To calculate the volume of CO2 formed at a pressure of 2.50 atm and a temperature of 125°C, we need to use the ideal gas law equation PV = nRT which is = 2.47 L.
Given:
Initial volume of methane gas (CH₄): 2.80 L
Initial temperature of methane gas: 25°C = 298.15 K
Initial pressure of methane gas: 1.65 atm
Initial volume of oxygen gas (O₂): 35.0 L
Initial temperature of oxygen gas: 31°C = 304.15 K
Initial pressure of oxygen gas: 1.25 atm
Final pressure of CO₂: 2.50 atm
Final temperature of CO₂: 125°C = 398.15 K
Calculations:
1. Calculate the initial moles of methane gas (CH₄) and oxygen gas (O₂)
Using the ideal gas law (PV = nRT), we can calculate the initial moles of methane gas and oxygen gas:
Moles of CH₄: (2.80 L)(1.65 atm) / (0.0821 L·atm/mol·K)(298.15 K) = 0.189 mol
Moles of O₂: (35.0 L)(1.25 atm) / (0.0821 L·atm/mol·K)(304.15 K) = 1.750 mol
2. Determine the balanced chemical equation for the combustion of methane
The balanced chemical equation for the combustion of methane is:
CH₄ + 2O₂ → CO₂ + 2H₂O
3. Calculate the moles of CO₂ produced
From the balanced chemical equation, we know that 1 mole of CH₄ reacts with 2 moles of O₂ to produce 1 mole of CO₂. Therefore, 0.189 mol of CH₄ will produce 0.0945 mol of CO₂.
4. Calculate the final volume of CO₂
Using the ideal gas law again, we can calculate the final volume of CO₂:
V = nRT/P = (0.0945 mol)(0.0821 L·atm/mol·K)(398.15 K) / (2.50 atm) = 2.47 L
Therefore, the final volume of CO₂ produced is 2.47 L.