101. Acidimetry has to deal with the titration of acids by means of bases, while alkalimetry has to deal with the titration. of bases by means of acids. In either case the principle involved is the same; it is to add to the acid or base being determined an equivalent amount of a standard solution of the other, and from the amount of the solution added, to calculate the amount of the acid or base initially present by means of the proper stoichiometrical equation. Thus for the titration of hydrochloric acid by means of sodium hydroxide, we would have

NaOH HCl :: Wt. NaOH used: Wt. HCl sought

40.01 36.47

Evidently, then, in order to be able to make an acid-alkali titration, we must be able to tell the point at which we have added an equivalent of base or acid corresponding to the stoichiometrical equation.

Stoichiometrical Point. In general we shall hereafter speak of the point which marks the addition of an equivalent of reacting substance, corresponding to the stoichiometrical equation, as the Stoichiometrical Point of a reaction, irrespective of whether the reaction is one of neutralization, double decomposition, or oxidation-reduction. The stoichiometrical point is really the theoretical point demanded by the equation.

End Point. By end point we shall mean the practical point at which we stop in a titration by virtue of the particular indicator or other device that is employed. Our aim in every titration is to arrange matters so that the end point shall be as nearly coincident with the stoichiometrical point as possible.

102.

Before proceeding to show how we seek to establish this coincidence in acidimetric-alkalimetric titrations, it will be

advantageous to present a very important relationship which has been established in regard to aqueous solutions, namely, in pure water, or in any aqueous solution whether it is that of an acid, a base, or a salt, there are always present both hydrogen ion and hydroxyl ion, and that whatever the concentration of the one, the concentration of the other is such that the product of the two concentrations is a constant for any given temperature, that is

Constant for any given temperature

or fixing the temperature at 25° we have specifically

This relationship, which is derivable as a special case of the Law of Mass Action, has been substantiated experimentally by the researches of Arrhenius,2 Kohlrausch and Heydweiler,3 Löwenherz, Lorenz and Bohi, Sörensen, and others.

5

Now it can be seen by virtue of the foregoing relationship that we can define a solution, so far as its acidity or its alkalinity is concerned, either in terms of its concentration of hydrogen ion or of its concentration of hydroxyl ion because the moment we know the value of the one we impliedly know the value of the other.

Thus consider a 0.1 molar solution of hydrochloric acid; at 25° its concentration of hydrogen ion is 0.092 10-1-03, or its concentration of hydroxyl ion is 10-12.93 because

=

In an analogous manner the concentration of hydrogen ion in a 0.1 molar solution of sodium hydroxide at 25° is equal to 10-12.91 because the concentration of hydroxyl ion is equal to 0.090 10-1.05.

=

1 The variation of the ionic product with temperature can be seen from the following figures for pure water, which are taken partly from Kohlrausch and Heydweiler, Wied. Ann. 53, 209 (1894) and partly from Noyes, Carnegie Publication No. 63 (1907):

In order, however, to avoid the disadvantage of a dual system of definition, the convention has been followed of using only the hydrogen ion concentration to characterize a solution irrespective of whether the solution is acid, neutral or alkaline, so that we have for instance,

for 0.1 molar HCl, the concentration of hydrogen ion is 10-1.03

In addition to the exponential form of expressing concentration of hydrogen ion, there is another nomenclature which is in use and which is due to Sörensen. In this latter system, the exponent alone is used with its negative sign dropped and the symbol på prefixed, thus,

This scheme of nomenclature, as originated by Sörensen, is very largely, although not exclusively, used in current chemical literature. It has the disadvantage that it cannot be used for solutions whose concentration of hydrogen ion is greater than unity because no provision is made for negative p; on the other hand the system lends itself readily to plotting results graphically.

103. — Let us now return to our problem: how to tell the point at which we have added an equivalent of base or acid corresponding to the stoichiometrical equation. In brief, the location of this point depends upon the rate at which the concentration of hydrogen ion in the solution changes value with respect to very small amounts of alkali (or acid) added as we approach and pass through the stoichiometrical point; the greater the rate at which the hydrogen ion concentration changes the greater the precision with which we can locate the stoichiometrical point; the more gradual the change, the less the precision.

7 Biochem. Ztg. 21, 159 (1909).

Strictly speaking, it is the percentage change and not the absolute change that is meant. The graphs which are subsequently given in this chapter, employing as they do på as ordinates and cubic centimeters as abscissæ, are in reality semi-logarithmic plots and consequently rapid change in the value of the ordinate means rapid percentage change in the concentration of hydrogen (or hydroxyl) ion.

To illustrate this we will follow the course of several titrations, plotting the concentration of hydrogen ion as a function of the amount of base (or acid) added.

First let us take up the titration of hydrochloric acid by means of sodium hydroxide. Thus for a solution containing at the start, 25.0 c.c. of 0.1 molar hydrochloric acid in a volume of 125 c.c., we have the following concentrations of hydrogen ion corresponding to the number of c.c. of 0.1 molar sodium hydroxide solution added; the temperature being 25°:

TITRATION OF HYDROCHLORIC ACID
BY MEANS OF SODIUM HYDROXIDE

104. We notice that there is a first interval where the change in the concentration of hydrogen ion is more or less gradual, then there is a very short interval where the change takes place very rapidly with respect to very small amounts of sodium hydroxide solution added, after which there is a third interval where the change takes place very slowly again.

The interval of abrupt change is the one that we are particularly interested in, because experiment shows in general that whenever we get a point of inflection in the hydrogen ion curve of an acidalkali titration, and the element of

the curve through the point of inflection is sensibly parallel to the hydrogen ion axis, then the point of inflection corresponds to a stoichiometrical point. Since this relationship is true in general, it enables us at once to lay down the necessary conditions for any acid-alkali titration. They are:

1. The hydrogen ion curve must show a point of inflection such that the element of the curve through the point of inflection is sensibly parallel to the hydrogen ion axis.

2. We must be able to locate the point of inflection.

Provided then that a titration furnishes a titration curve of the type mentioned, it follows that we will know that we have located the point of inflection if we can only tell when the concentration of hydrogen ion in the solution is passing through any of the values included by the element of the curve which is parallel to the hydrogen ion axis.

Thus for the titration under discussion, we will know that we have located the point of inflection and hence the stoichiometrical point, if we can only tell when the concentration of hydrogen ion in the solution has any one of the values lying between 10-4.0 and 10-9.0 because every value of the concentration of hydrogen ion within this range corresponds to an amount of alkali added which is sensibly the same as that required at the stoichiometrical point.

105. There are two ways of telling when the concentration of hydrogen ion in a solution being titrated has reached a certain value: (1) by use of the hydrogen electrode; (2) by means of the proper indicator.

The hydrogen electrode is not very widely used for this purpose as regards titrations, its drawbacks being the elaborate set-up of apparatus that is required and the length of time necessary to make a determination. J. H. Hildebrand, J. A. C. S. 35, 847 (1913), however, describes a simplified arrangement which overcomes these drawbacks to a large extent, and which was used by him in a detailed study of certain titrations.

The indicators used for measuring hydrogen ion concentration

'As will be shown later on in the chapter the converse of this proposition is not always true because there are stoichiometrical points for which there are no points of inflection.