DILUTION OF CONCENTRATED SOLUTIONS. 335 



The gilded brass stirrer with its glass insulated shaft was replaced by a glass one, 

 the shaft and the propeller blades being fused together. Some slight modification of 

 the water equivalent was made to suit the new conditions. The strong solutions were 

 very viscous and the rate of stirring was increased. 



Some slight change in the heating coil due to a short circuit of a few turns altered 

 the resistance of the heating coil but errors were eliminated by taking readings 

 of both ammeter and voltmeter each mimite. The heating occupied a thousand 

 seconds in all cases. 



Table VII. gives the data from which the variation of specific heat with concentra- 

 tion was obtained. 



Table VIII. gives the data for the heats of dilution of the solutions at various 

 concentrations, and at the temperature of the air. 



One of the curves in Diagram II. shows the nature of the relation between heat of 

 dilution and concentration. The points do not lie so evenly on the curve as in the 

 case of hydrochloric acid, and this is doubtless due to the greater difficulty of experi- 

 menting with a highly viscous solution. It is, however, interesting to note that the 

 points for higher concentrations lie most nearly on a straight line, which passes 

 through the axis of concentration at 12'5 molecules per 100 molecules of water. This 

 would correspond to a concentration of NaOH . 8H 2 0. 



The equation most nearly expressing this part of the curve is 



d = 784ofe -0-125 



VN 



and this may be considered to hold while the concentration changes from 

 NaOH . 6H 2 O to NaOH . 3H 2 ; within the same range the heat of dilution 

 changes to five times its value at the lower concentration. 



A curve (fig. 7) may be plotted connecting heat of dilution and the inverse of 

 concentration, and from it the total heat of dilution as found by THOMSEN can be 

 estimated from the relation 



The relation between Q and N for concentrations below NaOH . 6H 2 O is very 

 uncertain. Both THOMSEN and BERTHELOT found the heat of dilution to become 

 negative for high dilutions, and this also was observed in the above experiment for 

 concentrations below those recorded above. The effect, however, was very small. 



THOMSEN gives the number of calories evolved in changing the composition of the 

 solution from NaOH . 3H 2 O to NaOH . 5H 2 O as 2131 calories. Integrating the above 

 equation between these limits we get Q = 7840 log, f 7840 x 0125 x 2, which 

 gives 2083 calories. Thus although a quite different interpretation of the experi- 

 mental results is given, the results are in good agreement. 



By reference to the curve it is seen that a further dilution of four molecules of 



VOL. ccxv. A. 2 Y 



