What is the mass of CH₄ in a sample that occupies a volume of 16.5 L at STP?

Verified step by step guidance

1. Step 1: Recall the conditions of STP (Standard Temperature and Pressure). At STP, 1 mole of any ideal gas occupies a volume of 22.4 L. This is a key relationship to use in this problem.
2. Step 2: Use the given volume of CH₄ (16.5 L) and the molar volume at STP (22.4 L/mol) to calculate the number of moles of CH₄. The formula is: $n=\frac{V}{Vₘ}$, where $V$ is the volume of the gas and $Vₘ$ is the molar volume.
3. Step 3: Determine the molar mass of CH₄. The molecular formula CH₄ indicates that it contains 1 carbon atom and 4 hydrogen atoms. Using the periodic table, the molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.008 g/mol. Add these together: $12.01+4\times 1.008$.
4. Step 4: Use the number of moles of CH₄ (calculated in Step 2) and the molar mass of CH₄ (calculated in Step 3) to find the mass of CH₄. The formula is: $m=n\times M$, where $m$ is the mass, $n$ is the number of moles, and $M$ is the molar mass.
5. Step 5: Substitute the values for the number of moles and molar mass into the formula from Step 4 to calculate the mass of CH₄. Ensure the units are consistent and cancel appropriately to yield the mass in grams.

Key Concepts

Molar Volume at STP

At Standard Temperature and Pressure (STP), one mole of an 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, which is necessary for calculating mass.

Molar Mass of CH₄

The molar mass of methane (CH₄) is approximately 16.04 g/mol. This value is essential for determining the mass of the gas once the number of moles is calculated from the volume at STP.

Ideal Gas Law

The Ideal Gas Law (PV=nRT) relates pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T). While not directly needed for this specific question, understanding this law provides a foundational context for gas behavior under various conditions.