Cherylyn L. answered • 6d

PhD in Chemistry with 10 years of Tutoring and Teaching Experience

The gas tank of a certain luxury automobile holds 22.3 gallons according to the owners manual. If the density of gasoline is 0.8206 g/mL, determine the mass in pounds of the fuel in a full tank.

Density = ^{mass}/_{Volume} or D = ^{m}/_{V}

Given: V = 22.3 gal

D = 0.8206 g/mL

1) Rearrange the equation to solve for m

2) Find conversion factor(s) and convert V from gal to mL (by dimensional analysis) so the units cancel

3) Solve for m in g

4) Find conversion factor(s) and convert m from g → lbs

1) D = ^{m}/_{V} rearranges to m = D ∗ V

2) 1 gal = 3.785 L and 1 L = 1000 mL; 22.3 ~~gal ~~ ∗ ^{3.785 L}/_{1 gal } ∗ ^{1000 mL}/_{1 L } = 84 406 mL

3) m = 0.8206 ^{g}/_{mL}~~ ~~ ∗ 84 406 ~~mL ~~ = 69 260 g

4) 1 lb = 453.6 g; 69 260 ~~ g ~~ ∗ ^{1 lb}/_{453.6 g } = *153 lbs *