}}{text{Molar mass of N?}} frac{4 , text{g}}{28 , text{g/mol}} frac{4}{28} frac{1}{7} , text{mol} $$

Step 4: Calculate the Ratio of Molecules

The number of molecules is directly proportional to the number of moles. Therefore, the ratio of the number of molecules of O? to N? is:

$$ text{Ratio of molecules} frac{text{Moles of O?}}{text{Moles of N?}} frac{frac{1}{32}}{frac{1}{7}} frac{1}{32} times frac{7}{1} frac{7}{32} $$

So, the ratio of the number of molecules of O? to N? is 7:32.

Conclusion

Understanding and calculating the ratio of molecules in a gas mixture involves determining the molar mass of the components and converting the given weight ratio into a mole ratio. By following these steps, we can accurately find the ratio of the number of molecules in a gaseous mixture of oxygen and nitrogen in the weight ratio of 1:4.

For readers interested in more detailed information, the weight ratio of nitrogen and oxygen can be represented as a molar ratio, which simplifies the calculation. For a weight ratio of 7:8 (derived from 28:32), the mole ratio would be 1:1. For a weight ratio of 4:1, the mole ratio would be 32:7.

Understanding these principles is crucial for various scientific and industrial applications where the behavior of gases is important. Whether in the study of atmospheric chemistry, industrial processes, or environmental science, the knowledge of molecular ratios in gas mixtures is invaluable.