252 EQUILIBRIUM BETWEEN CARBON DIOXIDE OP ATMOSPHERE 



Combining the three equations by dividing III by IV and multiplying 

 by II, we find: tt-, 



C=^HC03 = ^;°""^'"° X A^gas X CcOa X CcO, (^1) 



-1^ Ionization 



and 



ChcOs = V k^"'''"° X ^«- X ^coa X Cco, (42) 



» -^ Ionization 



Now, for a solution saturated with calcium carbonate and gypsum at 

 about 18°, Ccos ^^y ^^ ^^^^ ^^ ^ ^^^* approximation to have a maximum 

 value of 1.64 X 10~^ as shown above (equation 40), the calcium ions produced 

 from the bicarbonate being neglected in this first approximation and only 

 those from the gypsum being considered.^ At 18° the solubihty constant 

 for carbon dioxide,^ fcgag, is 0.04183 if Ccos be expressed in atmospheres. 

 In the given case Ccoo is 0.0003 atmosphere. Inserting all these values 

 and the two known ionization constants of carbonic acid into equation (42), 



w^ ^^^ / q CiA — i7w 



Chco3 = V 7 ox 10-" X0.04183X0.0003 X 1-64 X 10-« 



and 



CHCOa = 0.0003 



For the calcium ions belonging to the bicarbonate we have 



Cca=iCHC03 = 0.00015 



We have found then the ionized portion of the calcium bicarbonate in 

 the saturated solution. To determine the total dissolved bicarbonate its 

 degree of ionization in the mixture must be ascertained. Its degree of 

 ionization will depend not on its own concentration alone, but, according to 

 the principle of isohydric solutions, also on that of the calcium sulphate 

 present. We may imagine, according to the method of Arrhenius, the water 

 divided between the two salts in such a way that each in its portion yields 

 the same concentration of the common ion calcium. Since there is 50 times 

 as much sulphate as bicarbonate, the latter will secure only about 2 per 

 cent of the water, the sulphate about 98 per cent, and the sulphate will 

 ionize practically as if it were present alone. Its degree of ionization is then 

 50.6 per cent (p. 250), and its concentration of calcium ions 0.00769 or 

 0.01538 calcium ion equivalent. This, then, must also be the concentration 

 of the calcium ion equivalents in the isohydric bicarbonate solution, and so 



^^ ^^^^ CjCa(HC03)2Xa = 0.01538 



* The amount of calcium bicarbonate found in solution by this first approximation 

 corresponds to 0.00015 gram ion of calciimi. The calcium ions from the carbonate are 

 negligible and therefore the total concentration of calcium ions from sulphate and bicar- 

 bonate is 0.00769 + 0.00015 or 0.00784, and the maximum value for CcOs is, corrected, 

 1.26X10-V0.00784 (equation 40) or 1.16X10-* in place of 1.64 XlO^*. No correction was 

 made for this small difference, the results of the first approximation being considered suffi- 

 ciently accurate, especially in view of the facts that the solubility of calcium sulphate will 

 be slightly affected by the presence of the bicarbonate in such a way as to counterbalance 

 this error and that the degrees of ionization of salts are uncertain. 



^ Geffcken, loc. cit. The total salt concentration (0.03 mole) is too small to require a 

 correction for the changed solubility of carbonic acid. 



