769 
a solubility product of 0.054. This product thus agrees perfectly 
with ours. 
The determination of Herz v. Muns and our own determinations, 
by two methods, show thus conclusively that we have to reckon with a 
solubility product of 0.055. 
UI. Determination of the concentration of Ca ions in solutions 
which hold other salts besides. 
1. The concentration of Ca’ ions of 0.02°/, CaCl, 6aq. in 0.5°/, NaCl. 
For the system CaCl, = Ca” + 2 Cl’ the following also holds: CaCl, <2 K Ca” Cl: 
K can be found if the degree of ionisation z of a given CaCl, solution is known. 
For Ca(NOs), 0,1 %/, (= 6m.M. per L.) « is 0,67 }). 
We have therefore 
[Ga(NO3)2] — « [Ga(NOs),] = K a Ca” a? (NO3)* 
or because 
[CGaNO,] = [Ca ] = [NO3] = 6 m.M. per L. 
1 — 0,67 = KX 0,673 (NOs)? 
1 — 0,67 = K X 0,675 X 0,036 
K = 30. 
This is therefore the dissociation constant for Ca(NO3); that for CaCl will 
differ very slightly from it. 
For 0,02°/, CaCl,6 aq. or 0,91 millimol per L., in 0,5°/, NaCl also holds: 
[CaCl,] = K Ga Cl?. 
The conc. of CY is given by the dissociation of 0,5°/) NaCl. Here « = 0,82 
(Osmot. Druck u. lonenlehre, p. 53); [Cl] thus becomes 7 m.M. In addition to 
this there is still [CI of 0,91 m.M. CaCl,, + half of which we may consider to 
be dissociated without committing a large error. The total [Cl’] then becomes 
+8m.M. 
Thus 
CaCl, = K (0,91 — CaCl) 0,064. K=30. CaCl, = 0,60 m.m. 
Of 0,91 m.m. CaCl, thus 0,06 m.m. is not dissociated while 0,31 m.m. is disso- 
ciated. The solution therefore contains 12,4 mgr. free Ca” per L. 
Experimentally it appears that an oxalate concentration of 0.18 
m.m. is necessary before turbidity results in a solution of NaCl 
0.5 °/, + CaCl, 6 aq. 0.02 °/,. From this follows a [Ca] of 
— 0.055 : 0.18 = 0.30 m.m., or 12 mgr. per L. This determination 
thus is perfectly in correspondence with the calculation. 
2. Determination of the concentration of Calcium ions in physio- 
logical salt solutions. 
In a solution of the composition: NaCl 0.7°/,, NaHCO, + 0.18°/,, 
KC} 0.02°/, and CaCl, 6 aq. 0.040°/,, with a certain carbonic acid 
') Osmot. Druck u. lonenlehre. I, p. 53. 
