WORK OF C. M. STINE. 25 



It is unnecessary to extend these calculations to the remaining, more concentrated 

 mixtures, since it is evident that the differences between the values calculated on 

 the basis that the two salts form the same hydrates in separate solutions that they 

 form in the mixtures, and the values for A obtained experimentally become increas- 

 ingly larger with increase in concentration. It is further evident that the hypothe- 

 sis is untenable from the fact that it would call for the elimination of 944 grams of 

 water per liter of solution in the case of the 2.5 N mixture of the above salts, and of 

 1,047 grams in the case of the 2.9 N mixture. 



At the moment of mixing the two solutions, each salt is prevented from forming 

 the hydrate which it ordinarily forms in separate solution by the amount of water 

 which has been eliminated from the sphere of action as solvent in the formation 

 of the hydrate of the other component of the mixture. Consequently, for the more 

 dilute solutions at least, the hydrates formed by a salt in separate solution should be 

 related to the hydrates formed by the same salt in the mixture at corresponding 

 concentrations, as the amount of water present as solvent in the single solution 

 is related to the amount present as solvent in the mixture. For example, take 

 calcium chloride and magnesium chloride, 0.15 N solutions of each. Referring to 

 tables 9 and 10, if X represents the unknown value of M for calcium chloride, in 

 the mixture 6 : X : : 1,000 : 897. 6.0 is the value of M for 0.15 N calcium chloride 

 in separate solution, and this has been corrected to 1,000 grams of solvent. The 

 figure 897 is found by subtracting from 1,000 the number of grams of water with 

 which the magnesium chloride combines when it forms the hydrate indicated for the 

 concentration in question in table 10, plus the difference between the amount of water 

 present in the solution and 1,000 grams, as given by the weight-normal correction. 



Having thus obtained the values of M for the salts in the mixture, it is possible 

 to solve for L' from the equation 



iooo -f-x ioooI 



M= 



18 



where L represents the theoretical lowering found for the salt by calculating it from 

 the value of a, which has been determined for the mixture in question. This value 

 of L' must then be corrected, in order to obtain the value as it would be observed, 

 by dividing it by the proper per cent. This percentage correction is found by de- 

 ducing the number of grams of water eliminated as water of hydration by the other 

 salt in the mixture, basing the calculation upon the value of M worked out for the 

 mixture. To this must be added the percentage correction which the weight- 

 normal correction has given. 



The sum of these values for V for the two salts in the mixture should then be 

 equal to A as found experimentally for the mixture, provided this hypothesis is 

 correct. In table 13 the values thus obtained are given. 



M c = the value for M deduced from the proportion. 

 L,' C C0T ' = i\\e value for L', with proper percentage correction. 

 Sum = sum of the two values for L' c cor - for the two salts multiplied by 

 the normality of the solution. 

 A = the lowering found experimentally for the same mixture. 



