Calculating Concentration from Titration Data

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

The repeated calculation of log a - x)/(b - x) for each aliquot from titration data is, to say the least, tedious. A computer program can do this simple job. After a little experience you will be able to write a program that would take as input the concentrations of all reactants, milliliters of acid, the time, and then print out k. There are standard computer programs ( library programs ) available that will accept your various values of In (a - x)/(b - x) and the corresponding times, calculate the mathematically best straight line through the points (the least squares line), and print out the slope and intercept of the line. 

Of the various methods available for the determination of ozone in gaseous mixtures (4), the spectrophotometric methods, particularly the ultraviolet, appeared to be most suited for the purpose. These methods are all based on the strong absorption maximum for ozone in the ultraviolet at 254 mjm,. Thus, one can determine ozone concentration with a Beckman spectrophotometer by the usual procedure. Several other instruments (I, 3, 6) have been specifically designed to measure ozone concentrations by this photometric method. The meters constructed by the authors also operate on this principle. The total ozone stream, or an aliquot of known proportion, is passed through the meter and the per cent transmittance at 253.7 mju, is read from the dial. The ozone concentration at this temperature and pressure is then either determined from a calibration curve (Figure 1), constructed from titration data (the dial could bo calibrated directly in concentration units), or calculated (3) using Beer s law ... 

Calculation of the Quantity of Analyte from Titration Data The examples that follow illustrate how analyte concentrations are computed when normalities are involved. Note that Example A7-5 is similar to Example 13-6 in Chapter 13. 

Surface protonation isotherms. Dots represent experimental data from titration curves at ionic strength I = 0.1 (Hematite, I = 0.2). References are indicated in Table 3.1. The concentration of protonated sites MOH is given in moles nr2. BET surface data were used to calculate the surface concentration. 

From the data shown in Fig.6.13, the concentrations of sodium dithionite and sulphite can be calculated by Equations 6.27 and 6.28 after calibration (determination of B and B ). This is achieved by measuring the limiting current in a solution with known dithionite and sulphite concentration (determined by titration), ft was found that B and B were equal to 0.75 0.01 and 0.74 0.04Almol 1 ... 

Fig. 15.4. Titration data from Tuominen (1967) for Cladonia alpestris, depicted as a function of pH versus concentration of added titrant. The closed circles represent forward titration data, while open circles stand for reversed titration data points. The upper curve is a calculated titration curve in pure water. The shaded area denotes the extent of pH buffering capacity exhibited by the lichen, relative to a non-buffering solution of pure water.

The data for the determination of the intrinsic equilibrium constants for Na and Cl are shown in Figures 5 and 6. For Na (Figure 5), the acidity quotients, pH-log (a /l - a ), are plotted as a function of the fractional ionization, a, and the log of the electrolyte concentration. The concentration term is multiplied by an arbitrary constant in order to separate the curves. The acidity quotients calculated from the potentiometric titration data as a function of a - 0.05 log [Na" ] are represented by the filled circles. For each ionic strength the points are extrapolated to a = 0. These extrapolated points are designated by open squares. These extrapolated points are then further extrapolated to 1 M electrolyte concentration. The open circle is the value for P K at zero charge and 1 M electrolyte concentration. 

It is important to know the dissociation constant of an indicator in order to use it properly in acid-base titrations. Spectrophotometry can be used to measure the concentration of these intensely colored species in acidic versus basic solutions, and from these data the equilibrium between the acidic and basic forms can be calculated. In one such study on the indicator wj-nitrophenol, a 6.36 X 10 M solution was examined by spectrophotometry at 390 nm and 25°C in the following experiments. In highly acidic solution, where essentially all the indicator was in the form HIn, the absorbance was 0.142. In highly basic solution, where essentially all of the indicator was in the form In , the absorbance was 0.943. In a further series of experiments, the pH was adjusted using a buffer solution of ionic strength I, and absorbance was measured at each pH value. The following results were obtained ... 

For each of the following precipitation titrations, calculate the cation and anion concentrations at equivalence as well as at reagent volumes corresponding to 20.00 mL, 10.00 mL, and 1.00 mL of equivalence. Construct a titration curve from the data, plotting the p-function of the cation versus reagent volume. 

The technique is generally unaffected by the state (ionic, imdissociated, sometimes complexed) of the analyte to be titrated. For example, the direct potentiometric determination of pH in a solution of a weak acid reports only the hydrogen ion concentration. Since the major portion of the acid is present in the undissociated form, direct potentiometry can not provide data yielding the total acid concentration. Potentiometric titration involves titrating the acid solution with a standard base, determining the equivalence point volume of standard base solution used, and calculating the total weak acid concentration from the stoichiometric data. 

Therefore, the values of pEMe0 determined by averaging the titration data from the initial section of the titration curve (characterized by a sharp e.m.f. reduction at small titrant additions) are just the dissociation constant of the studied oxide, to an accuracy determined by the natural spread of the experimental data. It should be emphasized, however, that the values of the pEMeQ concentration constant calculated in such a way, contain an appreciable error, caused by the fact that the initial concentration of the titrant in the halide melt is comparable in magnitude with that of oxygen-containing admixtures in the pure melt. 

All the routines described for the determination of the thermodynamic (concentration) parameters in metal oxide solutions include some indirectly obtained values. For example, the equilibrium concentration of metal cations is calculated proceeding from the quantity of the oxide-ion donor consumed for titration (precipitation). Direct determination of the concentration of metal cations in the melt (if it is possible) allows one to obtain more correctly the obtained solubility product values. Our paper [332] reports a method for correction of the solubility product values for oxides on the basis of the potentiometric titration data. The modification of the standard routine consists of the simultaneous use of two indicator electrodes, one of which is the membrane oxygen electrode and the other is a metal electrode, reversible to the cations the oxide consists of. This routine was used to estimate the solubility products of copper(I) and nickel(II) oxides in the molten KCl-NaCl equimolar mixture at 700 °C. Investigation of Cu20 by the proposed method is of considerable importance since, as will be shown further, the process of dissociation/dissolution of copper(I) oxide in molten alkali-metal halides differs from the generally accepted one which was considered, e.g. in Ref. [119]. 

In the first mode, known portions of the polymer were equilibrated with solutions of CaCl2 and HCl, as well as with their mixtures of known concentrations. The final composition of the bulk solutions in equilibrium with the polymeric phase was determined by titrating the excess HCl acid with NaOH and hy complexometric titration of the Ca ions with ethylenediamine tetraacetate (EDTA). From these data the concentrations of the electrolytes within the porous space of the polymeric material were calculated and then the apparent phase distribution coefficients k of HCl and CaCl2, defined as the ratio between the equihbrium concentrations of the corresponding electrolytes within and outside the polymeric beads. These calculations are strongly facifitated by the outstanding property of the neutral hypercrossfinked polystyrene sorbents, namely that their swelling does not depend on the electrolyte concentration, so that the volume of the porous space remains constant in all experiments. Thus,... 

The emf of the electrode assembly is measured while known volumes of either add or base are added to the suspension. These data, in turn, are converted to proton concentrations with the help of a calibration curve prepared from similar titration data obtained without the suspended solid in the cell. The values of ( h oh) then can be calculated with the expression... 

In this experiment you will determine the molar solubility of PbCl2 as a function of temperature by means of a precipitation titration to determine the molar concentration of chloride ion at each temperature. From this data you will calculate Kgp at each temperature, plot In Kgp versus 1/T, determine AH° and AS° from the slope and intercept, and then calculate AG<. ... 

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