202 



by (ij^ a^ . . . an~[ ■ the concentrations of the solutions obtained in 

 the different periods of lixiviation. 



BuNSEN ^) has shown tliat on washing a precipitate with water 

 there is obtained, after n washings with a volume V, the degree 

 of lixiviation : 



U=[l+~). . . (1) 



wherein W = nV inóicixtes the total volume of the added water. 



He further shows that the amount of water required to attain a 

 definite degree of lixiviation gets smaller and nears a value limit 



when the water is added each lime in smaller quantities. As value 

 limit for Ü we find: 



w 

 U=e~ . . . , (2) 



If now we wish to go further and try to obtain a larger degree 

 of lixiviation, we shall have to divide the mass itself into smaller 

 portions and apply the counter-current principle. Bunsen, in his 

 calculation, assumes that on each addition of water, the combined 

 liquid and the water added are mixed homogeneously. In practice, 

 this is mostly not the case. We will, however, provisionally adhere 

 to this assumption in order to deduce a few general data. 



Discontinuous lixiviation, according to the counter-current principle, at a 

 very great lixiviation velocity or a very long period of lixiviation. 



Let us suppose that the process is working in the usual manner. 

 In each period of the lixiviation, mixing takes place of definite 

 quantities of the mass (with volumes of liquid v) with a definite 

 volume of solution (or water, respectively) V, after which follows 

 filtration. 



Let us place the concentrations of the quantities underneath each 

 other in the following manner : 



h^ h^ h^ . . . . bn-2 bii—\ K 

 a^ «1 a.^ a^ . . . . a„_i a,( = 



After the lixiviation has taken place and filtration has been resorted 

 to, the concentrations of the residual lixiviated quantities and of the 

 appertaining filtrates may then be represented by 



1) Lieb. Ann 148, 269 (1868). The quantity v has been defined by Bunsen 

 slightly differently to that given above. 



