Dilution Calculations

   Dilution calculations are easy when you're in the middle of your chemistry class in college.   However, if you haven't done one in quite some time, it's easy to make mistakes.   One thing that is important to remember is that there is a difference between mass and volume percentages.  Rather than trying to remember chemical quantities that you may have forgotten (molarity and molality and others), I'll show you how to simply think through such a calculation (but I hope you haven't forgotten all of your chemistry!).   Let's illustrate the calculation procedure with the following example:

    A hydrogen peroxide (H₂O₂) solution is commercially available as a 35% by mass solution in water (H₂O).  You wish to prepare two solutions, one at 10% by mass hydrogen peroxide and one at 10% by volume hydrogen peroxide.  The densities you'll need are: d (commercial solution) =9.4 lb/gal, d (water) = 8.3 lb/gal, d (hydrogen peroxide) = 11.98 lb/gal.

10% by mass hydrogen peroxide solution

1.  Choose a basis for the calculation
   BASIS: 10.0 lbs of 10% by mass hydrogen peroxide
    10.0 lbs of solution = 9.0 lbs water + 1.0 lb hydrogen peroxide

2.  Measuring is done by volume, calculate the volume of solution which contains 1.0 lb of H₂O₂.
    lbs hydrogen peroxide/gal solution = d (commercial solution) x mass % of solution
    lbs hydrogen peroxide/gal solution = (9.4 lb/gal)(0.35) = 3.29 lb hydrogen peroxide/gal solution

3.  Scale up or down to find the volume of solution needed for 1.0 lb hydrogen peroxide
    1.0 lbs hydrogen peroxide  =  3.29 lbs hydrogen peroxide
   X gal solution                          1.0 gallons solutions

    X = 0.304 gallons solution, therefore 1.0 lbs hydrogen peroxide = 0.304 gal solutions

4.  Find the mass of water in the amount of solution needed to make 1.0 lb of hydrogen peroxide
    lbs solution = (volume solution) x (solution density) = (0.304 gal solution)(9.4 lbs/gal) = 2.86 lbs soln
    lbs water = (lbs solution) x (mass % water) = (2.86 lbs solution)(0.65) = 1.86 lbs water

5.  Find the extra water that needs to be added
According to our basis, we need a total of 9.0 lbs of water.  In the amount of solution that contains our needed weight of hydrogen peroxide, we found that there are 1.86 lbs of water, so we still need:
9.0 lbs water - 1.86 lbs water = 7.14 lbs water
volume extra water = (mass extra water)/(density of water)
volume extra water = (7.14 lbs water)/(8.3 lbs water/gallon) = 0.860 gal water

6.  Find your "MAGIC NUMBER"
For a 10% by mass hydrogen peroxide solution being prepared from a 35% by mass hydrogen peroxide solution, you need to add 0.860 gal of water for every 0.304 gal of solution:
0.860 gal water = 2.829
0.304 gal solution
    When preparing these solutions, multiple the volume of solution of 2.829 to find the volume of water to be added.

10% by volume hydrogen peroxide solution

1.  Choose a basis for the calculation
    BASIS:  1 gallon of 10% by volume hydrogen peroxide
    1.0 gallon solution = 0.9 gallons water + 0.1 gallons hydrogen peroxide

2.  Find the volume of hydrogen peroxide in 1.0 gallon of solution
    Since the solution concentration is on a mass basis, find the mass of hydrogen peroxide in one gallon, then convert to volume:

    lbs hydrogen peroxide/gallon solution = d (commercial solution) x mass % solution
    lbs hydrogen peroxide/gallon solution = (9.4 lb/gal)(0.35) = 3.29 lb hydrogen peroxide/gal solution
    gal hydrogen peroxide = lb hydrogen peroxide/d (hydrogen peroxide)
    gal hydrogen peroxide = (3.29 lb hydrogen peroxide)/(11.98 lb H₂O₂/gal H₂O₂)
    gal hydrogen peroxide = 0.275 gal hydrogen peroxide/gal solution

3.  Find the amount of water needed
    From part 2, we know that there is 0.275 gal hydrogen peroxide/gal solution.  Therefore:
    gal water/gal solution = 1.0 gal solution - 0.275 gal hydrogen peroxide
    gal water/gal solution = 0.725 gal water

    With a total of 0.275 gal hydrogen peroxide, the total volume of solution is 0.275/0.10 = 2.75.  So, the total volume of water needed for a 10% by volume hydrogen peroxide solution is:
    Extra water needed = Total soln volume - H₂O₂ volume - water volume already in solution
    Extra water needed = 2.75 gal - 0.275 gal - 0.725 gal = 1.75 gal water

4.  Find you "MAGIC NUMBER"
    For a 10% by volume hydrogen peroxide solution being prepared from a 35% by mass hydrogen peroxide solution, you need to add 1.75 gal water for every gallon of solution:

    1.75 gal water = 1.75
    1.00 gal solution
    When preparing these solutions, multiple the volume of solution by 1.75 to find the volume of water to be added.