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Ask the Expert Question-and-Answer Archive

by Ron Joseph

October, 2006

Converting Grams/Liter to Lbs/Gal Using a Density (WPG) Cup

Q: I am trying to explain to my laboratory technology students the mathematical reason that when using a 83.2 cm3 weight to volume cup, just multiplying the grams of the substance by 0.1 will give you the lbs/gallon.

A: This is a great question!  I've always wanted to attack this problem myself and now you have given me the excuse to do so.

The solution is nothing more than using conversion factors to convert grams/liter (g/L) to lbs/gal.

Here goes:

1 lb       =          453.6 g

1 gal     =          3.785 L

1L         =          1,000 g

Let the weight of the coating in the density cup = X g

Density of the coating     =          X g

                                                83.2 cm3

                                     =         X g

                                                0.083 L

Now let us convert grams to lbs, and liters to gallons:

                                    =          X g  *  3.785 L/gal

                                                453.6 g/lb  *  0.0832 L

                                    =          0.1*X

The definitions of grams and liters are based on the density of water.  One gram is the weight of 1 cm3 of water.  One liter = 1,000 g, and the density of water is 1,000 g/L. In American units the density of water = 8.32 lbs/gal and hence it is not coincidental that the density cup has a volume of 83.2 cm3 or 0.0832 L.

Best wishes,

Ron Joseph

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