End point, titration

Reagent generated Electrolyte composition Notes Substances titrated End-point detection f... 

In potentiometric titration the reaction is pursued by means of potentiometry interest is sometimes taken in the complete titration curve, but mostly in the part around the equivalence point in order to establish the titration end-point. 

In the practice of potentiometric titration there are two aspects to be dealt with first the shape of the titration curve, i.e., its qualitative aspect, and second the titration end-point, i.e., its quantitative aspect. In relation to these aspects, an answer should also be given to the questions of analogy and/or mutual differences between the potentiometric curves of the acid-base, precipitation, complex-formation and redox reactions during titration. Excellent guidance is given by the Nernst equation, while the acid-base titration may serve as a basic model. Further, for convenience we start from the following fairly approximate assumptions (1) as titrations usually take place in dilute (0.1 M) solutions we use ion concentrations in the Nernst equation, etc., instead of ion activities and (2) during titration the volume of the reaction solution is considered to remain constant. 

On the basis of the Henderson equation for titration of acid or base one can prove mathematically that the half-neutralization point represents a true inflection point and that as the titration end-point dpH/dA is maximal or minimal, respectively (the latter is only strictly true for titration of a weak acid with a weak base and vice versa). 

Considering the titration end-point or equivalence point, we in fact have to deal with the salt of a weak acid and a strong base or the reverse. Such a salt undergoes hydrolysis, e.g., for NaA, A + H20 HA + OH, so that the hydrolysis constant can be written as... 

The titration course can be illustrated (see Fig. 2.20) by a pAg curve whose values are obtained from the silver potential EAg = E g + RT/Fln aAg+ or at 25° C EAg = EAg - 0.05916 pAg. As AgN03 as a salt is fully dissociated into ions, the initial point of the curve is determined by the original concentration the later part of the curve up to the titration end-point can be obtained in the same way because the Ag+ concentration undergoes a simple reduction as a consequence of the withdrawal of Ag+ into the AgCl precipitate. At the... 

Majer65 in 1936 proposed measuring, instead of the entire polarographic curve, only the limiting current at a potential sufficiently high for that purpose if under these conditions one titrates metal ions such as Zn2+, Cd2+, Pb2+, Ni2+, Fe3+ and Bi3+ with EDTA66, one obtains a titration as depicted in Fig. 3.55 i, decreases to a very low value, in agreement with the stability constant of the EDTA-metal complex and the titration end-point is established by the intersection of the ij curves before and after that point correction of the i values for alteration of the solution volume by the titrant increments as in conductometric titration is recommended. 

It is certainly clear that a coulometric titration, like any other type of titration, needs an end-point detection system in principle any detection method that chemically fits in can be used, be it electrometric, colorimetric, photoabsorptionmetric, etc. for instance, in a few cases the colour change of the reagent generated (e.g., I2) may be observed visually, or after the addition of a redox, metal or pH indicator the titration end-point can be detected photoabsorptiometrically by means of a light source and photocell combination. Concerning the aforementioned coulometric titration of Fe(II), it is... 

It must be realized that the constant current (-1) chosen virtually determines a constant titration velocity during the entire operation hence a high current shortens the titration time, which is acceptable at the start, but may endanger the establishment of equilibrium of the electrode potentials near the titration end-point in an automated potentiometric titration the latter is usually avoided by making the titration velocity inversely proportional to the first derivative, dE/dt. Now, as automation of coulometric titrations is an obvious step, preferably with computerization (see Part C), such a procedure can be achieved either by such an inversely proportional adjustment of the current value or by a corresponding proportional adjustment of an interruption frequency of the constant current once chosen. In this mode the method can be characterized as a potentiometric controlled-current coulometric titration. 

In practice, the volume of titrant is plotted instead of the titration parameter, a. At the titration end-points Ej and E2, the volumes of titrant consumed indicate the respective amounts of the acids, while their pH values or better the pH heights around the half-neutralization points, h.n.p and h.n.p2, are related to the identities of the acids. Therefore, in the two-dimensional figure the abscissa represents the quantitative aspects and the ordinate the qualitative aspects. 

The second question concerns the quality of the chemical control, directed more at the chemical analysis proper and its procedure. Important factors here are sufficient specificity and accuracy together with a short analysis time. In connection with accuracy, we can possible consider the quantization of the analytical information obtainable. For instance, from the above example of titration, if we assume for the pH measurement an accuracy of 0.02, an uncertainty remains of 0.04 over a total range of 14.0, which means a gain in information of n1 = 14.0/0.04 = 350 (at least 8 bits) with an accuracy of 5% as a mean for the titration end-point establishment of both acids, the remaining uncertainty of 1% over a range of 2 x 100% means a gain in information of n2 = 200 (at least 7 bits), so that the two-dimensional presentation of this titration represents a quantity of information I = 2log nx n2 = 15 bits at least. 

If a slow continuous addition of base is made to the same soil used in Figure 10.3, a similar titration curve without the sawtooth pattern is seen. Figure 10.5 shows the titration curve obtained by the continuous slow addition of 0.1 M NaOH. Again, the curve is not a smooth line, and irregularities seen in this titration are seen in other titrations of this same soil. Note that no distinct titration end point is seen here as there is in Figure 10.2. However, it is possible to determine the amount of base needed to bring this soil to pH 6.5, which is a typical pH desired for crop production. 

Because of these interindividual variations in the kinetics of propranolol, the therapeutic dose of this drug is best determined by titration. End points of titration include relief of anginal symptoms, increases in exercise tolerance, and plasma concentration of propranolol between 15 and 100 ng/mL. For additional details on the pharmacokinetics of propranolol and other (3-receptor antagonists approved for clinical use in the treatment of angina pectoris, see Table 17.3 and Chapter 11. 

Although the CGTS can be used to monitor treatment clinically, e.g., to determine an appropriate titration end point such as minimal illness (CGTS of 2), a better measure of significant improvement is the CGT I, which was designed for that purpose and is more sensitive to treatment effect for research purposes. 

Fig. 4-5. Yields of HCN and 14N15N from the reaction of active nitrogen with 15NO-C2H4 mixtures ranging in composition from pure C2H4 to pure 15NO. The symbols ( ) and (O) represent experiments in which the ethylene flow rate was maintained at values in excess of titration end point while increasing increments of nitric oxide were added. The symbols ( ) and ( ) correspond to experiments in which nitric oxide flow rates were held at values in excess of titration end point while various amounts of ethylene were added (from Fersht and Back139 with permission of the National Research Council of Canada).

Calculate the quantity of fatty acids liberated in each subsample based on the equivalents of NaOH used to reach the titration end point, accounting for any contribution from the reagent, using the following equation ... 

Alkalinity co - I ICO, Acid-base titration Titrating with standardized 0.01 M H2S04 using phenolphthalein as indicator until the pink color disappears at about pH 8.3 titration of the same sample is then continued until the end point is reached at pH 4.5 using a bromocresol green-methyl red mixed indicator (total alkalinity) Applicable to natural and waste water. Concentrations of bicarbonate, carbonate, and hydroxide can be calculated. The titration end points can be measured potentiometrically 50,51,67-69... 

It is based on the addition of Mn2+ solution, followed by die addition of a strong alkali to die sample in a glass-stoppered bottle. Dissolved 02 rapidly oxidizes an equivalent amount of the dispersed divalent manganous hydroxide precipitate to hydroxides of higher valence states. In die presence of iodide ions in an acidic solution, the oxidized manganese reverts to die divalent state, with die liberation of a quantity of iodine equivalent to die original dissolved 02 content. The iodine is then titrated with a standard solution of thiosulfate. The titration end point can be detected visually with a starch indicator, or by potentiometric techniques. The liberated iodine can be determined colorimetrically. 

The solubility of metal-hydroxide precipitates in water varies depending on ionic strength and number of pairs and/or complexes (Chapter 2). A practical approach to determining the pH of minimum metal-hydroxide solubility, in simple or complex solutions, is potentiometric titration, as demonstrated in Figure 12.3. The data show that potentiometric titration of a solution with a given heavy metal is represented by a sigmoidal plot. The long pH plateau represents pH values at which metals precipitate the equivalence point, or titration end point, indicates the pH at the lowest metal-... 

After 700°C, Figure 7 shows appreciable acidity, with two steps visible for the NH4+-form. (Note the inflection at about pH 4.) The most acidity is seen after 400°C calcination, and again two end-points are clearly noted for the NH4+-exchanged sample, as shown in Figure 8. The curves are fairly sharp for these filtrate samples because there are no hydrolysis reactions (9) to provide a buffering effect, as illustrated in the slurry sample curves of Figure 7. A summary of the titration end-points is shown in Table III for all the above-noted samples calcined at the three different temperatures. 

A simple equation [(3-27) or (3-28)] may therefore be used in almost all practical situations involving titration end points. But, in the calculation of solubilities of sparingly soluble salts of polybasic weak acids, the concentration of anion may be so low that successive hydrolysis steps must be considered (Section 7-4). 

The scope of the present treatment does not include details of the various instrumental methods for the detection of EDTA titration end points. Nevertheless, we may mention spectrophotometric detection methods, which are of two types. The first is based on instrumental observation of the color changes of metal ion indicators. The second is based on the absorption of radiation in the visible or ultraviolet regions of the spectrum by the metal-EDTA complex. For example, MgY shows appreciable absorbance at a wavelength of 222 nm, whereas the reagent HjY ... 

For a ligand concentration at the nanomolar level, as frequently detected in oceanic waters, the stability constants which can be explored range between about 10 and lO" AT . In the case of stability constants higher than lO" M only the ligand concentration can be evaluated by direct titration (end-point detection), the constant remaining undefined (but >10" M ). In the case of K< Qp Af no complexation can be observed at all (when reasonable quantities of titrant are added) and neither Cl nor K are obtainable. 

Titration end point. The end point is achieved when the barely jrerceptible pink color of phenolphthalein persists. The flask on the left shows the titration less than half a drop prior to the end point the middle flask shows the end point. The final reading of the buret is made at this point, and the volume of base delivered in the titration is calculated from the difference between the initial and final buret readings. The flask on the right shows what happens when a slight excess of base is added to the titration mixture. The solution turns a deep pink color, and the end point has been exceeded. In color plate 9, the color change at the end point is much easier to see than in this black-and-white version. 

---