Febeuaby 2, 1906.] 



SCIENCE. 



177 



the aggregates as unstable, and supposing 

 the ions to slip along through continually 

 changing groups of water molecules. This 

 hardly seems compatible with the consider- 

 able interaction which must take place be- 

 tween the ions and the water molecules, to 

 reduce their degrees of freedom as much 

 as the figures indicate ; but it is the best 

 way out of the difficulty that 1 have found. 



I may remind you that Jones and his 

 fellow workers, in their study of the 

 freezing points and boiling points of con- 

 centrated solutions, have found deviations 

 from the laws of van't Hofi: and of Ar- 

 rhenius, which they have accounted for by 

 the assumption of the formation of such 

 molecular aggregates as I have described. 



One is tempted to follow out the sug- 

 gestions of this hypothesis to see if any gen- 

 eral relations can be found in the constants 

 A and C. There are really too many un- 

 known quantities in the expressions for 

 these constants to make it possible to pro- 

 ceed at all except by conjecture, and I have 

 already rioted so much in conjecture, that 

 to go further may seem to carry me beyond 

 the bounds of reason. Yet, if you will 

 indulge me, I will describe such indications 

 of general law as I have detected. Each of 

 the terms A and (7 is a sum of the heat 

 capacity of part of the solute and of the 

 change in heat capacity experienced by the 

 water molecules when they unite with it. 

 A refers to the molecules, C to the ions. 

 We need a knowledge first of the heat ca- 

 pacities of the molecules and of the ions 

 of the solute. In the case of sulphuric 

 acid, its heat capacity in the liquid state is 

 34, sufficiently near the value of A, which 

 is 37, to make it possible to suppose that 

 its undissociated molecule either does not 

 associate water molecules to itself or, if it 

 does do so, does not affect their heat ca- 

 pacities. To get the heat capacity of the 

 ions, I am reduced to adding together their 

 atomic heats obtained from the tables. In 



all but one case where a comparison is pos- 

 sible between this sum and the heat ca- 

 pacity of the solid solute, the two agree 

 well together. The sum for sulphuric acid 

 is 27, agreeing with the heat capacity 26 

 of the solid acid. Using this number for 

 a in the formula C^a-\-a{fj> — s), we 

 get ai(f> — s) ^ — 70. The symbol a ex- 

 presses the number of water molecules af- 

 fected by the presence of each ion, of which 

 there are 3 for each molecule of sulphuric 

 acid. If we venture to suppose that the 

 number of water molecules affected by 

 each ion is 8, the value of a is 24, and 

 <j> — s ^ — 3. Now the heat capacity of 

 the water molecules is 18, so that, on these 

 suppositions, the loss of heat capacity of 

 each water molecule due to its association 

 with an ion of the solute is one-sixth its 

 original heat capacity. This would involve 

 a loss either of 3 external degrees of free- 

 dom, translational or rotational, or of one 

 external and one internal degree of free- 

 dom. I choose the number 8 for the num- 

 ber of molecules of water affected by the 

 ion, because such might be the number of 

 those standing nearest the ion in a regular 

 arrangement which would be compatible 

 with freedom of motion. We may think 

 of the ion as at the center of a cube, with 

 the water molecules at its corners. If the 

 ion reaches out to more distant molecules, 

 the next larger group it will affect will 

 contain 14 molecules. 



To a close approximation the values of 

 C and a for hydrochloric acid, ammoniiim 

 chloride, sodium chloride and sodium hy- 

 droxide, lead to the same value — 3 for 

 (f> — s, on the supposition that a = 16, or 

 8 + 8. The same result for <^ — s is 

 reached for potassium chloride and potas- 

 sium hydroxide if we set a = 22, or 14 + 

 8. In the case of magnesium sulphate the 

 value of C is extraordinarily large, and 

 indicates a much larger group of water^ 

 molecules around the magnesium ion. That 



