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The balanced chemical equation for the complete combustion of methane (CH4) is:
CH4 + 2O2 → CO2 + 2H2O
From the ideal gas law, we can calculate the number of moles of carbon dioxide produced:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
n = PV/RT
n = (99.650 kPa)(54 L)/(8.314 J/mol·K)(294.25 K)
n = 2.23 mol CO2
From the stoichiometry of the balanced chemical equation, we see that 1 mole of CH4 produces 1 mole of CO2. Therefore, the number of moles of CH4 required is also 2.23 mol.
The molar mass of CH4 is 16.04 g/mol. Therefore, the mass of CH4 required is:
mass = n × molar mass
mass = 2.23 mol × 16.04 g/mol
mass = 35.74 g
Therefore, the mass of methane required is 35.74 g, not 35.20 g.