Radiometric Measurements of Constants of Indicators. 57 



perature that all measurements were made. Owing to the large value 

 of the heat of ionization of water, the value of its ionization constant 

 is much less at 20 than at 25. Just what this change is may be cal- 

 culated from the well-known Van't Hoff formula 



K! _ q (T 2 - TQ " 



1 K 2 ' R(T 2 X TO 



where K : and K 2 represent the ionization constants for water at tem- 

 peratures TI and T 2 . RI is the gas constant, which equals 1.986 calories 

 per degree, and q is the heat of ionization of water or 13,700 calories. 

 Inserting these values in equation 20, K w = 0.8lXlO~ 14 at 20. This 

 value was used for the calculation of the ionization constants of both 

 methyl orange and phenolphthalein. 



EXPERIMENTAL WORK ON METHYL ORANGE. 



Before discussing the tables showing the results of the calculations 

 based on the above deductions, it will perhaps be of interest to consider 

 a few of the more important results of the preliminary work on methyl 

 orange. Two mother solutions of known concentrations were pre- 

 pared, the one being methyl orange and the other sulphuric acid. 

 All solutions were made up at 20, and carefully purified substances 

 dissolved in conductivity water were employed in all cases. A number 

 of test solutions were prepared from the mother solutions, all of which 

 contain equal amounts of methyl orange but different amounts of sul- 

 phuric acid. The volume of each solution was 100 c.c. The solutions 

 thus presented a series of color shades, ranging from yellow to deep red. 

 The percentage transmissions I/I , were taken with a 20 mm. depth of 

 each solution for the same 4 or 5 wave-lengths of light. The region 

 of the spectrum to be studied is given by the ascending arm of the trans- 

 mission curve for methyl orange. This region for the above-named 

 indicator is between X =0.56/x and X =0.59//. The radiomicrometer 

 deflections in this region are necessarily small, and certain variations 

 which appear in the data can be explained in a large measure as due to 

 the vibrations of the building, which often prevented accurate readings. 



Special attention is called to a solution of methyl orange containing 

 an excess of alkali, and another solution containing an excess of acid. 

 Equation 19 shows that the calculation of c depends not only on the 

 percentage transmission of the solution in question, but also on the 

 percentage transmission for a solution in which all of the methyl orange 

 exists as the azo-base, and one in which all of the indicator has been 

 converted into the quinoid salt. It is thus necessary to know if any 

 alkali must be added to convert all of the methyl orange into the azo- 

 base and to prevent hydrolysis; and also how much acid is required to 

 form the quinoid salt and to suppress hydrolysis completely. Further- 

 more, the stability of these solutions must be considered. 



