Calculate the number of pounds of CO2 released into the atmosphere when a 20.0 gallon tank of gasoline is burned in an automobile engine. Assume that gasoline is primarily octane, C8H18, and that the density of gasoline is 0.692 g⋅mL−1. This assumption ignores additives. Also, assume complete combustion.
Answer?
To calculate the number of pounds of CO2 released, we need to calculate the moles of octane burned and use stoichiometry to determine the moles of CO2 produced. Then we can convert the moles of CO2 to pounds.
Step 1: Convert gallons to liters:
1 gallon = 3.78541 liters
Therefore, 20.0 gallons = 20.0 x 3.78541 = 75.7082 liters.
Step 2: Calculate the mass of gasoline:
Density = mass/volume
Mass = Density x Volume
Mass = 0.692 g⋅mL^−1 x 75.7082 liters x 1000 mL/L
Mass = 51924.5034 g
Step 3: Convert grams to moles of octane:
Molecular weight of octane (C8H18) = 114.221 g/mol
Moles = Mass / Molecular weight
Moles = 51924.5034 g / 114.221 g/mol
Moles = 454.04 mol
Step 4: Use stoichiometry to determine the moles of CO2 produced:
Balanced equation: 2C8H18 + 25O2 → 16CO2 + 18H2O
From the balanced equation, we can see that 2 moles of C8H18 produce 16 moles of CO2.
Therefore, Moles of CO2 = (454.04 mol C8H18 x 16 mol CO2) / 2 mol C8H18
Moles of CO2 = 3632.32 mol
Step 5: Convert moles of CO2 to pounds:
Molar mass of CO2 = 44.01 g/mol
Mass of CO2 = Moles of CO2 x Molar mass of CO2
Mass of CO2 = 3632.32 mol x 44.01 g/mol
Mass of CO2 = 159949.83 g
Converting grams to pounds:
1 pound = 453.592 grams
Therefore, Mass of CO2 in pounds = 159949.83 g / 453.592 g/lb
Mass of CO2 in pounds ≈ 352.55 lb
Therefore, when burning a 20.0 gallon tank of gasoline, approximately 352.55 pounds of CO2 are released into the atmosphere.
To calculate the number of pounds of CO2 released when burning a 20.0 gallon tank of gasoline, we need to follow several steps:
Step 1: Convert gallons of gasoline to liters.
- 1 gallon = 3.78541 liters
- So, 20.0 gallons = 20.0 * 3.78541 liters = 75.708 liters
Step 2: Calculate the mass of gasoline in the tank.
- To find the mass, we need to know the density of the gasoline.
- The given density is 0.692 g/mL.
- Mass = Volume x Density
- Mass = 75.708 * 0.692 grams
Step 3: Convert the mass of gasoline to moles.
- To convert grams to moles, we need to know the molar mass of octane (C8H18).
- The molar mass of carbon (C) = 12.01 g/mol
- The molar mass of hydrogen (H) = 1.01 g/mol
- Molar mass of octane (C8H18) = (8 * molar mass of carbon) + (18 * molar mass of hydrogen)
- Molar mass of octane (C8H18) = (8 * 12.01) + (18 * 1.01) grams/mol
- Calculate the moles of gasoline using the equation:
Moles = Mass / Molar mass
Step 4: Calculate the moles of CO2 produced.
- For complete combustion, one molecule of octane reacts with 25 molecules of oxygen to produce 16 molecules of CO2 and 18 molecules of water.
- So, the stoichiometric ratio is 16 moles of CO2 per 1 mole of octane consumed.
Step 5: Convert moles of CO2 to grams.
- The molar mass of CO2 (carbon dioxide) = 44.01 g/mol
- Convert moles to grams using the equation:
Mass = Moles of CO2 * Molar mass of CO2
Step 6: Convert grams to pounds.
- 1 pound = 453.592 grams
- Convert grams to pounds using the equation:
Pounds = Grams / 453.592
Now that we have outlined the steps, we can proceed to calculate the number of pounds of CO2 released into the atmosphere.