A driver with a nearly empty fuel tank may she is "running...

A driver with a nearly empty fuel tank may she is "running on fumes." If a 15.0 gallon automobile gas tank had only gasoline vapor remaining in it, what is the farthest the vehicle could travel if it gets 20.0 miles per gallon on liquid gasoline? Assume the average molar mass of molecules in gasoline is $105 \mathrm{g} / \mathrm{mol},$ the density of liquid gasoline is 0.75 $\mathrm{g} / \mathrm{mL}$ , the pressure is 743 $\mathrm{mm}$ Hg, and the temperature is $25^{\circ} \mathrm{C}$ .

A driver with a nearly empty fuel tank may she is "running on fumes." If a 15.0 gallon automobile gas tank had only gasoline vapor remaining in it, what is the farthest the vehicle could travel if it gets 20.0 miles per gallon on liquid gasoline? Assume the average molar mass of molecules in gasoline is
$105 \mathrm{g} / \mathrm{mol},$ the density of liquid gasoline is 0.75 $\mathrm{g} / \mathrm{mL}$ , the pressure is 743 $\mathrm{mm}$ Hg, and the temperature is $25^{\circ} \mathrm{C}$ .

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Key Concepts

Molar Mass

Molar mass represents the mass of one mole of a substance and is a key factor in converting between the number of moles determined by the ideal gas law and the mass of the substance. This conversion is necessary to relate the gaseous fuel to its equivalent liquid volume.

Density

Density, defined as mass per unit volume, links the mass of a substance to its physical volume. In problems involving phase differences (liquid versus vapor), density allows the calculation of the corresponding mass or volume of fuel.

Ideal Gas Law

The ideal gas law (PV = nRT) relates pressure, volume, temperature, and the number of moles of a gas. It is used to determine how many moles of gasoline vapor are present in a given volume under specified temperature and pressure conditions.

Unit Conversion

Accurate unit conversion is essential for ensuring consistency across calculations. This includes converting volumes from gallons to liters, pressures from mm Hg to atmospheres or Pascals, and temperatures from Celsius to Kelvin, which is critical when applying the ideal gas law.

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