Summary. 247 



From these ionization-constants (ivw) approximate values of the 

 internal-energy-increase At/ attending the reaction H 2 = H + -|- OH" 

 (the so-called heat of ionization) can be computed by the familiar equa- 



rflogKw At/ 



tion* derived from the Second Law of Energetics: 7= = ~^p2 



This is best done by integrating it under the assumption that At/ is a 

 linear function of the temperature as expressed by the equation At/ = 

 At/ -f- aRT. The integral then has the form : 



. K 2 . T 2 At/ T 2 T t 



From the values of the ionization-constant K at 0, 25, and 100, the 

 values of the constants At/ and a have been found to be 28460 and 



24.923, respectively. Therefore, the general equation for the energy- 

 increase attending the ionization becomes : 



At/ 28460 49.5 T, 



and that for the ionization-constant becomes : 



k>g 10 (10 16 /O = 84.450 ~~ 24.923 log 10 T. 



The values of the energy-increase in calories and of the ionization-constant 

 of water as calculated by these expressions are given in table 145. 



*This equation ceases to be even approximately exact at high temperatures where 

 the vapor-pressure of water becomes very large. The exact expression, which may 

 be derived through the consideration of an appropriate cyclical process, is as follows : 



^ir '^S y.r |-iwri-_qjyg) j 



where A/ is the energy-increase and &V is the volume-increase that attends the 

 ionization of one mol of water under the pressure p P, which is substantially identi- 

 cal with the vapor-pressure p, since the osmotic pressure P is in this case negligible 

 in comparison. Approximate values of &V up to 140 have been computed by 

 Tammann (Z. phys. Chem., 16, 144. 1894) which show it to be equal to about 26 

 ccm. at 140 ; and since it is shown to be increasing at a rate roughly proportional 

 to the compressibility of water, it probably has a value in the neighborhood of 40 

 c. cm. at 218. Assuming this to be the case, the last term in the above equation can, 

 with the help of the existing vapor-pressure data, be shown to have a value of about 



170 calories at 218, while the value of A/ as computed by the linear equation is 

 4155 at 218. Thus at temperatures above 200 this last term begins to form a sub- 

 stantial part of the whole. 



