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

Answer 1

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

Answer 2

This question requires a few conversions:

gallons x liters/gallon x mL/L x g/mL x pounds/g

You initially have 22.3 gallons.

There is 1 liter/ 0.264 gallons

There are 1000 mL/ 1 liter

From the density given we have 0.8206 g/mL

There is 1 pound / 453.6 grams

So we have: 22.3 gallons x (1 liter/ 0.264 gallons) x (1000 mL/ 1 liter) x (0.8206 g/mL) x (1 pound / 453.6 grams)

Multiplied all together we get: 153 pounds of gas in a full tank (3 significant figures because there is only 3 sig figs in the number of gallons given).