Final answer:
The density of platinum is converted from 21.5 g/cm³ to approximately 12.505 lb/gal by first converting grams to pounds, and then cubic centimeters to gallons using the appropriate conversion factors.
Step-by-step explanation:
You are asking how to convert the density of platinum from grams per cubic centimeter (g/cm³) to pounds per gallon (lb/gal). To do this conversion, we need to use a series of conversion factors. Platinum has a density of 21.5 g/cm³. There are 454 grams in a pound, and there are 3.78541 liters in a gallon, with one liter being equivalent to 1,000 cubic centimeters.
First, convert grams to pounds:
21.5 g/cm³ x (1 lb/454 g) = 0.04735 lb/cm³
Now, convert cubic centimeters to gallons:
0.04735 lb/cm³ x (1,000 cm³/1 L) x (1 L/3.78541 gal) = 12.505 lb/gal (rounded to three significant figures).
Therefore, the density of platinum is approximately 12.505 pounds per gallon.