The heat of combustion of octane (C8H18) is 47.8 kJ/g and one gallon of C8H18 has a mass of 2620 g. If a car using octane is driven 10,000 miles in one year and gets 25 miles per gallon of octane, what is the total energy
consumption?
1. 5.01 × 107 kJ
2. 8.45 × 102 kJ
3. 34 × 107 kJ
4. 7.80 × 103 kJ
5. −13 × 103 kJ
This is WAY too much work to do for one problem but here is how you go about it.
10,000 miles driven @ 25 miles/gallon = how many gallons of octane. Convert gallons to liters and grams (but I don't see a density), Knowing grams should get you to kJ/g in connection with the equation of
2C8H18 + 17O2 ==>16CO2 + 18H2O
To find the total energy consumption, we need to calculate the amount of octane consumed in one year and then multiply it by the heat of combustion.
First, let's calculate the amount of octane consumed in one year.
The car is driven 10,000 miles in one year and gets 25 miles per gallon of octane. So, the number of gallons consumed in one year is:
10,000 miles / 25 miles per gallon = 400 gallons
Since we know that one gallon of octane has a mass of 2620 g, the total mass of octane consumed in one year is:
400 gallons * 2620 g = 1,048,000 g
Next, let's calculate the total energy consumption.
The heat of combustion of octane is given as 47.8 kJ/g. So, the total energy consumption in one year is:
1,048,000 g * 47.8 kJ/g = 50,105,600 kJ
Therefore, the total energy consumption is approximately 5.01 × 10^7 kJ.
Therefore, the correct answer is option 1. 5.01 × 10^7 kJ.
To find the total energy consumption, we need to calculate the amount of octane burned and then multiply it by the heat of combustion.
First, let's find the total amount of octane burned in gallons:
Number of gallons = total miles driven / miles per gallon
Number of gallons = 10,000 miles / 25 miles per gallon
Number of gallons = 400 gallons
Now, let's find the total mass of octane burned in grams:
Mass of octane = number of gallons * mass per gallon
Mass of octane = 400 gallons * 2620 g per gallon
Mass of octane = 1,048,000 g
Next, let's calculate the total energy consumption in kJ:
Energy consumption = mass of octane * heat of combustion
Energy consumption = 1,048,000 g * 47.8 kJ/g
Energy consumption = 50,019,200 kJ
Therefore, the total energy consumption is 5.01 × 10^7 kJ.
So the correct option is 1. 5.01 × 10^7 kJ.