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The pressure gauge of a steel cylinder of methane gas (ch4) reads 405 psi. The cylinder has a volume of 1.89 l and is at a temperature of 35.0 c. How many grams of methane does the cylinder contain?
Accepted Answer
To calculate the grams of methane in the cylinder, we can use the ideal gas law: PV = nRT, where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (K)
1. Convert pressure to atm: 405 psi
(1 atm / 14.7 psi) = 27.6 atm
2. Convert temperature to Kelvin: 35.0 °C + 273.15 = 308.15 K
3. Solve for moles (n): n = (PV) / (RT) = (27.6 atm
1.89 L) / (0.0821 L·atm/mol·K
308.15 K) = 2.08 mol
4. Calculate mass in grams: 2.08 mol
16.04 g/mol (molar mass of CH4) = 33.4 g
Therefore, the cylinder contains approximately 33.4 grams of methane.
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