stoichiometrical point or points will furnish a region of abrupt change; such information must be obtained by experimentation. Table Region of abrupt change in the concentration of hydrogen ion when acid is titrated with KOH or NaOH Acid none none 112. The titration curve for phosphoric acid is particularly interesting and is given herewith in Fig. 17. The first and second points of inflection happen exactly at the respective stoichiometrical points; there is no third point of inflection. The data for the curve were obtained by diluting 25.00 c.c. of 0.0333 molar phosphoric acid to a volume of 125 c.c., and then titrating with 0.1 molar sodium hydroxide solution, the temperature being 25°: TITRATION OF PHOSPHORIC ACID Concentration of hydrogen ion in terms of p 5 10 15 20 25 30 35 12 The titration curve for citric acid is given by Hildebrand, loc. cit., § 105; also by C. E. Davis, E. T. Oakes, and H. M. Salisbury, loc. cit., § 110. 13 If boric acid is titrated in aqueous solution the curve shows no point of inflection, but if mannite is added to the boric acid solution in considerable quantity a curve is obtained which exhibits a point of inflection corresponding to the addition of 1 equivalent of NaOH. 113. Titration of Bases by Means of Acids. The principles that apply to the titration of acids likewise apply to the titration of bases; we get an abrupt change in the hydrogen ion concentration at the stoichiometrical point provided that we use an acid which is strongly ionized, as shown in Fig. 18, which gives the graph for the titration of sodium hydroxide by means of hydro With the di-acid alkalies, barium hydroxide and calcium hydroxide, we get only one region of abrupt change and this corresponds to the addition of two equivalents of monobasic acid. 114. The region of abrupt change for the common alkalies is given below: Table Region of abrupt change in concentration of hydrogen ion when base is titrated with a strongly ionized acid 115. Titration of Salts Which Show Hydrolysis. It is also possible to titrate salts by means of acids or bases as the case may be, if the concentration of hydrogen ion in the salt solution undergoes an abrupt change at the end point. In order that this change may happen, it is necessary that the concentration of hydrogen ion in the solution of the salt at the start of the titration shall be greater than 10-5 if we are using a base to titrate with, or less than 10-9 if we are using an acid. Now the concentration of hydrogen ion in a solution of a salt is a function both of the concentration of the salt and of the constitution of the salt. For the concentrations of salt which obtain for the weights of salt and volumes of solution usually employed for volumetric analysis the concentration of hydrogen ion for different solutions of the same salt does not vary much. For different salts, however, the concentration of hydrogen ion in the solution varies greatly according to the constitution of the salt. The explanation of this latter fact is to be found in the relationship between the constitution of a salt and hydrolysis. Hydrolysis is the double decomposition which takes place in an aqueous solution of a salt by which the respective ions of the salt combine to a greater or less extent with the hydrogen and hydroxyl ions of the water to form undissociated acid and undissociated base according to the following scheme, in which MA represents the salt resulting from the base MOH and the acid HA: MAM++ A The extent to which the undissociated base MOH and the undissociated acid HA are formed, determine the concentration of hydrogen ion in the solution. If they are formed in equivalent quantities, the concentration of hydrogen ion in the solution will be the same as that existing in water itself, namely 10-7. If MOH is formed in greater quantity than HA, then the concentration of M+ will be less than that of A- and consequently the concentration of OH- will be less than that of the H+. Hence the = concentration of H+ will be greater than 10-7 by virtue of the relation that CH+ XCон-10-14. Similarly if HA is formed in greater quantity than MOH the concentration of hydrogen ion will be less than 10-7. Now we have pointed out that for purposes of titration the concentration of hydrogen ion in the salt solution at the start of the titration must be considerably different from 10-7, namely it must be greater than 10-5 or less than 10-9. This condition will obtain if the base MOH and the acid HA are each readily soluble and their ionization constants are of a sufficiently different order of magnitude; indeed, the ionization constant of the one must be about 108 times the value of the other. This then limits the titration of salts by means of acids or bases to those cases where the salt is either the salt of a very weak base and a strong acid, or the salt of a strong base and a very weak acid.14 116. Salts of Weak Bases and Strong Acids. - Examples of this class are very few, the TITRATION OF ALUMINUM SULPHATE BY titration of aniline hydroMEANS OF SODIUM HYDROXIDE chloride15 and aluminum sulphate being about all that are ordinarily encountered. The titration curve for the latter is given herewith; from this it will be noticed that there is a first region of abrupt change corresponding to the stoichiometrical point, Al2(SO4)3 + 6 NaOH = 2 Al(OH)3 + 3 Na2SO4 which takes place at a concentration of hydrogen ion lying between 10-60 and 10-7.0. Concentration of hydrogen ion in terms of P 3 5 10 15 20 25 30 35 40 45 FIG. 19 14 Strictly speaking, a strong acid or base does not have an ionization constant, because its ionization ratio varies with concentration, but for the purpose in hand we can assume a constant value equal to unity as fairly representative of the ionization ratio of a strong acid or base. 15 Hildebrand, loc. cit., § 105. There is a second region between 10-9-5 and 10-9-8 but this apparently does not correspond to any stoichiometrical relation. The data for the curve were obtained by dissolving 0.278 g. Al2(SO4)3 in 125 c.c. water and titrating with 0.1 molar sodium hydroxide solution, the temperature being 25°: - 117. Salts of Strong Bases and Weak Acids. Examples of this class of salts are more numerous and more frequently encountered. Thus we have the following sodium or potassium salts: Salt Sodium or potassium Table Region of abrupt change in concentration of hydrogen ion when salt is titrated with HCl, HNO3, or H2SO4 118. The case of sodium carbonate is particularly interesting because of the wide application which this salt finds in the standardization of the acids ordinarily used in acidimetry-alkalimetry, namely, hydrochloric, nitric, and sulphuric. It is to be observed |