First off, insoluble is a relative term. Remember, we're talking about grams in thousands of gallons of water. A compound that will only solvate, or become dissolved,
at a rate of one gram in tens of millions of grams of water would properly be called "insoluble in water" when given the standard three descriptive choices of "freely soluble", "slightly soluble", and "insoluble".
The technique used by Krajewska in Ref 9 is a common lab practice known as serial dilution.
Preparing serial dilutions for which the concentration is accurately known involves three key tools: an analytical balance, volumetric pipettes, and volumetric flasks. An analytical balance is capable of weighing masses
down to 0.0001 gram (g) or 0.1 milligrams (mg), typically with an accuracy of ± 0.0001 g. A volumetric pipette is calibrated "to deliver" (TD),
meaning that if it is filled to the calibration mark and then drained properly, it will deliver an exact volume ± a small, known amount of error. A volumetric flask, conversely, is calibrated "to contain" (TC), meaning that it will contain an accurately
known volume, ± a small, known amount of error, if filled to the calibration mark.
Krajewska used another common trick by using a better solvent in her stock solution (the first solution). Since she was testing using human subjects, ethanol was the obvious choice.
Using an analytical balance, she weighed 2.5 mg (0.0025 g) of the capsaicinoid into a 1 L volumetric flask, added 20 mL of 95% by volume (v/v) ethanol, and allowed the
capsaicinoid to dissolve in the ethanol.
The volumetric flask was then filled to "Quantity Sufficient" (QS, sometimes used as a verb in labspeak, as in "will you please QS that flask with DI water for me"), that is, filled to the calibration mark, with a 2.5% weight-to-volume (w/v) sucrose solution. The alcohol, though diluted, helps to keep the capsaicinoid in solution; at this point,
the concentration of alcohol is (20 mL * 0.95) / 1000 mL * 100% = 1.9% (v/v). The concentration of sugar is (2.5% (w/v) / 100%) * 980 mL / 1000 mL * 100% = 2.45% (w/v).
The capsaicinoid content is 0.0025 g / 1000 mL * 100% = 0.00025% (w/v). Since one million mL of solution would contain 1x106 mL * 0.00025% (w/v) / 100% = 2.5 grams of capsaicinoid, the solution can also be said to contain 2.5 "parts per million" (ppm) of capsaicinoid.
Krajewska states that she then used successive 1:1 dilutions to prepare the samples for the test. That would have gone something like this:
Use a 25 mL volumetric pipette to accurately transfer 25 mL of the stock solution to a 50 mL volumetric flask. QS the flask with 2.5% (w/v) sugar solution.
This is the first dilution call it Solution A. Since it was 25 mL of stock to 25 mL of sugar water, it is called a 1:1 dilution; also, since it was 25 mL of stock solution diluted in 50 mL total, it could be referred to as a 50% dilution. It contains 25 mL * 0.00025% (w/v) / 100% = 0.0000625 g of capsaicinoid in 50 mL of
solution, so it is 0.0000625 g / 50 mL * 100% = 0.000125% (w/v) capsaicinoid, or 1.25 ppm capsaicinoid. This is exactly half the capsaicinoid concentration of the stock solution, which makes sense given that it was a 50% dilution. Note that the sugar content remains essentially the same, since sugar water is used to QS the flask.
Use a 25 mL volumetric pipette to accurately transfer 25 mL of Solution A to a 50 mL volumetric flask. QS the flask with 2.5% (w/v) sugar solution.
Solution B is now, predicably, 0.0000625% (w/v) capsaicinoid, or 0.625 ppm capsaicinoid. The ethanol content Solution B is also 1/4 of the alcohol concentration of the stock solution.
Continue to make successive 1:1 dilutions as needed.
Per Krajewski, samples used in the test ranged from 0.625 ppm down to 0.019 ppm capsaicinoid, so she made seven 1:1 serial dilutions and used numbers 2 through 7.
Is there a limit to the number of serial dilutions that you can make with reasonable accuracy? Yes. With each successive pipette transfer and flask QS, the small error mentioned above
is compounded, like interest on an unpaid credit card. The worse the accuracy of the glassware, the faster the error compounds.
Last updated 31 January 2015.
(c) 1999-2016 Mike Whittemore
All graphics (c) 1999-2016 Mike Whittemore
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