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Calculate the volume occupied by 32 g of methane gas (CH4) at 30 °C and 1.0 atm. The molar mass of CH4 is 16 g. R = 0.082 Latm/Kmol. T = 273 + °C

Calculate the volume occupied by 32 g of methane gas (CH4) at 30 °C and 1.0 atm. The molar mass of CH4 is 16 g. R = 0.082 Latm/Kmol. T = 273 + °C

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Calculate the Volume Occupied by Methane Gas** Given: - Mass of methane (CH₄): 32 g - Temperature: 30°C - Pressure: 1.0 atm Constants: - Molar mass of CH₄: 16 g/mol - Ideal gas constant (R): 0.082 Latm/Kmol - Temperature in Kelvin (T): T = 273 + °C Calculate the volume occupied by methane gas using the ideal gas law. **Step-by-Step Solution:** 1. Calculate the number of moles of CH₄: - Number of moles (n) = mass/molar mass - \( n = \frac{32 \text{ g}}{16 \text{ g/mol}} = 2 \text{ mol} \) 2. Convert temperature from Celsius to Kelvin: - \( T = 273 + 30 = 303 \text{ K} \) 3. Use the ideal gas law equation \( PV = nRT \) to find the volume (V): - \( 1.0 \text{ atm} \times V = 2 \text{ mol} \times 0.082 \text{ Latm/Kmol} \times 303 \text{ K} \) - \( V = \frac{2 \text{ mol} \times 0.082 \text{ Latm/Kmol} \times 303 \text{ K}}{1.0 \text{ atm}} \) - \( V = 49.692 \text{ L} \) Therefore, the volume occupied by 32 g of methane gas at 30°C and 1.0 atm is approximately 49.692 liters.
Transcribed Image Text:**Calculate the Volume Occupied by Methane Gas** Given: - Mass of methane (CH₄): 32 g - Temperature: 30°C - Pressure: 1.0 atm Constants: - Molar mass of CH₄: 16 g/mol - Ideal gas constant (R): 0.082 Latm/Kmol - Temperature in Kelvin (T): T = 273 + °C Calculate the volume occupied by methane gas using the ideal gas law. **Step-by-Step Solution:** 1. Calculate the number of moles of CH₄: - Number of moles (n) = mass/molar mass - \( n = \frac{32 \text{ g}}{16 \text{ g/mol}} = 2 \text{ mol} \) 2. Convert temperature from Celsius to Kelvin: - \( T = 273 + 30 = 303 \text{ K} \) 3. Use the ideal gas law equation \( PV = nRT \) to find the volume (V): - \( 1.0 \text{ atm} \times V = 2 \text{ mol} \times 0.082 \text{ Latm/Kmol} \times 303 \text{ K} \) - \( V = \frac{2 \text{ mol} \times 0.082 \text{ Latm/Kmol} \times 303 \text{ K}}{1.0 \text{ atm}} \) - \( V = 49.692 \text{ L} \) Therefore, the volume occupied by 32 g of methane gas at 30°C and 1.0 atm is approximately 49.692 liters.
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