Units of Concentration (v/v, w/v, w/w and ppm)
These units of concentration are most often seen and used with commerical products.  Expect for 'ppm' they are not used often in the lab.
 
Percent Concentration Volume/Volume (v/v):  used with 2 liquids.
      % Concentration = Vsolute      X  100%
                                       Vsolution

    eg.   5 mL of vinegar are dissolved in 100 mL of vinegar solution.  What is its v/v concentration.

        % concentration =    5 mL of vinegar    X 100%  = 5%
                                        100 mL of solution
 

Example #1   A photographic stop bath contains 140 mL of pure acetic acid in a 500 mL bottle of solution.  What is the v/v concentration?
 
        % concentration = 140 mL of vinegar  X 100% = 28%
                                        500 mL of solution
 

Percent Concentration Weight/Volume (w/v): used with one solid and one liquid
This means there is a certain mass, in grams, in every 100 mL of solution.
 
eg.   a 3% H2O2 topical antibiotic solution means that there is 3 grams of H2O2 in every 100 mL of solution.
 

Percent Concentration Weight/Weight (w/w): used with two solids
Useful when dealing with alloys of precious metals.
 
eg.  A ring with a mass of 12.0 grams contains 11.1 grams of pure silver.  What is the w/w%?

    % concentration =   11.1 grams of solute      X  100% = 92.5% w/w of silver
                                    12.0  grams of solution
 


Parts per Million Concentration (ppm)
Environmental solution are often very low in concentration.  We often use terms like:
1 part per million (ppm): 1 part out of 1 X 106 parts
1 part per billion (ppb): 1 part out of 1 X 109 parts
1 part per trillion (ppt): 1 part out of 1 X 1012 parts

1 ppm = 1 drop in a full bathtub
1 ppb = 1 drop in a full swimming pool
1 ppt = 1 drop in 1000 full swimming pools
 

We express ppm concentration in a variety of units depending on what we need to use.  But they are all interrelated.
 
ppm =   1 g        =       1 g      =        1 mg       =    1 mg     =   1 microgram
            106 mL        1000 L             1 L               1 kg                    1 g
 
Example #2   Dissolved O2 in water shows a concentration of 250 mL of water At SATP and 2.2 mg of O2.  What is the concenrtaion in ppm?
ppm concentration = 1 mg   =   2.2 mg   =  8.8 mg/L = 8.8 ppm
                                   1 L          0.25 L

Go to the
Concentration Unit Calculations Other than Molarity Workshsheet