Understanding the Molecules in 2.5 Grams of Carbon Dioxide

Carbon dioxide, or CO2, is a significant greenhouse gas that plays a crucial role in various chemical and environmental processes. When considering small amounts of CO2, like 2.5 grams, it is helpful to understand the number of molecules involved. This article will guide you through the steps to calculate the number of molecules in 2.5 grams of CO2, using molar mass and Avogadro's number.

Steps to Calculate the Number of Molecules in 2.5 Grams of CO2

The process of calculating the number of molecules in a given mass of CO2 involves a few straightforward steps. These steps are:

Determine the Molar Mass of CO2: Carbon (C) has a molar mass of about 12.01 g/mol, and Oxygen (O) has a molar mass of about 16.00 g/mol. Since CO2 consists of one carbon atom and two oxygen atoms, its molar mass can be calculated as follows: Calculate the Number of Moles in 2.5 Grams of CO2: Using the molar mass, convert the mass of CO2 into moles. Use Avogadro's Number to Determine the Number of Molecules: Finally, multiply the number of moles by Avogadro's number to get the number of molecules.

Step-by-Step Calculation

Let's break down each step with the necessary calculations:

Step 1: Calculate the Molar Mass of CO2

Carbon (C) has a molar mass of 12.01 g/mol, and Oxygen (O) has a molar mass of 16.00 g/mol. Since CO2 consists of one carbon and two oxygen atoms:

molMass CO2 12.01 g/mol 2 × 16.00 g/mol 44.01 g/mol

Step 2: Calculate the Number of Moles in 2.5 Grams of CO2

The number of moles can be calculated using the mass and molar mass:

number of moles mass / molar mass 2.5 g / 44.01 g/mol ≈ 0.0568 mol

Step 3: Use Avogadro's Number to Find the Number of Molecules

Avogadro's number, which represents the number of particles in one mole of a substance, is approximately 6.022 × 1023 molecules/mol. Therefore, the number of molecules can be calculated as:

number of molecules number of moles × Avogadro's number ≈ 0.0568 mol × 6.022 × 1023 molecules/mol ≈ 3.42 × 1022 molecules

Thus, there are approximately 3.42 × 1022 molecules in 2.5 grams of CO2.

Converting with a Given Solution

Let's consider a similar problem to practice with a given solution:

Given: 2.5 g of CO2 6.02 × 1023 - Avogadro's number constant 44 g/mol - Molar mass of CO2 Solution: 2.5 g × (6.02 × 1023 molecules / 44 g) 3.42 × 1022 molecules

The solution provided simplifies the process by directly multiplying the mass of CO2 by the number of molecules per gram, using the molar mass as the conversion factor.

Additional Practice

Considering the example: 3.6 g of CO2:

Given the molar mass of CO2 is 44 g/mol and Avogadro's number, you can calculate the number of molecules as follows:

3.6 g CO2 × (6.022 × 1023 molecules / 44 g) ≈ 5 × 1022 molecules

This example further reinforces the direct relationship between mass, molar mass, and the number of molecules.

Conclusion

Understanding the number of molecules in a given mass of CO2 involves simple but critical calculations using molar mass and Avogadro's number. This knowledge is essential in various scientific fields, including chemistry, environmental science, and climate studies. By mastering these calculations, you can better comprehend the impact of CO2 in our environment and contribute to informed decision-making in environmental policies.