THERMODYNAMICAL SYSTEM OF GIBBS 97 



Be Formed Out of others* If the substances Si, S2,. . -Sn are 

 not all independent of each other, i.e., if some of them can be 

 formed out of others, the number of components is no longer 

 the minimum number in terms of which every possible variation 

 of the state of the system can be expressed. For example, if 

 the system contains a solution of sodium chloride in water in 

 equilibrium with the sohd hydrate, NaCl-H20, it may be 

 convenient to regard the hydrate as a component, as well as 

 sodium chloride and water. Every independent variation of 

 the system can be expressed in terms of the tw^o components 

 sodium chloride and water, but these two components are not 

 independently variable in the sohd hydrate. Their ratio is 

 fixed. 



Consider a system containing, in addition to other sub- 

 stances, water, sodium chloride and the solid hydrate NaCl-H20, 

 and let the components Si, S2 and S3 be water, sodium chloride 

 and the hydrate respectively. We will suppose that the other 

 components S4,... Sn are independent of each other. The 

 general condition of equilibrium, which may be written more 

 briefly in the form 



2^577 - Ipdv + 2mi5toi + 2M25m2 . . . + ^UrMn ^ (73) [23] 



still holds, but the equations of condition 



25mi = 0, S5m2 = 0, S5m3 = 0, (74) [24] 



do not necessarily hold, since the total amount of water and 

 sodium chloride in the system may decrease and the total 

 amount of the hydrate may increase. It is therefore necessary 

 to replace (74) by equations representing the relation between 

 the quantities of these substances. Thus, if b grams of sodium 

 chloride combine with a grams of water to form (a + 6) grams 

 of the hydrate, the quantity (Sms) of the hydrate contains 



7 (dms) of water, and for the constancy of the actual total 



a + 6 



am.ount of water in the system (i.e., the sum of the amount of 

 * Gibbs, I, p. 67, line 24; p. 70, line 9. 



