AND CALCIUM CARBONATE, ETC., OF WATER SOLUTIONS. 263 



partial pressure of carbon dioxide to one-ninth its present value. In view, 

 however, of the unknown change of solubility of calcium carbonate (the 

 change in the ion product constant), it must remain undecided whether a 

 rise of temperature would be a favorable or an unfavorable factor in the 

 crystallization of gypsum free from carbonate. The formation of bicarbon- 

 ate would also be directly proportionate to the square root of the solubility 

 constant according to equations (40) and (42). 



SUMMARY OF RESULTS. 



(1) From Arrhenius's data on the solubility of silver acetate, valerate, 

 and butyrate in the presence of the sodium salts of the same acids, it was 

 shown that the solubility or ion products are approximate constants, as 

 calculated on the basis of the well-estabhshed principle of isohydric solu- 

 tions. This, with the results of others,^ removes the discrepancy existing 

 in the relation between the solubility product and the ionization of strong 

 electrolytes and gives us a safer empirical foundation for the consideration 

 of the equilibrium conditions existing between two precipitates, one which 

 is in harmony with the fundamental work of Guldberg and Waage. 



(2) The second ionization constant of carbonic acid may be taken as 

 7.0 X 10~" as calculated from McCoy's data with the aid of corrections sug- 

 gested but not carried out by the latter. 



(3) The solubihty product of calcium carbonate is found to be 1.26 X 10~* 

 on the basis of Schloesing's experiments on the solubility of calcium car- 

 bonate at 16° under varying partial pressures of carbon dioxide. 



(4) The solubility of calcium carbonate and calcium bicarbonate is ap- 

 proximately proportionate to the square root of the partial pressure of 

 carbon dioxide in the presence of a large excess of calcium sulphate. 



(5) The theory of the equilibrium conditions between calcium sulphate 

 and calcium carbonate and bicarbonate has been developed and may prove 

 useful in the study of the natural waters of the present day. 



(6) Considering the results given in tables 5,^ 6,^ and 8,* we find that the 

 favorable factors for the crystalHzation of pure gypsum should be: 



(a) The absence of other sulphates which in moderate proportions 

 render gypsum less soluble and consequently enable solutions to take up 

 more calcium bicarbonate than pure aqueous saturated solutions of gypsum 

 can dissolve. 



(6) The presence of sodium chloride in the proportion of about 8 to 25 

 per cent.* 



(c) A very low partial pressure of carbon dioxide, the solubility of cal- 

 cium carbonate varying approximately as the square root of the partial 

 pressure of carbon dioxide, according to (4). 



(d) An increase of temperature by decreasing the coefficient of absorp- 

 tion of carbon dioxide would possibly, but not certainly, be a favorable fac- 

 tor, the formation of calcium bicarbonate being proportionate to the square 

 root of the absorption coefficient of carbon dioxide, which falls with increase 

 of temperature. 



' A. A. Noyes, loc. cit.; Findlay, loc. cit. ^ Page 254. ' Page 258. * Page 261. 

 « Solutions 5, 6, 7, table 7, p. 260. 



