284 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If instead of the system considered above we study a system of the 

 type represented by a mixture at its eutectic point, we may derive 

 a set of equations, entirely similar to the above, which show the change 

 of the eutectic temperature with the pressure, and the change of the 

 eutectic temperature at constant pressure, or of the eutectic pressure at 

 constant temperature, when a solute is added to the mixture. 



These examples will suffice to show the way in which equations 

 I-XX may be applied to the derivation of other thermodynamic 

 equations. 



The Laws of Chemical Equilibrium. 



Hitherto we have considered only those processes in which each 

 molecular species persists without any change except that of passing 

 from one phase to another. We will now consider those processes in 

 which the molecular species react with each other to form new species, 

 and it will be shown that the activity of a given species is not only a 

 measure of the tendency of that species to escape into some other phase, 

 but is also a perfect measure of the tendency of the species to take 

 part in any chemical reaction. In other words, the activity is an exact 

 measure of that which has been rather vaguely called the "active 

 mass " of a substance. 



Let us consider the reaction represented by the following equation, 



aA ■\-hB+ ■ ■ ■'^oO+ 2^P + • ■ ', 



where a mols of the substance A, h mols of B, etc., combine to form o 

 mols of 0, p mols of P, etc. The several substances may exist in the 

 pure state, or in mixtures ; may be in one phase or in different phases, 

 and there may be other substances present which take no part in the 

 reaction. In other words, we are considering any system whatever in 

 which a given chemical reaction occurs. Let us find the conditions for 

 equilibrium in this reaction. 



We may choose a liquid which is an ideal solvent for each of the 

 substances taking part in the reaction. If this ideal solvent is brought 

 in contact with the system through a membrane permeable only to the 

 substances which take part in the reaction, these substances will enter 

 the solvent, and when the system comes to a final condition there will 

 be equilibrium in the chemical reaction, both in the original system 

 and in the ideal solution. Moreover, the activity of each of the mole- 

 cular species must be the same throughout the original mixture and in 

 the ideal solution. 



