Calculating the Mass of Carbon Dioxide in Grams

Carbon dioxide (CO2) is a vital compound in our atmosphere, playing a crucial role in the Earth's climate and chemical processes. In this article, we will explore how to determine the mass of CO2 in grams based on the number of molecules. This information is particularly useful for environmental studies, atmospheric science, and educational purposes.

Understanding the Molar Mass of CO2

First, let's define the molar mass of CO2. The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). The molar mass of CO2 can be calculated by adding the molar masses of its constituent elements:

1. Carbon (C): 12.01 g/mol

2. Oxygen (O): 16.00 g/mol (since there are two oxygen atoms, the mass is 16.00 g/mol × 2 32.00 g/mol)

So, the molar mass of CO2 is:

12.01 g/mol (carbon) 32.00 g/mol (oxygen) 44.01 g/mol

Using Avogadro's Number to Find Mass

Avogadro's number states that one mole of any substance contains 6.022 × 1023 atoms or molecules. This number is crucial for converting between the number of molecules and moles. Let's use this to find the mass of CO2 with different numbers of molecules.

Mass of 7.7 × 1022 Molecules of CO2

Step 1: Calculate the number of moles of CO2 from the given number of molecules.

(frac{7.70 times 10^{22} text{ molecules}}{6.022 times 10^{23} text{ molecules/mol}} 0.128 text{ mol})

Step 2: Convert moles to grams using the molar mass.

0.128 mol × 44.01 g/mol 5.63 g

Step 3: Verification using fractions.

(7.70 times 10^{22} text{ molecules} times frac{44.01 text{ g/mol}}{6.022 times 10^{23} text{ molecules/mol}} approx 5.63 text{ g})

General Case: Mass of 6.023 × 1023 Molecules of CO2

For a general case, where we have 6.023 × 1023 molecules of CO2, which is equivalent to one mole:

1 mole × 44.01 g/mol 44.01 g

Additional Calculations

1. 3.0 × 1023 Molecules of CO2:

(frac{3.0 times 10^{23} text{ molecules}}{6.022 times 10^{23} text{ molecules/mol}} approx 0.498 text{ mol})

0.498 mol × 44.01 g/mol 21.93 g

2. 3.4 × 1022 Molecules of CO2:

(frac{3.40 times 10^{22} text{ molecules}}{6.022 times 10^{23} text{ molecules/mol}} 0.05647 text{ mol})

0.05647 mol × 44.01 g/mol 248.512 g

Note that these calculations are based on the assumption that the gas is at standard temperature and pressure (STP). For different conditions, the molar volume and molar mass of CO2 would change.

Conclusion: Understanding the relationship between the number of molecules and the mass of CO2 is crucial in various scientific and environmental contexts. By using Avogadro's number and the molar mass, you can easily convert between the number of molecules and their mass in grams.