How many molecules are in 1.0 L of O₂ at STP? How may grams of O₂?

Verified step by step guidance

1. Step 1: Recall that at Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 L. Use this information to calculate the number of moles of O₂ in 1.0 L. The formula is: \( \text{moles of O}_2 = \frac{\text{volume of O}_2}{22.4 \ \text{L/mol}} \).
2. Step 2: Use Avogadro's number \( 6.022 \times 10^{23} \ \text{molecules/mol} \) to calculate the number of molecules in the moles of O₂ obtained in Step 1. The formula is: \( \text{molecules of O}_2 = \text{moles of O}_2 \times 6.022 \times 10^{23} \).
3. Step 3: To calculate the mass of O₂, first determine the molar mass of O₂. Since oxygen has an atomic mass of approximately 16.00 g/mol, the molar mass of O₂ is \( 2 \times 16.00 = 32.00 \ \text{g/mol} \).
4. Step 4: Use the moles of O₂ calculated in Step 1 and the molar mass of O₂ to find the mass. The formula is: \( \text{mass of O}_2 = \text{moles of O}_2 \times 32.00 \ \text{g/mol} \).
5. Step 5: Combine the results from Steps 2 and 4 to report the number of molecules and the mass of O₂ in 1.0 L at STP.

Key Concepts

Molar Volume at STP

At Standard Temperature and Pressure (STP), one mole of any ideal gas occupies a volume of 22.4 liters. This concept is crucial for converting between the volume of a gas and the number of moles, allowing us to determine how many molecules are present in a given volume.

Avogadro's Number

Avogadro's Number, approximately 6.022 x 10²³, represents the number of molecules in one mole of a substance. This constant is essential for calculating the total number of molecules in a given number of moles, which is necessary for answering the first part of the question regarding the number of molecules in 1.0 L of O₂.

Molar Mass of O₂

The molar mass of O₂ (oxygen gas) is approximately 32 grams per mole, calculated from the atomic mass of oxygen. This value is important for converting moles of O₂ into grams, which is needed to answer the second part of the question about how many grams of O₂ are present in 1.0 L at STP.