Titration stoichiometry calculations

In order to effectively utilize the stoichiometry of the reaction involved in a titration, both the titrant and the substance titrated need to be measured exactly. The reason is that one is the known quantity, and the other is the unknown quantity in the stoichiometry calculation. The buret is an accurate (if carefully calibrated) and relatively high-precision device because it is long and narrow. If a meniscus is read in a narrow graduated tube, it can be read with higher precision (more significant figures) than in a wider tube. Thus a buret provides the required precise measurement of the titrant. 

As with gravimetric analysis, the weight of the sample (the denominator in Equation (4.33)) is determined by direct measurement in the laboratory or by weighing by difference. The weight of the analyte in the sample is determined from the titration data via a stoichiometry calculation. As discussed previously, we calculate moles of substance titrated (in this case, the analyte) as in Equation (4.21) ... 

Here are some examples to illustrate stoichiometry calculations in volumetric analysis. The key step is to relate moles of titrant to moles of analyte. We also introduce the Kjeldahl titration as a representative volumetric procedure. 

The concentration of a substance in solution is usually expressed as molarity (M), defined as the number of moles of a substance (the solute) dissolved per liter of solution. A solution s molarity acts as a conversion factor between solution volume and number of moles of solute, making it possible to carry out stoichiometry calculations on solutions. Often, chemicals are stored as concentrated aqueous solutions that are diluted before use. When carrying out a dilution, only the volume is changed by adding solvent the amount of solute is unchanged. A solution s exact concentration can often be determined by titration. 

The advantages of using molarity are twofold (1) Stoichiometry calculations are simplified because numbers of moles are used rather than mass, and (2) amounts of solution (and therefore of solute) are measured by volume rather than by mass. As a result, titrations are particularly easy (Section 3.10). 

Until the second equivalence point, we can obtain the analytical concentration of HM and from the titration stoichiometry. At 25.01 mL, the values are calculated as... 

Although there are reports involving the use of hydrogen alone,161 the surface composition of supported Pt-Ru bimetallic catalysts are more commonly measured using a selective titration method.162-164 The titration stoichiometry of the reaction between chemisorbed oxygen and gaseous CO is different for the two metals the ratio of surface metal/02/C0/C02 is 1/0.5/2/1 for Pt and 1/1/1/0.3 on Ru.164 These ratios are independent of surface composition and the concentration of Ru and Pt in the surface can be calculated from the equations ... 

Knowing the stoichiometry of the titration reaction(s), we can calculate the moles of analyte. 

Where Is the Equivalence Point In discussing acid-base titrations and com-plexometric titrations, we noted that the equivalence point is almost identical with the inflection point located in the sharply rising part of the titration curve. If you look back at Figures 9.8 and 9.28, you will see that for acid-base and com-plexometric titrations the inflection point is also in the middle of the titration curve s sharp rise (we call this a symmetrical equivalence point). This makes it relatively easy to find the equivalence point when you sketch these titration curves. When the stoichiometry of a redox titration is symmetrical (one mole analyte per mole of titrant), then the equivalence point also is symmetrical. If the stoichiometry is not symmetrical, then the equivalence point will lie closer to the top or bottom of the titration curve s sharp rise. In this case the equivalence point is said to be asymmetrical. Example 9.12 shows how to calculate the equivalence point potential in this situation. 

By now you are familiar with our approach to calculating titration curves. The first task is to calculate the volume of Ag+ needed to reach the equivalence point. The stoichiometry of the reaction requires that... 

The chemical compositions of the samples, obtained from chemical analyses are reported in Table 1. In order to check the chemical analyses, the mother and washing liquors were collected, analysed and their acidity was titrated. In all cases, the alkaline cations were detected only as traces. The acidimetric titration allowed us to determine the HPA amount remaining in the solution. On the other hand, the samples separated after precipitation and washings were weighted in order to calculate the precipitate yields. The results are reported in table 1 where the samples are designated as MxY (M being the alkaline or ammonium cation, Y the heteroatom, x the stoichiometry deduced from chemical analyses. 

By correlating the observed spectral changes with the concentrations of added cycloamylose, dissociation constants of the cycloamylose-substrate adducts may be calculated (Rossotti and Rossotti, 1961). Values of the dissociation constants determined in this manner for a variety of complexes are presented in Table II. In most cases, stoichiometries of the complexes have been shown to be 1 1 from the presence of distinct isosbestic points in the spectrophotometric titrations. In a few cases, additional spectral perturbations are observed as the cycloamylose concentration is increased, indicating more complex modes of association. Methyl orange, for example,... 

Chemisorption measurements (Quantachrome Instruments, ChemBET 3000) were conducted in order to determine the metal (Co) dispersion. Therefore, the nanomaterial catalysts were reduced under a hydrogen flow (10% H2 in Ar) at 633 K for 3 h. The samples were then flushed with helium for another hour at the same temperature in order to remove the weakly adsorbed hydrogen. Chemisorption was carried out by applying a pulse-titration method with carbon monoxide as adsorbing agent at 77 K. The calculation of the dispersion is based on a molar adsorption stoichiometry of CO to Co of 1. 

In titration calculations, you must consider the reaction stoichiometry. 

To learn that the solubility constants (products), of sparingly soluble salts can be obtained from a potentiometric titration the activity of one constituent ion is determined directly from the emf at the end point, and the salt stoichiometry then allows to be calculated. 

For Reaction 16-1, the titration curve in Figure 16-2 is symmetric near the equivalence point because the reaction stoichiometry is 1 1. Figure 16-3 shows the curve calculated for the titration of Tl+ by IO3 in 1.00 M HC1. 

The calculation of rate constants from steady state kinetics and the determination of binding stoichiometries requires a knowledge of the concentration of active sites in the enzyme. It is not sufficient to calculate this specific concentration value from the relative molecular mass of the protein and its concentration, since isolated enzymes are not always 100% pure. This problem has been overcome by the introduction of the technique of active-site titration, a combination of steady state and pre-steady state kinetics whereby the concentration of active enzyme is related to an initial burst of product formation. This type of situation occurs when an enzyme-bound intermediate accumulates during the reaction. The first mole of substrate rapidly reacts with the enzyme to form stoichiometric amounts of the enzyme-bound intermediate and product, but then the subsequent reaction is slow since it depends on the slow breakdown of the intermediate to release free enzyme. 

The hydroxy a-amino acids l-serine and l-threonine, used as models for the 2-amino-2-deoxy glyconic acids, have been complexed with Ni(II) at 37 °C in aqueous solutions of 0.15M potassium nitrate. Values for the stability constants were obtained from iso-pH titration data which were collected by alternate, small, incremental additions of metal ion and potassium hydroxide being made such that the pH of the solution remained nearly constant. The data were consistent with the predominance of MLn species, along with additional protonated and hydrolyzed complexes. There was no evidence for the involvement of the hydroxyl group in chelation. By the same iterative computations the complexes formed between borate and mannitol have been analyzed, and the stability constants have been calculated. Complexes with mannitohborate stoichiometries of I.T, 1 2, 1 3, and 2 1 were proposed. 

We can predict the pH at any point in the titration of a polyprotic acid with a strong base (see Toolbox 11.1). First, we have to consider the reaction stoichiometry to recognize what stage we have reached in the titration. Next we have to identify the principal solute species at that point and the proton transfer equilibrium that determines the pH. We then carry out the calculation appropriate for the solution, referring to the previous worked examples if necessary. In this section, we see how to describe the solution at various stages of the titration our conclusions are summarized in Tables 11.3 and 11.4. 

The p0 dependence of oxygen nonstoichiometry (8) was determined by using coulometric titration. The data were analyzed using a simple point defect model and thermodynamic quantities were calculated. From this model, the standard enthalpy for oxidation (AH0f) and disproportionation (A77D) were determined to be -140.7 and 228.7 kJ/mol, respectively. The mobilities of the electron holes, electrons, and oxygen ions were calculated from the conductivity data using the defect concentrations determined from the stoichiometry and point defect model. 

This acid must be titrated with 0.00450 mol base equivalents for neutralization to occur at the end point. We calculate moles Ca(OH)2 used in the titration from stoichiometry ... 

Titration is a technique that can be used to measure the number of surface metal atoms. The procedure involves first chemisorbing (chemical bonds formed between adsorbing species and surface atoms) molecules onto the metal atoms exposed to the reaction environment. Second, the chemisorbed species are reacted with a second component in order to recover and count the number of atoms chemisorbed. By knowing the stoichiometry of these two steps, the number of surface atoms can be calculated from the amount of the recovered chemisorbed atoms. The technique is illustrated for the problem at hand ... 

A titration curve may for convenience be considered to consist of three portions the region before the equivalence point, the equivalence point, and the region beyond the equivalence point. At all points except at the beginning before any titrant has been added, two redox couples are present, corresponding to the sample and the titrant. In the region before the equivalence point, the potential is calculated conveniently from the known concentration ratio of the sample redox couple. After the equivalence point the concentration ratio of the titrant redox couple is known from the stoichiometry. At the equivalence point both the sample and titrant redox couples are present in the stoichiometric ratio. 

---