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Answer :
Final answer:
To find the mass of methane in a cylinder, you can apply the ideal gas law and rearrange it to solve for the number of moles, which when multiplied by the molar mass gives the mass in grams. The mass of methane in the cylinder is closest to 6.2 kg.
Explanation:
To calculate the mass of methane contained in a 54-liter cylinder at 15°C and 170 bar, we first need to use the ideal gas law, which is PV = nRT. The volume is 54 liters, which is equivalent to 0.054 cubic meters since 1,000 liters equals 1 cubic meter. The pressure is 170 bar which is equal to 170 × 10⁵ Pa. The gas constant R in SI units is 8.314 J/mol·K, and the temperature must be converted to Kelvin by adding 273 to the Celsius temperature, so T = 15 + 273 = 288 K.
The ideal gas law can be rearranged to solve for n, the number of moles of methane:
n = PV / RT.
Substituting the given values:
n = (170 × 10⁵ Pa × 0.054 m³) / (8.314 J/mol·K × 288 K),
n = 403.3 moles of CH₄.
The molar mass of methane (CH₄) is approximately 16 g/mol, so to find the mass (m) we multiply the number of moles by the molar mass:
m = 403.3 moles × 16 g/mol,
m = 6452.8 g or 6.4528 kg.
Therefore, the mass of methane in the cylinder is closest to option B. 6.2 kg.
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