Stoichiometric titration

Figure 9-4. Typical results of a normal and stoichiometric titration binding analysis.

To obtain accurate estimates of the number of binding sites (n), binding experiments (usually titrations) need to be performed under conditions where the total concentration of A is relatively high, specifically that cAit0, 1 / KAs these conditions define a stoichiometric titration where effectively all of the B added is bound until the sites on A are saturated. Titrations under these conditions are insensitive to the value of the association constant, so to obtain reliable estimates of KAss, data are needed from titrations at much lower concentrations, where cA, toi- V-Kaw It should be clear from this discussion that it is not easy to evaluate both n and accurately, and it is usually necessary to do a global analysis of several data sets, obtained under different concentration conditions. 

A stoichiometric titration is one with a known reaction path, for which a chemical reaction can be written, and having no alternative or side reactions. 

However, at the present time the Mo(VI)/Mo(IV) scheme is no more than a hypcthesis for these two enzymes. Further work, particularly stoichiometric titrations and more fast-reaction studies, as well as oxygen tracer work, is called for to help to clarify matters. 

With sufficiently large starting concentrations, the most accurate analyses ( 0.1%) can be achieved with ion-selective electrodes by means of a quantitative and stoichiometric titration. With smaller starting concentrations the end point determination becomes... 

As a corollary to the above it should be pointed out that the exchange is in some instances stoichiometric and therefore the amount of cation in solution can be estimated by passage through a hydrogen exchanger as above and subsequent titration of the acid in the effluent. 

Direct Titrations. The most convenient and simplest manner is the measured addition of a standard chelon solution to the sample solution (brought to the proper conditions of pH, buffer, etc.) until the metal ion is stoichiometrically chelated. Auxiliary complexing agents such as citrate, tartrate, or triethanolamine are added, if necessary, to prevent the precipitation of metal hydroxides or basic salts at the optimum pH for titration. Eor example, tartrate is added in the direct titration of lead. If a pH range of 9 to 10 is suitable, a buffer of ammonia and ammonium chloride is often added in relatively concentrated form, both to adjust the pH and to supply ammonia as an auxiliary complexing agent for those metal ions which form ammine complexes. A few metals, notably iron(III), bismuth, and thorium, are titrated in acid solution. 

The point in a titration where stoichiometrically equivalent amounts of analyte and titrant react. 

For a titration to be accurate we must add a stoichiometrically equivalent amount of titrant to a solution containing the analyte. We call this stoichiometric mixture the equivalence point. Unlike precipitation gravimetry, where the precipitant is added in excess, determining the exact volume of titrant needed to reach the equivalence point is essential. The product of the equivalence point volume, Veq> and the titrant s concentration, Cq, gives the moles of titrant reacting with the analyte. 

Earlier we made an important distinction between an end point and an equivalence point. The difference between these two terms is important and deserves repeating. The equivalence point occurs when stoichiometrically equal amounts of analyte and titrant react. For example, if the analyte is a triprotic weak acid, a titration with NaOH will have three equivalence points corresponding to the addition of one, two, and three moles of OH for each mole of the weak acid. An equivalence point, therefore, is a theoretical not an experimental value. 

The equivalence point of a redox titration occurs when stoichiometrically equivalent amounts of analyte and titrant react. As with other titrations, any difference between the equivalence point and the end point is a determinate source of error. 

Instead, an excess of KI is added, reducing the analyte and liberating a stoichiometric amount of The amount of produced is then determined by a back titration using Na2S203 as a reducing titrant. 

In a titrimetric method of analysis the volume of titrant reacting stoichiometrically with the analyte provides quantitative information about the amount of analyte in a sample. The volume of titrant required to achieve this stoichiometric reaction is called the equivalence point. Experimentally we determine the titration s end point using a visual indicator that changes color near the equivalence point. Alternatively, we can locate the end point by recording a titration curve showing the titration reaction s progress as a function of the titrant s volume. In either case, the end point must closely match the equivalence point if a titration is to be accurate. Knowing the shape of a titration... 

Locate the equivalence point for each of the titration curves in problem 1. What is the stoichiometric relationship between the moles of acid and moles of base at each of these equivalence points ... 

X 10 , 7.8 X 10 , and 6.8 X 10 k The titration curve shown here is for H4Y with NaOH. What is the stoichiometric relationship between H4Y and NaOH at the equivalence point marked with the arrow ... 

Sodium -tolueuesulfinate dihydrate can be used equally well. The checkers used anhydrous sodium -toluenesulfinate from Aldrich Chemical Company, Inc. This material was determined by titration to be 87% pure and gave lower yields. The yield stated was obtained by using stoichiometric amounts based on calculated purity. Sodium p-toluenesulfinate from other suppliers was found less pure and gave considerably lower yields. 

In view of these results, periodate titrations of malonaldehyde were carried out at several pH values other than 4. However, in no instances were stoichiometric amounts of periodate reduced the deoxy sugars gave similar results. 

The reaction with the standard solution should be stoichiometric and practically instantaneous. The titration error should be negligible, or easy to determine accurately by experiment. 

With a knowledge of the pH at the stoichiometric point and also of the course of the neutralisation curve, it should be an easy matter to select the appropriate indicator for the titration of any diprotic acid for which K1/K2 is at least 104. For many diprotic acids, however, the two dissociation constants are too close together and it is not possible to differentiate between the two stages. If K 2 is not less than about 10 7, all the replaceable hydrogen may be titrated, e.g. sulphuric acid (primary stage — a strong acid), oxalic acid, malonic, succinic, and tartaric acids. 

Cation of a weak base titrated with a strong base. The pH at the stoichiometric end point is given by ... 

The method may also be applied to the analysis of silver halides by dissolution in excess of cyanide solution and back-titration with standard silver nitrate. It can also be utilised indirectly for the determination of several metals, notably nickel, cobalt, and zinc, which form stable stoichiometric complexes with cyanide ion. Thus if a Ni(II) salt in ammoniacal solution is heated with excess of cyanide ion, the [Ni(CN)4]2 ion is formed quantitatively since it is more stable than the [Ag(CN)2] ion, the excess of cyanide may be determined by the Liebig-Deniges method. The metal ion determinations are, however, more conveniently made by titration with EDTA see the following sections. 

Discussion. Potassium may be precipitated with excess of sodium tetraphenyl-borate solution as potassium tetraphenylborate. The excess of reagent is determined by titration with mercury(II) nitrate solution. The indicator consists of a mixture of iron(III) nitrate and dilute sodium thiocyanate solution. The end-point is revealed by the decolorisation of the iron(III)-thiocyanate complex due to the formation of the colourless mercury(II) thiocyanate. The reaction between mercury( II) nitrate and sodium tetraphenylborate under the experimental conditions used is not quite stoichiometric hence it is necessary to determine the volume in mL of Hg(N03)2 solution equivalent to 1 mL of a NaB(C6H5)4 solution. Halides must be absent. 

When the titration curve is symmetrical about the equivalence point the end point, defined by the maximum value of AE/AV, is identical with the true stoichiometrical equivalence point. A symmetrical titration curve is obtained when the indicator electrode is reversible and when in the titration reaction one mole or ion of the titrant reagent reacts with one mole or ion of the substance titrated. Asymmetrical titration curves result when the number of molecules or ions of the reagent and the substance titrated are unequal in the titration reaction, e.g. in the reaction... 

In such reactions, even though the indicator electrode functions reversibly, the maximum value of AE/AV will not occur exactly at the stoichiometric equivalence point. The resulting titration error (difference between end point and equivalence point) can be calculated or can be determined by experiment and a correction applied. The titration error is small when the potential change at the equivalence point is large. With most of the reactions used in potentiometric analysis, the titration error is usually small enough to be neglected. It is assumed that sufficient time is allowed for the electrodes to reach equilibrium before a reading is recorded. 

K Fe(CN)6 oxidation Compound F is stoichiometrically inactivated by oxidation with K.3Fe(CN)6 (Shimomura and Johnson, 1967) thus, it is possible to estimate the molecular extinction coefficient (e) of the 388-390 nm absorption peak by titrating F with K.3Fe(CN)6- The e value obtained by the titration in 50% ethanol was 15,400 (assuming the reaction to be one-electron oxidation) or 30,800 (assuming two-electron oxidation). Two other methods of lesser precision were used to determine the true s value 1) the dry weight of the ethyl acetate extract of an acidified solution of F gave an e value of 14,100 2) the comparison of NMR signal intensities gave a value of 11,400 2,000 in water (H. Nakamura, Y. Oba, and A. Murai, 1995, personal... 

In the context of the stability of the nitrosoamine intermediate in the diazotization of heteroaromatic amines relative to that in the case of aromatic amines, the reversibility of diazotization has to be considered. To the best of our knowledge the reverse reaction of a diazotization of an aromatic amine has never been observed in acidic solutions. This fact is the basis of the well-known method for the quantitative analysis of aromatic amines by titration with a calibrated solution of sodium nitrite (see Sec. 3.3). With heteroaromatic amines, however, it has been reported several times that, when using amine and sodium nitrite in the stoichiometric ratio 1 1, after completion of the reaction nitrous acid can still be detected with Kl-starch paper,... 

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