Titration data

In titration of a strong acid, the strong base added removes the acid linearly with respect to the added base. The number of millimoles of strong acid decreases linearly, approaching zero at the equivalence point, and the base increases linearly after the equivalence point. These quantities can be computed from pH readings and plotted to give a V-shaped pair of lines hitting zero at the equivalence point. By definition, 

We multiply by the volume of the solution at the point to get the number of millimoles of acid left, which is equal to the original amount, NaVa, minus the base added,  

V = v + v. Now, if the ionic strength, and thus /+, is constant during the titration, the function 10 F should be a linear one versus t (, the only variable on the right-hand side of equation (7-4). 

Vg is the volume of base added to reach equivalence, a fixed value, so that the function increases linearly with Vf, after equiv- 

Traditional methods require many readings as the end is approached, and they may be poor as the solutions become more dilute. These and other advantages have brought this method to the attention of analytical chemists. It was introduced by Gunnar Gran in 1952.1 

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The second derivative of a titration curve may be more useful than the first derivative, since the end point is indicated by its intersection with the volume axis. The second derivative is approximated as A(ApH/AV)/AV, or A pH/AV. For the titration data in Table 9.5, the initial point in the second derivative titration curve is... 

Directions are provided in this experiment for determining the dissociation constant for a weak acid. Potentiometric titration data are analyzed by a modified Gran plot. The experiment is carried out at a variety of ionic strengths and the thermodynamic dissociation constant determined by extrapolating to zero ionic strength. 

The text listed below provides more details on how the potentiometric titration data may be used to calculate equilibrium constants. This text provides a number of examples and includes a discussion of several computer programs that have been developed to model equilibrium reactions. 

Isoxazol-5-ones can exist in three different types of structures, cf. 45- 7 (R = H). Early investigators assigned structures to these compounds on the basis of unreliable chemical evidence thus the NH structure 47 was favored because the silver salt of 3-phenyl-isoxazol-5-one reacts with methyl iodide to give a product which was incorrectly (see reference 44) formulated as the iV-incthyl derivatives (cf. also reference 46). Bromine titration data led to assignment of an incorrect structure to 3,4-diphcnylisoxazol-5-one cf. article I (Volume 1), Section II,A. Comparison of the dipole moments of 3-phenyIisoxazol-5-one with those of the methyl derivatives 45 (R = Me) and 46... 

Calculate the molar concentration (molarity) of a solute from titration data (Toolbox L.2 and Example L.2). 

Chemical-shift Data and Titration Data" for the N-Terminal Di[ C]methylamino Groups of Glycophorins, Glycophorin Glycopeptides, and Related Peptides and Glycopeptides... 

The pH-titration data for the N-terminal JV, JV -[ C]dimethylamino species were analyzed for the best pK values and Hill coefficients (n) by using the following equation. 

C Chemical-shift Data and Titration Data for the N-Terminal Mono( C)methyIamino Groups of Glycophorin-related Glycopeptides and Peptides ... 

This method is applicable when the fluorescence of a ligand is quenched in presence of DNA or RNA and provides base-dependent specificity [135]. In fluorescence quenching experiments the titration data is plotted according to the Stern-Volmer equation ... 

In this activity, you will first standardize a NaOH solution by using the solution to titrate a known mass of oxalic acid (H2C204). Then, you will use your standardized solution to titrate a sample of vinegar. Vinegar is a solution of acetic acid (HC2H302). From your titration data, you will be able to calculate the number of moles and the mass of the acetic acid in your vinegar sample and determine the percent of acetic acid in vinegar. 

Even if we make the stringent assumption that errors in the measurement of each variable ( >,. , M.2,...,N, j=l,2,...,R) are independently and identically distributed (i.i.d.) normally with zero mean and constant variance, it is rather difficult to establish the exact distribution of the error term e, in Equation 2.35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and in the treatment of potentiometric titration data (Sutton and MacGregor. 1977 Sachs. 1976 Englezos et al., 1990a, 1990b). 

The authors studied, as they call it, "acid-base equilibria in glacial acetic acid however, as they worked at various ratios of indicator-base concentration to HX or B concentration, we are in fact concerned with titration data. In this connection one should realize also that in solvents with low e the apparent strength of a Bronsted acid varies with the reference base used, and vice versa. Nevertheless, in HOAc the ionization constant predominates to such an extent that overall the picture of ionization vs. dissociation remains similar irrespective of the choice of reference see the data for I and B (Py) already given, and also those for HX, which the authors obtained at 25° C with I = p-naphthol-benzein (PNB) and /f B < 0.0042, i.e., for hydrochloric acid K C1 = 1.3 102, jjrfflci 3 9. IQ-6 an jjHC1 2.8 10 9 and for p-toluenesulphonic acid Kfm° = 3 7.102( K ms 4 0.10-6) Kmt = 7 3.10-9... 

Since soy lecithin ( 20% extract from Avanti) was selected as a basis for absorption modeling, and since 37 % of its content is unspecified, it is important to at least establish that there are no titratable substituents near physiological pH. Asymmetric triglycerides, the suspected unspecified components, are not expected to ionize. Suspensions of multilamellar vesicles of soy lecithin were prepared and titrated across the physiological pH range, in both directions. The versatile Bjerrum plots (Chapter 3) were used to display the titration data in Fig. 7.33. (Please note the extremely expanded scale for %.) It is clear that there are no ionizable groups... 

C. Each Figure shows titration data for compositions inside of the miscibility gap (where the "curve" is linear), as well as enthalpies in a single-phase region. Data from the literature are also shown for comparison with the present results (13-161. Table I shows values of the compositions of the aqueous and amphiphilic phases for n-butanol/water at 30.0 and 55.0 °C and for n-butoxyethanol/water at... 

Sets of parameters such as burette volume, reagent strength, increment size and time interval, end-point potential, format of results, etc., can be stored and recalled from memory as standard methods for routine analyses. An alphanumeric keyboard is used to enter or change the parameters, to take individual pX or mV readings and to control the rinsing and the refilling of the automatic burette. Raw titration data and computed analytical results can be printed out as a permanent record, and titration curves can be produced on a chart recorder or VDU. 

Table 2 pA), values of various monobasic acids and aminium ions as determined by Hyperquad analysis of titration data at 1 x 10 3 M in anhydrous ethanol, T = 25.0 °C... 

For other cases, such as La3+ where more detail is required about the nature of the species present in solution, titration data can be computer fit to more complicated multi-equilibrium models containing Mx 1 v( OR)v forms whose stoichiometry is suggested by information gained from independent spectroscopic or kinetic techniques. One must be mindful of the pitfalls of simply fitting the potentiometric data to complex multi-component models for which there is no independent evidence for the various species. Without some evidence for the species put into the fit, the procedure simply becomes an uncritical mathematical exercise of adding and removing various real and proposed components until the goodness of fit is satisfactory. 

Derived from fits of the potentiometric titration data in methanol and in ethanol using the program... 

Consideration of these primary processes together with the voltammetric results for the M/ OH systems (Figures 1-3), the potentiometric titration data (Figure 4), and the voltammetric data for O2 reduction at metal electrodes (Figure 5) and in the presence of metal ions at a glassy carbon electrode (Figures 6 and 7), prompts the formulation of self-consistent reaction Schemes for the three metals in combination with OH and O2 (Schemes I,... 

Based on your titration data and calculations for determination 1 ... 

Fitting of experimental titration data to determine the rate constants for a reversible reaction ethanol + acetic Acid <-> ethyl acetate +water ... 

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) ... 

The moles of EDTA, and therefore the moles of CaC03, are computed from the titration data ... 

The surface complexation models used are only qualitatively correct at the molecular level, even though good quantitative description of titration data and adsorption isotherms and surface charge can be obtained by curve fitting techniques. Titration and adsorption experiments are not sensitive to the detailed structure of the interfacial region (Sposito, 1984) but the equilibrium constants given reflect - in a mean field statistical sense - quantitatively the extent of interaction. 

In Fig. C microscopic acidity constants of the reaction AlOHg =AIOH + H+ for y-AI203 are plotted as a function of AIOH. The data are for 0.1 M NaCICV This figure illustrates (within experimental precision) the conformity of the proton titration data to the constant capacitance model. Calculate the capacitance. 

Figure 7. Covariability between values of C and Kd yielding best fit of diprotic surface hydrolysis model with constant capacitance model to titration data for TiC>2 in 0.1 M KNOj (Figure 5). The line is consistent with Equation 29. The crosses represent values of C and log found from a nonlinear least squares (NLLS) fit of the model to the data, with the value of capacitance imposed in all cases the fit was quite acceptable. The values of and C found by Method I (Figure 6) also fall near the line consistent with Equation 29. The agreement between these results supports the use of the linearized model (Equation 29) for developing an intuitive feel for surface reactions.

Returning to our introductory remarks about the existence of various models for the oxide/solution interface, It may be appropriate to point out that the results of very relevant experiments based on electrokinetic measurements are often not used in conjunction with titration data. Granted that there may be additional difficulties in identifying the precise location the slipping plane and hence the significance of the electrokinetic c potential may be open to debate, both titration and electrokinetic data ought to be combined where possible to elucidate the behaviour of the oxide/solution Interface. 

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