14-6 THEORY OF CONCENTRATED SOLUTIONS. 



The numbers in the third column are the values of the 

 amount of bisulphate in solution multiplied by a constant so as to 

 convert one of them into the actual experimental expansions 

 given by Holmes and Sageman. If the formation of bisulphate 

 can account for the volume changes on mixing, these calculated 

 expansions should agree with the experimental ones. It is 

 evident that the agreement is an excellent one. 



These calculations show, moreover, that the theory of binary 

 mixtures developed by the author of the present paper is applic- 

 able to the investigation of equilibria in ternary liquid systems- 

 when one component is in large excess. 



The method of evaluating p and x given above may become 

 rather laborious, and, moreover, needs very accurate experi 

 mental data in order to give anything like constant values for />. 

 A much shorter but somewhat less accurate method of obtaining 

 the same result is given below. 



From the mass action equation (y—x) (i — V— x) = Kx 1 

 we have seen that when chemical combination is practically com- 

 plete the relation between x and y is given by two straight lines 

 equally inclined to the axes. These straight lines meeting at the 

 point y = £ x = £ are the tangents to the extremities of the 

 deviation curve, i.e., tangents at the points y = o and y = I. 

 If chemical combination is not complete then the curve giving 

 the relation between x and y has a maximum at y = ^, but the 

 corresponding x value is less than one half. Since the deviation 

 is proportional to x, we have the relationship 



actual distance of maximum in deviation curve 

 actual value of x above y axis 



^ actual distance of point where tangents meet 



above y axis. 



(>' = 1) 



By plotting the experimental expansions for the system 

 K 2 S0 4 — HjSOj on a large scale, it is found that the tangents 

 to the curve at the points y = o and y = i meet at a point 

 x = 630 when the maximum experimental expansion is 394. 

 There is, of course, a considerable degree of uncertainty in the 

 estimation of this point ; hence the probable inaccuracy of the 

 result. 



In the case before us we see then that if combination were 

 complete ( x = V), the measured expansion would be ( 630 units. 

 Hence x 394 



\ 6 3° 



0-313 



p = 0-79. 



The values previously obtained by solving the separate equa- 

 tions for /> and x were x = .316. p = .80. 



