Calculating from mass

Calculations. The atoms of incorporated lsO is calculated from mass spectral data. When the ratio of the peak heights at mass-to-charge ratio (m/e) 44, 46 and 48 for CO2 is X-.Y-.Z, assuming that the height of each peak is strictly proportional to the number of CO2 molecules, the atom fraction of l80 in CO2, C, is given by ... 

The overall molarity of NaOH can be calculated from mass, molar mass, and volume ... 

Where D.. can be calculated from mass transfer coefficients or an uptake Aalf-time. For example, for air-water exchange is given by... 

Here, / is the membrane thickness in the swollen state at constant pH and temperature, and is the ratio of the solute concentration in the membrane to the solute concentration the solution at equilibrium, which can be calculated from mass balance. 

The kinetics of intercalation have been followed by FTIR and QCM gravimetry. For example, the frequency change of a QCM with a 20-layer CdAr film (exposed to H2S) was followed as a function of immersion time in a CdCl2 solution (Fig. 3.5.5) (46). The percent conversion [calculated from mass of film on QCM and stoichiometry in Eq. (3) reaches 100% within about 100 min immersion. In contrast, time-resolved FTIR spectra of CdBe/H2S and HgBe/H2S films immersed into Cd2+ and Hg2+ solutions, respectively, indicated that the intercalation of metal ions into the LB film of BeH takes 24-48 h to complete (21). The kinetics of the sulfidation reaction [Eq. (4) are discussed in a later section. 

Several years ago, one of the authors found that nickel, platinum, and some other hydrogenating agents, when deposited on fresh synthetic silica-alumina cracking catalyst, made a new catalyst that would isomerize paraffin and naphthene hydrocarbons in the presence of hydrogen at elevated pressures and nominal temperatures. Table I shows some early typical results calculated from mass spectrometer analyses of the products obtained by passing methyl cyclopentane, cyclohexane, and n-hexane over a catalyst composed of 5% nickel in silica-alumina at the indicated reaction conditions. Isomerization of a number of other hydrocarbons has also been studied and reported elsewhere (2). 

Hydrocarbon types were estimated using the substractive method of Poulson (15,16) for the fractions boiling above 175°F. The hydrocarbon compound composition of the C5-175°F naphtha was determined by gas chromatography. Paraffin and naphthene contents of the 175°-350°F naphtha and of the 350°-550°F light oil were calculated from mass spectra. Liquid displacement chromatography on Florisil was used to determine the amount of polar material in the 550°-850°F heavy oil. 

Table 1.5 Measures for mixing efficiency calculated from mass contour plots yielded by CFD simulation - benchmarking cross-shaped mixers with and without static mixing elements (SME) [71].

Calculated from mass loss measurements. b Found by chemical analysis of aluminium alloys after the runs. 

Density measures the mass of a unit volume of material. Units of g/cm3 are commonly used. SI base units of kg/m3 are also used. One g/cm3 is equal to one thousand kg/m3. Density (p) is calculated from mass (m) and volume (V) using the formula ... 

Calculated from mass balance Based on MWP charge... 

The two elements calcium and aluminum are RLEs. The assumption is usually made that aU RLEs are present in the primitive mantle of the Earth in chondritic proportions. Chondritic (undifferentiated) meteorites show significant variations in the absolute abundances of refractory elements but have, with few exceptions discussed below, the same relative abundances of lithophile and siderophile refractory elements. By analogy, the Earth s mantle abundances of refractory lithophile elements are assumed to occur in chondritic relative proportions in the primitive mantle, which is thus characterized by a single RLE/Mg ratio. This ratio is often normalized to the Cl-chondrite ratio and the resulting ratio, written as (RLE/Mg)N, is a measure of the concentration level of the refractory component in the Earth. A single factor of (RLE/Mg) valid for all RLEs is a basic assumption in this procedure and will be calculated from mass balance considerations. 

Fig. 7 Typical variation in gas composition in the drying chamber during secondary drying. Open circles experimental values determined in a laboratory freeze dryer filled triangles theoretical values calculated from mass transfer theory and freeze dryer characteristics. (M.J. Pikal, Eli Lilly Co., unpublished results.)...

Greenbaura et al. (3) report equilibrium constants for reaction b in the temperature range 1573-1724 K using the molecular flow effusion method. Also Hildenbrand et al. (4) report equilibrium constants for reaction c and d which were calculated from mass spectrometrlc ion intensities. The Aj.H (298.15 K) values by 2nd and 3rd law analysis for these data and the corresponding AjH (298.15 K) values are listed below. 

Although mass titration was originally designed as a method of determination of PZC, surface charging curves can also be calculated from mass titration data [60]. 

Calculated from mass spectra (assuming no isotope effect), detected in the reaction mixture after photolysis. The starting ethers and yields of Me20 are as follows MeOEt, 0.0613 mmol MeO-n-Pr, 0.0117 mmol Et20, 0.0059 mmol EtO-n-Pr, 0.0081 mmol THF, 0.0026 mmol. 

Figure 8. Effect of sulfite with N2 sparging at 25 and 55°C. Curves calculated from mass transfer model. Including CaCOs°/CaSO,° solid solution (Figure 10). pH , 4.5 O and A, 5.0 0,5.5 , 5.75 and A, 6.0 and A, S5°C.

The ablation rates calculated from mass loss measurements using a quartz crystal microbalance (QCM) [63] or mass spectrometry [64] reveal a so-called Arrhenius tail [63] (linear increase of products at low fluences, followed by a much faster increase). 

Once the theoretical yield from a crystallizer has been calculated from mass and energy balances, there remains the problem of estimating the CSD of the product from the kinetics of nucleation and growth. An idealized crystallizer model, called the mixed suspension-mixed product removal model (MSMPR), has served well as a basis for identifying the kinetic parameters and showing how knowledge of them can be applied to calculate the performance of such a crystallizer, ... 

Analysis by x-ray fluorescence. d Calculated from mass balance. 

To relate the concentrations of point and electronic defects to temperature and externally imposed thermodynamic conditions such as oxygen partial pressures, the defects are treated as chemical species and their equilibrium concentrations are calculated from mass action expressions. If the free-energy changes associated with all defect reactions were known, then in principle diagrams, known as Kroger-Vink diagrams, relating the defect concentrations to the externally imposed thermodynamic parameters, impurity levels, etc., can be constructed. 

The relative atomic mass of an element can be calculated from mass spectra data as follows ... 

The empirical formula can be calculated from mass percent data. The molar mass can be calculated using the ideal gas equation. The molecular formula can then be determined. 

In practice, the value of ft depends on how the driving force is expressed. Care needs to be taken when determining values for and S for VP/PV modeling. Different values are obtained if these two parameters are derived from thermodynamic principles or calculated from mass concentrations. 

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