Cerium calculations

The total cerium content in the single crystal samples on the basis of rare-earth elements is determined by photometry after Ce(III) oxidation by ammonium persulfate. The Ce(III) content is calculated from the difference. Comparison of the determination results of the total cerium content obtained by photometric and atomic emission methods for Li GdlBO ljiCe demonstrated the elaborated procedure precision and systematic error absence. 

As a result, the electromotive force (EMF) of the cell is zero In the presence of fluoride ions, cerium(IV) forms a complex with fluoride ions that lowers the cerium(IV)-cerium(IIl) redox potential The inner half-cell is smaller, and so only 5 mL of cerium(IV)-cenum (III) solution is added To the external half-cell, 50 mL of the solution is added, but the EMF of the cell is still zero When 10 mL of the unknown fluonde solution is added to the inner half-cell, 100 mL of distilled water IS added to the external half-cell The solution in the external half-cell is mixed thoroughly by turning on the stirrer, and 0 5 M sodium fluonde solution is added from the microburet until the null point is reached The quantity of known fluonde m the titrant will be 10 times the quantity of the unknown fluoride sample, and so the microburet readings must be corrected prior to actual calculations... 

In Sections 10.11-10.16 it is shown how the change in pH during acid-base titrations may be calculated, and how the titration curves thus obtained can be used (a) to ascertain the most suitable indicator to be used in a given titration, and (b) to determine the titration error. Similar procedures may be carried out for oxidation-reduction titrations. Consider first a simple case which involves only change in ionic charge, and is theoretically independent of the hydrogen-ion concentration. A suitable example, for purposes of illustration, is the titration of 100 mL of 0.1M iron(II) with 0.1M cerium(IV) in the presence of dilute sulphuric acid ... 

Fig. 10.14 Titration of 100 mL of 0.14/ iron(II) with 0.14/ cerium(IV) sulphate (calculated).

The standard redox potential is 1.14 volts the formal potential is 1.06 volts in 1M hydrochloric acid solution. The colour change, however, occurs at about 1.12 volts, because the colour of the reduced form (deep red) is so much more intense than that of the oxidised form (pale blue). The indicator is of great value in the titration of iron(II) salts and other substances with cerium(IV) sulphate solutions. It is prepared by dissolving 1,10-phenanthroline hydrate (relative molecular mass= 198.1) in the calculated quantity of 0.02M acid-free iron(II) sulphate, and is therefore l,10-phenanthroline-iron(II) complex sulphate (known as ferroin). One drop is usually sufficient in a titration this is equivalent to less than 0.01 mL of 0.05 M oxidising agent, and hence the indicator blank is negligible at this or higher concentrations. 

Determine the volume of the standard cerium(IV) sulphate solution which has reacted with the nitrite solution, and therefrom calculate the purity of the sodium nitrite employed. 

E.22 (a) How many CaH2 formula units are present in 5.294 g of CaH2 (b) Determine the mass of 6.25 X 1024 formula units of NaBF4, sodium tetrafluoroborate. (c) Calculate the amount (in moles) of 9.54 X 1021 formula units of Cel3, cerium(III) iodide, a bright yellow, water-soluble solid. 

The agreement is also satisfactory for lithium and sodium sulfide. The oxide was used in calculating the lithium radius, 0.60 A., for in this compound it is safe to assume that the anions are not in mutual contact. It is further highly pleasing to note that even in zirconium and cerium oxide, containing quadrivalent cations, our theoretical radii are substantiated by the experimental inter-atomic distances for this makes it probable that even in these crystals the ions are not greatly deformed. 

The valences of the rare-earth metals are calculated from their magnetic properties, as reported by Klemm and Bommer.14 It is from the fine work of these investigators that the lattice constants of the rare-earth metals have in the main been taken. The metals lutecium and ytterbium have only a very small paramagnetism, indicating a completed 4/ subshell and hence the valences 3 and 2, respectively (with not over 3% of trivalent ytterbium present in the metal). The observed paramagnetism of cerium at room temperature corresponds to about 20% Ce4+ and 80% Ce3+, that of praseodymium and that of neodymium to about 10% of the quadripositive ion in each case, and that of samarium to about 20% of the bipositive ion in equilibrium with the tripositive ion. 

A common approach for identifying the enriched elements in a material is to calculate the enrichment factor (EF). The EF of an element, M, is obtained by comparing its concentration with that of a reference element, R, such as cerium or... 

Powder XR diffraction spectra confirm that all materials are single phase solid solutions with a cubic fluorite structure. Even when 10 mol% of the cations is substituted with dopant the original structure is retained. We used Kim s formula (28) and the corresponding ion radii (29) to estimate the concentration of dopant in the cerium oxide lattice. The calculated lattice parameters show that less dopant is present in the bulk than expected. As no other phases are present in the spectrum, we expect dopant-enriched crystal surfaces, and possibly some interstitial dopant cations. However, this kind of surface enrichment cannot be determined by XR diffraction owing to the lower ordering at the surface. 

From the biological data obtained by using cerium radionuclides and a comparative study with other members of the lanthanide family, the following biological parameters were selected and used in calculating q, (MPC)a, and (MPC)W values for cerium (ICRP, 1959) fi = (the fraction of ingested radionuclide reaching the blood) 0.0001... 

Fractions of absorbed cerium depositing in gonads were calculated from data in Table 20 by taking average ratios of radioactivity in testes or ovaries to that in liver and skeleton and multiplying these by the above liver and skeletal deposition fraction. 

An opportunity to use the thermodynamic cycle shown in Fig. 7 was provided by the requirement to estimate stability constants for cerium(IV) complexes of a series of hydroxypyridinones. As stability constants for their cerium(III) analogues had been measured and F °(Ce /Ce ) values established, stability constants for one bidentate and two tetradentate 3-hydroxy-2-pyridinones could be obtained. Log P4 for the former was calculated to be 40.9, log P2 for the complexes of the tetradentate ligands 40.6 and 41.9. These very high values, expected for a 4+ cation, are paralleled by high pCe values between 37 and 38 for the tetradentate ligands (147). 

Figure 21. Calculated Ce—O—S phase diagram at 1073 K. The circles and triangles correspond to conditions for which Ce202S and cerium oxide were experimentally determined stable. (Reprinted with permission from ref 175. Copyright 2000 Elsevier.)...

Two types of catalysts, Rh/SiO and Rh-CeO /SiO, were used. The reactivity tests (185°C, 1 atm.) showed that the presence of cerium affected the activity and also the selectivity of Rh/SiO catalysts. The total conversion (calculated as mole per cent of CO converted) after 8 hours on stream was 3.8% on Rh/SiO and 1.9% on the cerium containing catalyst. What is most striking is that the selectivity to oxygenates shifted from 6 to 71% by the addition of cerium. On Rh/SiO, acetaldehyde was obtained as the major oxygenated product whereas on Rh-CeO /SiO catalysts ethanol was the most abundant product. 

The appropriate Equations 7 or 8 and Equation 6 were used to calculate values of [Ce(IV)] and [cis ] from the measured values of At. The values of A0 used were those obtained by extrapolation to / = 0, and the values of Am were those calculated for / = 00. The calculated values of Am agreed within a few per cent with values measured after reactions had been allowed to go to completion. The observations are consistent with the data presented above on the amount of Cr(OH2)6+3 produced and on the absorptivity coefficients of the cerium(IV) and of rw-Cr(0H2)2(C204)2 , Cr(OH2)4C204+, and Cr(OH2)6+3. 

It is apparent that Cr(C2C>4)3 3, m-Cr(OH2)2(0204)2 , and Cr(0H2)4C2044 react smoothly with cerium(IV) in acidic-sulfate media, 1 mole of oxalate being oxidized for each 2 moles of cerium(IV) consumed. The observations made are consistent with the view that the three reactions proceed, at least initially, according to the stoichiometries represented by the respective Reactions 3,1, and 2. The initial absorbances of reactant solutions (values obtained by extrapolation of measured absorbances to zero time) agree well with the values calculated, on the basis of Beer s law, from the absorptivity coefficients of the components. Further, as the reactions in 1.83Af sulfuric acid proceed, the absorbances of the solutions move toward the values expected for the assumed products at rates which demonstrate the reactions are first order in cerium(IV) and complex—see, for example, Figure 2. We thus find no indication that reaction intermediates contribute measurably to the absorbances of reactant solutions, or that reaction conditions cause the rapid equilibration of any of the oxalato complexes with other species... 

To calculate the voltage at the equivalence point, we add the Nernst equations for Reactions B and C, as we did for the cerium and iron reactions in Section 16-1. Before doing so, however, multiply the permanganate equation by 5 so that we can add the log terms ... 

---