AND CALCIUM CARBONATE, ETC., OF WATER SOLUTIONS. 257 



If such a solution is now allowed to evaporate under a partial pressure 

 of 0.0003 atmosphere of carbon dioxide to one-quarter its original concen- 

 tration, we should have left a solution containing approximately 0.08 gram 

 molecule of sulphates per liter, whose degree of ionization may be taken as 

 39 per cent.' Then Cso, = 0.08x0.39 = 0.0312 



and the maximum concentration of carbonate ions would be 



Consequently 



Ooo.-°-§^ = eMXlO- 



Chco. = 0.00039X^11^ 



and the concentration of ionized calcium bicarbonate is 0.0003 mole. Its 

 degree of ionization is 63.4 per cent and the total concentration of calcium 

 bicarbonate 0.00047 mole. Comparing this result with the original solu- 

 bility of the bicarbonate (0.000264 mole), we find that while the solubility 

 of the gypsum is decreased (see below) by the accumulation of the other 

 sulphates, the solubihty of the bicarbonate increases, in consequence of the 

 decreasing concentration of the calcium ions. 



The total original gypsum in solution was 0.0091 gram molecule per 

 liter. By evaporation of the solution to one-quarter of its volume, Cgo^ 

 has become 0.0312, and consequently 



0.000059 _ 

 ^^*- 0.0312 -00019 



which we may consider as derived entirely from the ionization of the gypsum. 



Its degree of ionization in a 0.08 molar solution of sulphates is about 39 

 per cent, and therefore the total concentration of the gypsum left in solution 

 is about 0.0019/0.39 or 0.0049 gram molecule. A quarter of a liter would 

 contain 0.0012 gram molecule, and therefore of the total original 0.0091 

 gram molecule 0.0079 gram molecule or about 90 per cent would have 

 crystallized out. The weight of this would be 1.07 grams (calculated as 

 calcium sulphate).^ 



The total original concentration of calcium bicarbonate was 0.000264 

 gram molecule, and we have left a quarter of a liter with 0.00047/4 gram 

 molecule. Consequently, 0.000147 gram molecule or 0.0147 gram of cal- 

 cium carbonate should be deposited with 1.07 grams of calcium sulphate, 

 corresponding to a contamination of 1.37 per cent. 



A further evaporation to one-eighth of the original volume should de- 

 posit according to similar calculations 0.101 gram calcium sulphate with 

 0.0047 gram calcium carbonate, representing 4.7 per cent. 



With a partial pressure of 0.00003 atmosphere of carbon dioxide the 

 original solubility of the bicarbonate would be 8.3 X 10~^ moles. By concen- 

 tration of 1 liter to one-quarter of a liter, the solubility would be increased 



' The degree of ionization of magnesium sulphate, the chief sulphate left. 

 ^ During the evaporation to one-half liter, we should expect a deposit of 0.72 gram sul- 

 phate with 0.0104 gram carbonate or 1.44 per cent, carbonate would be present. 



