according to the American insurance companies, a driver will travel 12,000 miles in a single year. gasoline may be taken as primarily c8h18. the drives vehicle gets 25.0 miles per gallon. the density of octane is 0.703 g/ml. how much gasoline in gallons is used in one year?

2C8H18+25O2-16CO2+18H2O

To calculate the amount of gasoline used in one year, we need to use the given information about the driver's annual mileage, fuel efficiency, and the density of octane.

First, let's convert the annual mileage from miles to gallons of gasoline used. We know that the driver travels 12,000 miles in a year and the vehicle gets 25.0 miles per gallon. So we can calculate:

Gasoline used in one year = Annual mileage / Fuel efficiency
= 12,000 miles / 25.0 miles per gallon
= 480 gallons of gasoline

Now, let's calculate the mass of the gasoline used. We know the density of octane is 0.703 g/ml. Since density is mass per unit volume, we can use this information to calculate:

Mass of gasoline used = Density of octane * Volume of gasoline used
= 0.703 g/ml * 480 gallons * (3.78541 liters/gallon) * (1000 ml/liter)
≈ 10,079.8644 grams of gasoline

Finally, let's convert the mass of gasoline used to gallons. We need to use the fact that the molar mass of octane (C8H18) is 114.22 g/mol and the given balanced equation:

2C8H18 + 25O2 → 16CO2 + 18H2O

Using the stoichiometry of the equation, we can calculate the molar ratio of octane to carbon dioxide (CO2).

Molar ratio of octane to carbon dioxide = 16 moles CO2 / 2 moles C8H18
= 8 moles CO2 / 1 mole C8H18

Now we can calculate the molar amount of octane used:

Molar amount of octane used = Mass of gasoline used / Molar mass of octane
= 10,079.8644 g / 114.22 g/mol
≈ 88.1483 moles of octane

Finally, we can calculate the volume of octane in gallons by multiplying the molar amount by the molar ratio and then dividing by the fuel efficiency:

Volume of octane in gallons = (Molar amount of octane * Molar ratio of octane to CO2) / Fuel efficiency
= (88.1483 moles * 8 moles CO2 / 1 mole C8H18) / 25.0 miles per gallon
= 22.0371 gallons

Therefore, approximately 22.0371 gallons of gasoline would be used in one year.

To calculate the amount of gasoline used in one year, we need to convert the given information into the necessary units and then use the relevant equations.

Given:
- Total miles driven in one year: 12,000 miles
- Fuel efficiency of the vehicle: 25.0 miles per gallon
- Density of octane (gasoline): 0.703 g/ml

Step 1: Calculate the amount of fuel (gasoline) consumed per mile:
To find the amount of fuel consumed per mile, we need to divide the total distance traveled by the fuel efficiency. Using the given information, we can calculate:

Fuel consumed per mile = 1 gallon / 25.0 miles ≈ 0.04 gallons/mile

Step 2: Further convert the fuel consumption rate to gallons by multiplying by 12,000 miles:
Fuel consumed per year = Fuel consumed per mile × Total miles driven in one year
Fuel consumed per year = 0.04 gallons/mile × 12,000 miles
Fuel consumed per year = 480 gallons

Therefore, approximately 480 gallons of gasoline would be used in one year, according to the given information.