pa VALUi• AND ITS IMPLICATIONS pressure (concentration) of hydrogen ions or of hydroxyl ions, much more information is needed to give the full and true picture of the system under examination. If the solution be diluted ten-fold the presence of a strong or weak acid is determined. Such an experiment will also indicate whether a good buffer system is in operation, but the system may still be intrinsically of buffer type but produce a change of pH simulating a weak acid if addi- tional traces of acid or alkali are added. This is because the titration curve of a weak acid is sigmoid in character and extends roughly over four units on the pH scale. The symmetry is centred round the half neutralised point, the pH value of which is an accurate measure of the ionisation constant (K) expressed on the pH scale, i.e. pK. Thus, a weak acid of pK 4.7 will be half neutralised by caustic soda at this pH value and in tenth normal solution the pure acid will give a pH value about 2.7 (actually, in the instance of acetic acid the pH value is 2.85). In the range of about pH 3 to 4 and 6 to 7 the stability of the buffer system in relation to added acid or alkali will be lessened, but its stability to dilution will be sensibly the same as at the middle range 4to6. The best check on the buffering ability of a solution is to see what pH changes occur when a strong acid or alkali is added. Normally this involves a titration curve, but within a given range of pH value a quick procedure is to determine the volume of Normal hydrochloric acid (or sodium hydroxide) needed to alter the pH value of 100 mi. of the experimental solution by one unit. This quantity can be called the "buffer" index. Bearing in mind the sigmoid shape of buffer solutions, it is advisable to carry out the titration over a range of 2 units of pH. Certain solutions do not show much change in pH value when small quantities of acid or alkali are added. For example, N/100 hydrochloric has a pH value of 2-0, and if 1 mi. of N/10 acid were added to 25 mi. the fall in pH value would be 0.15. The same amount of N/10 hydrochloric acid added to distilled water would reduce the pH value from 7 to 2, a change of 5 units. This is because the pH scale is logarithmic and the change in hydrogen ion concentration is purely arithmetic and its value on a logarithmic base depends on which part of the pH scale is in use. A consideration of the ionisation constants of acids and bases is important in the ordinary laboratory titrations. In many instances if the pK is known then the end point of the titration will be something of the order of 2 units of pH, higher or lower as the case may be. The complete theory of indicators is, however, somewhat complex, but for practical purposes indicators may be defined as substances having one colour in solution at or below a certain characteristic pH, a second colour at or above another pH value, and an intermediate mixed colour, due to the presence of both the two forms of extreme colour, at pH values intermediate between these two. For example, bromcresol purple is yellow at pH 5-2 or below, and purple at pH 6.8 or above. Between 5.2 and 6.8 the indicator 295

JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS assumes intermediate tints, any such tint being characteristic of some particular pH, and given by a definite ratio of the yellow and purple forms of the indicator. It should be remarked that this is not true of "one-colour" indicators such as phenol- and thymol-phthalein, which are colourless below pH 8-3 and pH 9.5 respectively. These indicators show no change of tint, but only an increasing intensity of colour as the pH values rise, this intensity depend- ing also on the amount of indicator used. With "two-colour" indicators the depth of colour at any pH in the effective range depends on the concentration of indicator, but not the tint or shade, which is affected only by the hydrogen ion concentration. Of course, whenever matching is required, both tint and intensity must be alike, and even in ordinary titrations it is best to know how much indicator is present and always to use the same number of drops for a given volume of solution to be titrated. Every indicator has a characteristic range of about 1-6 units of pH, and a large part of the pH scale is covered by the different indicators, some of which change in acid, some in more or less "neutral," and others in alkaline solutions. Actually the indicators are either acids or bases, and participate in, or interfere with, the acid-base equilibrium of any solution to which they are added it is necessary, therefore, that indicator colours should be very intense and brilliant, so that only a very minute quantity is needed to give a useful colour in solution, thus reducing any interference to a minimum. This can be illustrated by bromcresol purple mentioned above 10 drops of a 0.04 per cent solution of this indicator would be ample if used in the titration of 100 c.c. of a colourless solution, and would give a concentration of 0.0002 per cent or 0.2 parts in 100,000, a quantity unlikely to interfere with the pH value of any but the most feebly buffered liquids (such as distilled or pure water). Another property required of indicators is that they shall assume their final colour instantly when added to a solution. It will be seen that the pH value at which the end point of any acid- alkali titration is reached depends on the indicator used. This is a very important matter, and since the pH value at which an acid or a base is completely converted into its salt depends on its strength or ionisation constant, it will be clear that it is necessary to use the correct indicator for every titration. The titration curve of hydrochloric acid with caustic soda shows that from pH 3-5 or 4.0 the curve rises very suddenly, the rise con- tintting to pH 10 or above. Consequently any indicator changing between pH 3.5 and, say, 10.0 will change colour very suddenly, as the acid is titrated through the equivalence point. The sudden alteration in colour is what is commonly described as a good "end-point" and is caused by the similarly sudden change in pH value slow changes in pH value mean slow changes in indicator colour and no satisfactory end-point. In this example (hydro- chloric acid and sodium hydroxide), as has been long known in laboratory 296