LAWS OF PRECIPITATION. v 117 



to be insoluble in the liquid present, such compound will be produced and 

 precipitated. To illustrate, if a solution of BaCl 2 be added to a solution 

 of Na 2 S0 4 , the ion Ba can unite with the ion S0 4 and produce the insoluble 

 compound BaS0 4 , which will be precipitated. 



The above is a statement of the empirical facts. The explanation of 

 these facts under the theory of dissociation is given by Ostwald as follows : 

 In any given case there is a constant relation between the amount of a 

 compound which can be held in solution and the number of free ions of 

 that compound. Upon this statement are based the laws of precipitation 

 from solutions. Says Ostwald: 



In solutions a state of equilibrium subsists between the ions of the electrolyte 

 and the nondissociated portion. To take the simplest possible case, if we have a 

 binary electrolyte C, which can break up into ions A and B', and if a, b, and c 

 represent the concentrations of these three constituents in a given solution, then the 

 following simple formula holds good: ab=kc. 



Now, the two kinds of ions are produced in equivalent quantities, in the above 

 case, hence a=b. If, further, the total amount of the electrolyte =1, and a repre- 

 sents the ionized portion, then a=b=- and c= ,v being the volume of the solu- 



v v 



tion in which unit quantity (a molecular weight in grammes) of the electrolyte is 



contained. By carrying out the substitution we get the formula -^ r=kv, which 



J J b b (1 — a) 



expresses the state of ionisation of an electrolyte at the dilution v. a 



In the saturated aqueous solution of an electrolyte we have a complex equilib- 

 rium. On the one hand the solid is in equilibrium with the nonionised portion of 

 itself which is in solution, while on the other hand this nonionised portion is in 

 equilibrium with the dissociated part — i. e., with the ions of the same substance. 

 The first equilibrium comes under the law of proportional concentration, or, since 

 we are dealing here with a substance of unalterable concentration on the one hand, 

 the concentration of the nonionised portion in the solution must have a perfectly 

 definite value. For the second equilibrium we have in the simplest case — i. e., when 

 the ions of the compound are monovalent — ab=kc, a and b representing the concen- 

 trations of the ions and c the concentration of the nonionised portion. 



Now, since c is constant at a given temperature, as we have already seen, kc, 

 and therefore ab, must be constant also. Equilibrium is thus established between a 

 precipitate and the liquid above it when the product of the concentrations of the two 

 ions, into which the precipitate falls, has a definite value. This product may be 

 termed the solubility product for the sake of brevity. 



"Ostwald, W., Foundations of analytical chemistry, translated by George McGowan, Macmillan & 

 Co., London, 1895, p. 59. 



