[haha]

I am not quite sure how to use specific gravity in the following problem:

I have Vitamin D3 that has 1,250,000IU/g with a specific gravity (SG) of 0.95.  I want to make a final solution of 50,000IU/mL.  How many mL of the final solution will I have if I start with 150mL of Vitamin D3?


Potential Answer 1:

D=M/V
Density = Specific Gravity
SG=M/V
V= M/SG = 1250000IU/g / 0.95 = 1315789.47IU/mL
1315789.47IU/mL / 50000IU/mL * 150mL = 3947.368mL final vol


Potential Answer 2:

D=M/V
Density = Specific Gravity
SG=M/V
M = SG*V = 0.95 * 150mL = 142.5g
142.5g * 1250000IU/g / 50000IU/mL = 3562.5mL final vol


Which way is correct but more importantly why is the incorrect answer wrong?  Thank you all for your help.

[Hunter2]

What does IU/g or IU/ml mean. IU what unit is it?

From logical the second solution would be the right one.

The UI has nothing to do with mass or volume, so it cant be calculated with specific gravity.

[haha]

What does IU/g or IU/ml mean. IU what unit is it?

From logical the second solution would be the right one.

The UI has nothing to do with mass or volume, so it cant be calculated with specific gravity.

IU = International Unit.  Vitamin D3 is not typically measured in g or mL, but in IU.  To simplify the thought the IU remains constant therefore IU/g can be considered a mass and IU/mL can be considered a volume.  IU is only a unit of measure for Vitamin D3, along with a few other vitamins.

[Arkcon]

This page provides the conversion factor for 3 vitamins from IU to mg:  https://dietarysupplementdatabase.usda.nih.gov/conversions.html  I don't know why you need it, but its easy enough to find.

Anyway, look at it this way:  You have a suitcase full of 1,250,000 dollars.  You need a paper bag with 50,000 dollars.  How do you get it?

[haha]

The IU isn't the issue in the 2 different answers above.  There is a math issue with using the specific gravity in the density formula (D=m/V).  The only difference in the two answers is that one is dividing by SG and the other is multiplying by SG.  Therefore one of these calculations is incorrectly using of the density formula.

[AWK]

V= M/SG = 1250000IU/g / 0.95 = 1315789.47IU/mL

?
V has unit mL not IU/mL