the density of mercury is 13.53 g/cm^3. what is the density in lbs/gallon

Question

i need to do this using dimensional analysis 

Answer 1

To use dimensional analysis effectively, one need to know the various conversion factors that are involved.

Here, one needs to know the conversion factor for grams to pounds, and for cm³ to gallons.

454 grams = 1 pound

1 gallon = 3.875 liters = 3785 cm³

 

Done in a continuous manner using dimensional analysis:

13.53 g/cm3 x 1 lb/454 g x 3785 cm3/1 gal = 112.8 lbs/gallon

 

 

Done separately:

Converting 13.53 g to pounds:
13.53 g x 1 pound/454 g = 0.0298 pounds
Converting 1cm3 to gallons:
1cm3 x 1 gallon/3785 cm3 = 0.000264 gallons
Density expressed as pounds/gallon = 0.0298 pounds/0.000264 gallons = 112.87 lbs/gallon = 112.9 lbs/gallon