INDICATOR OR TITRIMETRIC METHODS A very large number of indicators (q.v.) used in determining acidity owe their utility to the fact that they undergo a change of colour within a certain range of hydrogen-ion concentration and can therefore be used to determine this concentration. Thus, phenolphthalein is colourless in solutions having a hydrogen-ion concentration stronger than i pink at and deep red at or = 8, pH = 9 and = io respectively. The causes of the colour changes cannot be discussed in detail, but it may be said that, as the phenolphthalein is a very weak acid, it exists almost entirely as undissociated molecules in the relatively more strongly acidic (less alkaline) solution, but commences to ionize, owing to salt formation, as the solution becomes more alkaline, and is fairly fully ionized in the most alkaline solution. Con currently, the ion undergoes a change of structure from the colourless phenolic to the coloured quinonoid form (see COLOUR AND CHEMICAL CONSTITUTION), and it is to this cause, rather than to any difference between the colours of undissociated mole cules and of ions (as Ostwald supposed), that the colour change is due. Similar explanations apply to all indicators used in acidimetry, for they are all either weak acids or weak bases and are capable of undergoing such tautomeric changes so rapidly as to give their indications instantly.
The process of neutralization of a strong acid by a strong base will be followed. If we take, say, 10 c.c. of a decinormal solution of hydrochloric acid, it has initially a hydrogen-ion concentration of (approx.), i.e., PH =1; the gradual addition of a deci normal solution of, say, caustic soda, brings about a diminution of hydrogen-ion concentration in the solution. When 9 c.c. have been added the concentration of free acid will be reduced to 1 o i.e., p. = 2, but thereafter the curve begins to undergo a rapid change, passes through the neutral point 7) when io c.c. have been added, and starts to reproduce a precisely similar curve on the alkaline side. It is obvious, therefore, that in titrat ing a strong acid by a strong base (or vice versa) any indicator which shows its colour change between PH 4 and PH 10 will be satisfactory and give a titration of about 9.95—I0.05 instead of the theoretical io c.c. (provided the solutions are not too dilute). Hence methyl-orange (range 3.0-4.5), methyl-red (4.0-6.o), lit mus (6.o-8.o), or phenolphthalein (8.o—io.o) will be equally satisfactory. The case is far otherwise, however, if one has to titrate a weak acid by a strong base, for, as the curve for acetic acid shows, an indicator has to be used of the range 7-10 and, of the above four, only phenolphthalein fulfils this condition. A very weak acid, such as boric acid (q.v.) cannot be titrated as such, because its titration curves show no perceptible change at the theoretical neutral point.
Similar considerations apply mutatis mutandis to the titration of strong alkalis by strong or weak acids, and of weak alkalis (e.g., ammonia) by strong acids; thus, the titration of ammonia by, e.g., hydrochloric acid, is the reverse of the sodium hydroxide— acetic acid titration, and an indicator, showing changes in the range 4-7, such as methyl-orange or methyl-red, is therefore suitable. Also, the direct titration of extremely weak bases, such as urea, is as impossible as that of boric acid. It will be clear, moreover, that the titration of weak bases by weak acids is impracticable by these methods.
Polybasic acids sometimes have their successive stages of dis sociation so far apart, and therefore so well defined, that if they are in suitable ranges they can be detected by the use of two indicators. Thus, phosphoric acid has a first dissociation constant = I•I X and a second, K2= = I•95X so it behaves in the first stage as a strong acid, and in the second as a weak acid; methyl-orange therefore indicates completion of the stage = and phenolphthalein enables the stage KH2PO4-I-KOH = to be detected. The third stage of dissociation of the acid is so feeble that the titration is impossible.
In many liquids of biological importance (soil extracts, blood sera, cultures, etc.) there are complex mixtures of weak acids, weak bases, amphoteric electrolytes (e.g., gelatin and proteins, which function either as weak acids or as weak bases, according to conditions) and colloids (q.v.), which are extremely sensitive to very slight changes of Owing to their nature, however, they are able to exert a "buffering" effect, i.e., they tend to minimize such changes when external circumstances would tend to impose them. In connection with such liquids, a knowledge of their "reaction" or is of great importance, and W. M. Clark and H. A. Lubs have specially synthesized a whole series of indicators which give brilliant colours and offer a wide selection of ranges. For fuller details of this aspect of indicators the works of S. P. L. Sorensen, G. S. Walpole and also of others (see Bibliography) must be consulted ; but the principles underlying their use may be given very briefly.
If the weak acid above is partially neutralized by a strong base, say sodium hydroxide, the sodium salt may be assumed, without appreciable error, to be completely dissociated, for this is nearly true of all salts of strong bases. If s equivalents of base have been added per litre of acid of concentration c (as before) the concentration of un-neutralized acid is c—s; hence [H'].+ [HA] = c—s, and since [HA] + [A'] =c, because the total concentra tion of salt and acid is still c. we therefore have [H'] =K[HA]/[A'] =K • but as [H'] is very small sd-[111 compared with the other quantities in the fraction, we have [H] =K(c—s)/s=KX (un-neutralized acid)/(salt). From this equation two deductions can be made: (I) The logarithmic equivalent is p H = —log [H'] = — logK + log s C-s (2) If s=c/2, i.e., if the acid is half neutralized [111=K. This is the state of affairs when a two-colour indicator is half way through its colour change (although its ionization constant is an apparent one, owing to complications due to changes of structure) ; hence indicators are most effectively employed in solutions of acidity numerically equal to their apparent ionization constant, i.e., of —logK.
The logarithmic equation in (I) enables a buffer solution of any desired to be prepared but numerous pairs of solutions have been studied and charted so that the ratio s/(c—s) and the corresponding are to be seen at a glance. Thus, by taking appropriate volumes of N/5-acetic acid and N/5-sodium acetate, we have 20 c.c. of a buffer solution of the PH shown: These values are nearly those calculated from the formula given (where K= I .8 X or logK = 4•i45 ; c — s = acetic acid; and s= sodium acetate—the same as c of acetic acid and s of sodium hydroxide), but slight corrections have been introduced. The corresponding curve enables intermediate values to be obtained.
All buffer solutions depend upon the action of a weak acid, a weak base, or an amphoteric electrolyte, glycocoll being a good example of the last type.
The application of the foregoing principles to the determination of (in, say, a feebly acidic solution of gelatin) will now be sketched briefly. The method is useless for coloured solutions, such as physiological fluids and electrometric methods have to be used for these. (See above.) If the is not known even approximately, tests with a few different indicators would soon give a rough idea; but in order to facilitate this preliminary survey use may be made of an ingenious device known as a "universal" indicator, which is a mixture of several indicators so designed that addition of a few drops to a solution gives a colour characteristic of the the suc cession of colours according with that which is found in the spectrum :— Having by this or any other means obtained an approximate idea of the it is then possible to select (I) an indicator and (2) a buffer solution of suitable ranges. Thus, if the universal indicator has given a reddish-orange tint, we must select an indi cator and a buffer covering the range say, acetic acid— sodium acetic, and methyl-red (red at PH4.4 ; yellow at 6.o) or bromophenol-blue (yellow at 3•o; bluish-purple at 4.6). A definite number of drops of the indicator is added to 20 c.c. of each of the five acetate buffer solutions (4.o-5.6) and also to 20 c.c. of the solution under investigation, all the solutions being contained in cylindrical vessels of clear glass standing on a white tile and equally illuminated (in the absence of a colorimeter). The tint in the unknown solution is seen to be between those in, say, the tubes corresponding to pH 4.4 and 4.8, and solutions of PH 4.5, 4.6, and 4.7 are then prepared so that a closer match may be made and the determined to within o•I unit.
BrBLIOGRAPHY.-E. Salm, Z. physikal. chem., 1906, 57, P. 471 ; E. B. R. Prideaux, Theory and Use of Indicators (1917) ; H. A. Lubs, "Indi cators and their Industrial Application" (J. Ind. Eng. Chem., 1920, 12, p. 273) ; L. Michaelis, Die Wasserstoffionenkonzentration (1922) ; W. M. Clark, Determination of Hydrogen-ion Concentration (Baltimore, 1923) ; I. M. Kolthoff and N. H. Furman, Indicators (New York, 1926) . (A. D. M.)