Carbon dioxide and water gas are obtained from the complete combustion of 50 ml of propane. The volumes were measured at a temperature of 298 K and a pressure of 101 kPa.
a) Write the chemical equation for this reaction. b) Calculate the volume of oxygen needed in this case.
c) What is the volume of carbon dioxide obtained? d) Calculate the mass in grams of carbon dioxide.
a) The chemical equation for the complete combustion of propane is:
C3H8 + 5O2 -> 3CO2 + 4H2O
b) To calculate the volume of oxygen needed, we need to determine the stoichiometric ratio between propane and oxygen. From the balanced chemical equation, we can see that 1 mole of propane reacts with 5 moles of oxygen.
First, let's convert the volume of propane to moles. We'll need to know the molar volume of a gas at the given temperature and pressure. Assuming ideal gas behavior, the molar volume at 298 K and 101 kPa is approximately 24.79 L/mol.
Given that the initial volume of propane is 50 ml, which is equivalent to 0.05 L, we can calculate the moles of propane by dividing the volume by the molar volume:
moles of propane = volume of propane / molar volume = 0.05 L / 24.79 L/mol ≈ 0.002015 mol
Since the stoichiometric ratio is 1:5 between propane and oxygen, we multiply the moles of propane by 5 to obtain the moles of oxygen needed:
moles of oxygen = 5 * moles of propane = 5 * 0.002015 mol ≈ 0.010075 mol
To convert the moles of oxygen to volume, we use the molar volume again:
volume of oxygen = moles of oxygen * molar volume = 0.010075 mol * 24.79 L/mol ≈ 0.249 L
Therefore, approximately 0.249 L (or 249 mL) of oxygen is needed in this case.
c) From the balanced chemical equation, we can see that 3 moles of carbon dioxide are produced for every mole of propane combusted. Since we have already calculated the moles of propane to be approximately 0.002015 mol, we can multiply this by 3 to find the moles of carbon dioxide produced:
moles of carbon dioxide = 3 * moles of propane = 3 * 0.002015 mol ≈ 0.006045 mol
To convert the moles of carbon dioxide to volume, we use the molar volume:
volume of carbon dioxide = moles of carbon dioxide * molar volume = 0.006045 mol * 24.79 L/mol ≈ 0.150 L
Therefore, approximately 0.150 L (or 150 mL) of carbon dioxide is obtained.
d) To calculate the mass of carbon dioxide, we need to use the molar mass of carbon dioxide, which is 44.01 g/mol.
mass of carbon dioxide = moles of carbon dioxide * molar mass = 0.006045 mol * 44.01 g/mol ≈ 0.266 g
Therefore, the mass of carbon dioxide obtained is approximately 0.266 grams.