Octane, an alkene with the chemical formula C8H18 and a heat of combustion of 46.8 MJ/kg,
is the main constituent of gasoline. Assume gasoline contains 100% octane and has a density of 703 kg/m3.
The combustion reaction of octane is 2C8H18 + 25O2 ? 16CO2 + 18H2O. A typical car requires 3.4 MJ of
energy to travel 1 km taking into account the various inefficiencies; and a typical driving distance is 15,200
km per year. How many liters of octane does the car burn and what is the total mass of CO2 released from
burning the octane in the engine? For that you will need to calculate some molecular weights, which you
can do knowing: MW(H) = 1 g/mol, MW(C) = 12 g/mol, MW(O) = 16 g/mol.
The Correct Answer and Explanation is :
The car burns approximately 1570.8 liters of octane per year and releases a total of 3409.7 kg (or 3.41 metric tons) of CO₂ into the atmosphere.
Explanation:
- Understanding Octane and Combustion:
- Octane (C₈H₁₈) is a hydrocarbon and the primary component of gasoline.
- The combustion reaction follows:
[
2C_8H_{18} + 25O_2 → 16CO_2 + 18H_2O
] - This means that 2 moles of octane produce 16 moles of CO₂.
- Energy Requirements:
- The car requires 3.4 MJ/km and travels 15,200 km/year.
- The total energy needed per year is:
[
3.4 \times 15,200 = 51,680 \text{ MJ}
]
- Finding the Mass of Octane:
- Given that octane releases 46.8 MJ/kg, the required fuel mass is:
[
51,680 \div 46.8 = 1104.3 \text{ kg}
]
- Finding the Volume of Octane:
- Octane has a density of 703 kg/m³, so the volume required is:
[
1104.3 \div 703 = 1.57 \text{ m³} = 1570.8 \text{ liters}
]
- Calculating CO₂ Emissions:
- Molecular weight of octane = 114 g/mol
- Molecular weight of CO₂ = 44 g/mol
- Using stoichiometry, 2 moles of octane (228 g) produce 16 moles of CO₂ (704 g).
- This means burning 1 kg of octane produces:
[
\left(\frac{16}{2} \times \frac{44}{114} \right) \times 1 = 3.09 \text{ kg of CO₂}
] - So, total CO₂ released:
[
1104.3 \times 3.09 = 3409.7 \text{ kg}
]
Thus, over a year, the car emits 3.41 metric tons of CO₂, significantly contributing to greenhouse gas emissions.
Now, I’ll generate an image to visually represent this data.
Here is an illustration showing the car consuming 1570.8 liters of octane per year and emitting 3409.7 kg of CO₂ per year. The image visually represents fuel consumption and carbon dioxide emissions in a typical urban setting. Let me know if you need any modifications!