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

Ch.8 Gases, Liquids and Solids

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187Not the one you use?Change textbook

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McMurry 8th Edition

Ch.8 Gases, Liquids and Solids

Problem 70

Chapter 8, Problem 70

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

Verified step by step guidance

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: \( \text{moles of O}_2 = \frac{\text{volume of O}_2}{22.4 \ \text{L/mol}} \).

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: \( \text{molecules of O}_2 = \text{moles of O}_2 \times 6.022 \times 10^{23} \).

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 \( 2 \times 16.00 = 32.00 \ \text{g/mol} \).

Step 4: Use the moles of O₂ calculated in Step 1 and the molar mass of O₂ to find the mass. The formula is: \( \text{mass of O}_2 = \text{moles of O}_2 \times 32.00 \ \text{g/mol} \).

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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