from the Standpoint of Physical Chemistry. 229 



perature was developed by van't HofT. The principle is of 

 great importance, but it does not appear to have received the 

 attention it merits in the study of penological problems. 



The basic principle of van't HofFs law is that change of 

 temperature displaces the equilibrium within a solution. If, 

 then, crystallization of a magma can be brought about, in one 

 case at a higher and in another case at a lower temperature, 

 the chemical state of the solution as regards compounds exist- 

 ing within it will be different in the two cases. Change of 

 pressure between the depths of the earth and the surface is an 

 effective agent in changing the temperature at which crystalli- 

 zation begins. Pressure alone, as has been pointed out by 

 several writers,* is not capable of causing great variations in 

 the melting-points of minerals; but it is quite conceivable, and 

 in fact probable, that within a complex solution the variation 

 of the temperature of crystallization caused by relief of pres- 

 sure is often attended by displacements of equilibrium, such 

 that reactions proceed further in one direction or another and 

 the relative proportions of the various compounds present is 

 altered. These displacements of equilibrium find correspond- 

 ing expression in the point at which crystallization is initiated 

 and in the minerals deposited. The change thus begun tends 

 to progress continuously in the same direction and may result 

 at the final consolidation in an association of crystallized prod- 

 ucts quite different from what would be found under conditions 

 of greater pressure. f 



* A. Harker : The Natural History of Igneous Rocks, New York, 1909, pp. 

 163 and 194. 



f The effects of temperature and pressure upon reactions within a system 

 of the nature of a magmatic solution are expressed by two fundamental equa- 

 tions. The first is van't Hoff's formula 



logK'-logK = £(-± — 



in which K' and K are the constants of mass-action at the (absolute) tem- 

 peratures T' and T, q is the heat of the reaction per unit considered, and R 

 is the gas-constant (= 2 cal.) 



From this equation it follows that with decrease of temperature (T greater 

 than T') a reaction which evolves heat (q positive) is driven forward or in 

 that direction in which heat is given out. (It will be noted that this is in 

 accord with Le Chatelier's theorem.) 



If, for example, two substances, A and B, unite to form AB with evolution 

 of heat, the formation of the compound AB will increase as the temperature 

 is lowered, and the greater the value of q the greater will be the amount of 

 the compound formed. 



The effect of pressure in inducing crystallization at a higher temperature 

 is expressed by the formula 



&p w 



"AT ~ T( yi -r 2 ) 

 in which Ajp is the pressure required to cause crystallization to begin at the 

 temperature increased AT degrees above the normal crystallizing point, w is 

 the latent heat of fusion, T is the absolute temperature, and 7'j and v 2 are 

 the specific volumes of the substance in the liquid and solid forms respectively. 



