272 REPORTS ON THE STATE OF SCIENCE. 



it is evident that, other things being equal, those indicators will give the 

 sharpest and most satisfactory end-point which exhibit the greatest 

 difference in depth of colour or tint between their two forms, because it is 

 then an easy matter to detect a very small change in ionisation. Does 

 the end-point depend upon the amount of indicator present ? In the 

 case of two-coloured indicators, such as methyl orange and methyl red, 

 it does not, for we always titrate to a certain fractional change of the 

 indicator. With mono-coloured indicators, such as phenolphthalein, it is 

 different. In this case we go on adding alkali until there is a perceptible 

 colour in the solution — that is to say, until there is a certain amount of 

 coloured substance in the solution. If there is a large quantity of indi- 

 cator present, this amount may be a very small fraction of it ; if a small 

 quantity, this amount may be a large fraction, and a glance at the 

 equation 



K„ x = concentration H° 



o 



will show that the smaller a is, the higher is the concentration of hydrogen 

 ions indicated. A limit is, however, put on this by the insolubility of the 

 indicator. In the particular case of phenolphthalein, the more indicator 

 we use the more sensitive it is to small concentrations of hydrions, and the 

 nearer is its ' end-point ' to 10" 7 , the theoretical neutral point. Owing 

 to its insolubility, however, it is doubtful whether it can be used to indicate 

 concentrations of hydrogen ions higher than 10~ 7 \ 



This influence of the amount of indicator present in the solution has 

 not been sufficiently recognised, and may partly account for the differences 

 in the values for the end-point of phenolphthalein given by different 

 observers. 



It may be remarked that it is possible for the amount of indicator 

 present to affect the titration in another way. It has already been said 

 that if a two-coloured indicator is used, the titration is continued until a 

 certain fraction of the indicator, say about 95 per cent., is changed over 

 into the form of ions. Now this change, or neutralisation, of the indicator 

 does actually require a certain definite amount of alkali for its completion, 

 and the more indicator is present the more alkali will be needed. Most 

 indicators of this class are, however, used in such dilute solution that this 

 effect is negligible ; and it is further important to notice that even if the 

 concentration of the indicator is moderately high, the accuracy of the 

 titration will not be affected if the indicator is originally put into the 

 solution in the same form as it will have at the end of the titration. . From 

 this point of view, such indicators as methyl orange, methyl red, nitro- 

 phenol, must be used in the form of their sodium or potassium salts. 



Bearing all these facts in mind it is possible to draw up a table showing 

 the ' end-points ' of various indicators when used in the ordinary manner 

 in titration. Thus we have already seen that the colour change of methyl 

 red is only complete when the concentration of hydrogen ions is something 

 less than 10~ 6 ; and the end-point observed when methyl red is used as an 

 indicator in the ordinary manner lies somewhere between 10~ 5 ' 7 and 10" 6 ' 4 , 

 the variation being relatively unimportant, and due to the inability of the 

 eye to detect small changes in colour without a special apparatus. The 

 following table gives the values of the end-points of the more common 

 indicators ; the actual numbers are probably not extremely accurate in 



