270 REPORTS ON THE STATE OF SCIENCE 



weak acid, and let its degree of ionisation in solution be represented by «. 

 Then the application of Ostwald's dilution law gives : — 



K„ x concentration undissociated molecules = concentration dissociated 

 molecules x concentration H°. 



or K , x - = concentration H° ; 



a 



where K a is the dissociation constant of the indicator. 



The degree of ionisation of an indicator, and therefore its colour, 

 depends only on the constant K,„ and the concentration of hydrogen ions 

 (hydrions) in the solution. 



If a = I 



E,,= concentration H° . (Cj,). 



Hence, when the concentration of hydrions in the solution is numerically 

 equal to the dissociation constant of the indicator, the latter is half in 

 the form of unionised molecules, and half in the form of ions, and exhibits 

 a colour exactly midway between the two extreme colours of its unionised 

 and ionised forms. 



If C„ = 10 K,„ a = 9 per cent. ; that is to say, the indicator is practi- 

 cally entirely in the undissociated form, and the colour of a solution con- 

 taining this, or a greater, concentration of hydrogen ions will be practically 

 that due to the undissociated form of the indicator. On the other hand, 

 if C„ = i\j K„, o = 91 per cent., and the colour of such a solution, and of 

 any still more weakly acid, will be that clue to the ions of the indicator. 



This is an important conclusion ; if we know the strength of the indi- 

 cator, we can say at once within what concentrations of hydrions its 

 colour change will take place. 



These conclusions may be demonstrated in the following way. A 

 number of aqueous solutions are prepared, so that the concentrations of 

 hydrions in them are respectively 10~ 3 , 10~ 4 , 10 -5 , 10 '', 10 ~ 7 (neutral point 

 at 25°), 10" 8 , 10-°, 10- 10 , 10" n . 2 ' The range of sensitiveness of an indicator 

 can then be tested by placing small equal quantities of it in turn in the 

 different solutions. Thus methyl orange is fomid to be completely red 

 in the 10 -3 solution, orange-coloured at 10 -4 , and yellow at 10 -5 . We 

 conclude therefore that the dissociation constant of methyl orange must 

 be somewhere in the neighbourhood of 10" 4 , and that it can be used to 

 indicate hydrion concentrations varying from 10 -3 to 10~ 5 . Methyl red 

 is completely red at 10 -4 , light red at 10~ 5 , and yellow at 10~ G . Hence 

 its dissociation constant is about 10 -5 , and its range of sensitiveness is 

 approximately from 10" 4 to 10" 6 . Phenolphthalein is colourless at 

 10 -7 , faintly coloured at 10^ 8 , and deeply coloured at 10~ 9 , and so on. 3 



2 Formulae for the preparation of these solutions are given by Noyes, J own. Avirr. 

 Chem. Soc, 1910, p. 815. 



3 Professor Walker proposes the use of the terms ' relative acidity ' and ' relative 

 basicity,' in order to avoid the mathematical expressions 10 3 &c. Thus since the 

 concentration of hydrions in pure water at 25° is 10"', a solution with a concentration 

 of 10 * would have a ' relative acidity ' of 10 ; and one with a concentration of 10 ' s , 

 a ' relative basicity ' of 10. This nomenclature should probably be found convenient 

 by analysts. 



