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

Ch.8 Gases, Liquids and Solids

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

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McMurry 8th Edition

Ch.8 Gases, Liquids and Solids

Problema 72

Capitolo 8, Problema 72

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

Guida verificata passo dopo passo

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.

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}{V ₘ}

, where

V

is the volume of the gas and

V ₘ

is the molar volume.

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

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.

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.

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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.

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00:53

Molarity

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.

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01:10

Calculating Molar Mass

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.

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