How the program works:
Ammonium Sulfate is very soluble in water so saturated ammonium sulfate is a 4.1M solution at 25oC, 4.06M at 20oC, 3.97M at 10oC, 3.93M at 4oC and 3.9M at 0oC. The molecular formula of ammonium sulfate (NH4)2S04 and the molecular weight is 132.14, so that saturation occurs at 541.8 g/L at 25oC, 536.49 g/L at 20oC, 524.6 g/L at 10oC, 519.1 g/L at 4oC and 515.35 g/L at 0oC. The specific volume of ammonium sulfate is also dependent on the temperature but is about 0.54 ml/g, meaning that if you add 1g of ammonium sulfate to an aqueous solution, the volume will increase by about 0.54ml. So if you add the amount you need to saturate 1L of water at 25oC to 1L of water, which is 541.8 g of ammonium sulfate, you will not get a saturated solution. 1L of water plus 541.8g of Ammonium Sulfate gives 1L plus 541.8 * 0.54 mls, equal to 1,293 mls final volume, so the solution will 1,000/1,293 * 100 percent saturated, which is about 77%. And if you want to make, for example, a 25% solution up to 50% by adding solid ammonium sulfate, that calculation is also not as simple as you might think- because the ammonium sulfate contributes so much extra volume you need more solid ammonium sulfate to take a solution from 25% saturation to 50% saturation than you needed to raise it from 0% to 25% saturation. Because of this most people use a table or nomogram to figure out how much ammonium sulfate to add. You can find tables to do this in many places (e.g. see the chapter by Englard and Seifter in Methods in Enzymology volume 182, published in 1990, also see Scopes, R. K. "Protein Purification: Principles and Practice", Springer-Verlag New York, 1994). Or you can use our unique (as far as we know) online program which will conveniently calculate the necessary amount for you. The tables are good to get the amounts you need to add to 1L or 100mls of solution, and you then have to generally calculate for the volume you actually have from there. Our program also factors in the volume you are working with, saving you further calculations so you can head straight to your balance. Our program uses the equation;
G = Sat(M2-M1)/(SatM-(SpecVol/1000*132.14*SatM*M2))
In which G = the weight of Ammonium Sulfate to add in grams per liter, Sat is the number of grams/Liter in a saturated solution of Ammonium Sulfate, M2 = the molarity you want to achieve, M1 = the starting molarity, SatM is the molarity of a saturated solution of Ammonium Sulfate. SpecVol is the specific volume of Ammonium Sulfate, which is the amount of volume 1g will add to an aqueous solution, which is about 0.54 mls. Sat, SatM and SpecVol all vary with the temperature, and the program takes into account. The number 132.14 is the molecular weight of Ammonium Sulfate. The equation and the various factors used are based on those published in supplement 13, section A.3F.1 of "Current Protocols in Protein Science", edited by Coligan et al., John Wiley (1998).
This program and the different publications listed above may give slightly different results, so who is right? There are many reasons why different calculations give somewhat different results, so it is better to stick to one table or protocol that you know works, since whether you actually have 50% or 50.8% saturated Ammonium Sulfate is not really that important, so long as you can reproducibly make whatever concentration is appropriate for whatever you are doing.