Question

Question:The gas tank of a certain luxury automobile holds 22.3 gallons according to the owner’s manual. If the densityof gasoline is 0.8206 g/mL, determine the mass in kilograms and pounds of the fuel in a full tank.

Short answer

The mass of fuel in the fuel tank in kilograms and pounds is 69.3 kg and 153 lb.

Step-by-step solution

Defining the gallon, kilograms, and pounds

Gallon –

It is a unit of volume to measure the liquid volume. It is used in the oil industry to measure the capacity or volume of oil in the barrel.

Density –

It is a physical quantity which is the ratio of mass to volume.

\(Density\,\, = \,\,\frac{{Mass}}{{Volume}}\)

Determining the mass in kilograms and pounds

It is given that the volume of the gas tank is 22.3 gal.

The density of gasoline is 0.8206 g /mL.

Now,

\(\begin{array}{c}1\,\,gallon\,\, = \,\,3785.41\,\,milliliters\\22.3\,\,gallon\,\, = \,\,22.3\,\,\left( {gallon\, \times \,\frac{{3785.41\,mL}}{{gallon}}} \right)\,\,\\ = \,\,84414.68\,mL\,\,\\ = \,\,8.441468\, \times \,{10^4}\,\,mL\end{array}\)

Therefore, the mass of fuel in the fuel tank in kilograms is

Rounding off up to 3 significant figures, we get 69.3 kg.

The mass of fuel in pounds

\(\begin{array}{c}69.27\,\,kg\,\, = \,\,69.27\,\,\left( {kg\, \times \,\frac{{2.20462\,\,lb}}{{kg}}} \right)\,\\\, = \,\,152.71421\,\,lb\end{array}\)

Rounding off, we get 153 lb.

Hence, the mass of fuel in the fuel tank in kilograms and pounds is 69.3 kg and 153 lb.