Question E.9: Density as a Conversion Factor The mass of fuel in a jet mus...
Density as a Conversion Factor
The mass of fuel in a jet must be calculated before each flight to ensure that the jet is not too heavy to fly. A 747 is fueled with 173,231 L of jet fuel. If the density of the fuel is 0.768 g/cm³ , what is the mass of the fuel in kilograms?
SORT Begin by sorting the information in the problem into
given and find.
GIVEN: fuel volume = 173,231 L
density of fuel = 0.768 g/cm³
FIND: mass in kg
STRATEGIZE Draw the conceptual plan beginning with the given quantity, in this case the volume in liters (L). Your overall goal in this problem is to find the mass. You can convert between volume and mass using density (g/cm³ ). However, you must first convert the volume to cm³. Once you have converted the volume to cm³, use the density to convert to g. Finally, convert g to kg.
CONCEPTUAL PLAN
RELATIONSHIPS USED
1 \ mL = 10^{-3} \ L
1 mL = 1 cm³
d = 0.768 g/cm³
1000 g = 1 kg
(These conversion factors are in the inside back cover of your book.)
SOLVE Follow the conceptual plan to solve the problem. Round the answer to three significant figures to reflect the three significant figures in the density.
173,231 \ \cancel{L}\times\frac{1 \ \cancel{mL}}{10^{-3} \ \cancel{L}} \times \frac{1 \ \cancel{cm^3}}{1 \ \cancel{mL}}\times \frac{0.768 \ \cancel{g}}{1 \ \cancel{cm^3}} \times \frac{1 \ kg}{1000 \ \cancel{g}} =1.33 \times 10^5 \ kgCHECK The units of the answer (kg) are correct. The magnitude makes sense because the mass (1.33\times 10^5 kg) is similar in magnitude to the given volume (173,231 L or 1.73231 10^5 \ L), as you would expect for a density close to one (0.768 g/cm³).