Volume calculation from density

Physical and Thermodynamic Properties of Pure Chemicals Data Compilation This comprehensive data base is designed primarily for the chemical engineer and, consequently, includes many thermodynamic quantities such as enthalpies and free energies of formation, standard entropies, and so on. Molar volume calculated from density, and van der Waal s surface, and volume are also cited. Supplementary updates are published periodically. 

Molar masses, glass transition temperatures, and fractional free volume (calculated from densities and Paul and Park s series of increments) of the polymers are summarized in Tables I and II (6-8). Fractional free volume (Vf) calculated by the method of Park and Paul (P) differs for different gases, depending on the diameters of the gas molecules. Here, the values for O2 and N2 are given as examples. As expected, the values for Vf increase with decreasing kinetic diameter of the gas molecules. 

Calculated from density at 25 °C and volume expansion at elevated temperatures. Ref. 2. 

The partial molar volume data of Table I on ammonia was calculated from density data in Landolt-Bornstein(57). The values of partial molal volume at infinite dilution can be expressed as ... 

The results of image analysis of macroporous epoxies showing a narrow and bimodal pore size distribution are summarized in Table 3. The volume fraction, ( ), is always calculated from density measurements. The validity of the data obtained with digital image analysis is of utmost importance in order to draw correct conclusions concerning the structure-property relationships. 

The elution volumes for n-hydrocarbons show a straight line relationship vs the logarithms of their molar volumes. Molar volumes, calculated from the densities of compounds other than n-hydrocarbons, must be modified to have the elution volumes of these compounds conform to the same calibration line (elution volume vs log molar volume) as that for the n-hydrocarbons. W. W. Schulz (1 ) related the elution behavior of branched alkanes in the range of Cy-C] ] to the average numbers of gauche arrangements (Zg) which the molecule can assume. 

Values of molar volumes can be calculated from densities measured for the liquid salt, or can be calculated as for hypothetical subcooled liquid at 298.15 K using the group contribution method [47]. As expected, the molar volumes of 1,3-dialkylimidazolium salts and quaternary ammonium salts increase progressively as the length of alkyl chain of the substituent increases. Some molar volumes values at 298.15 K are listed in Table 1.3. 

In estimating the bulk compositions of the other terrestrial planets, there are not nearly so many constraints. Determination of a planet s mass (obtained from its gravitational effect on the orbits of moons or nearby spacecraft) and volume (calculated from its diameter as measured by telescopes) enables the calculation of its mean density. A meaningful comparison of planet mean densities requires that we correct for the effects of self-compression due... 

N2 02, neopentane) in the zeolites A, X, L, mordenite, omega, and a synthetic offretite type have been determined from isotherms. These have been compared with the void volumes calculated from the known crystal structures. For most adsorbates the measured and calculated void volumes are in good agreement. However, helium and nitrogen exhibit anomalous behavior. A void volume-framework density relation for zeolites is given. 

For the denaturation of / -Lg in 40% 2-chloroethanol, the presently reported partial specific volume measurements result in a AV value of —590 ml/mole. This value is very close to that previously reported for the denaturation of this protein by 6.4M urea, —610 ml/mole (27). Although this similarity of AV values is striking, it might be the result of a fortuitous compensation of various effects. The change in volume calculated from the difference in partial specific volumes is the sum of a number of contributions (28), such as differences in electrostriction in the two media, changes in the density of solvent components when they interact... 

Volume percentages of organic matter identifiable under the microscope only correlate well with total organic carbon contents if the unstructured groundmass is included in the volume calculation. From a relationship between TOC values, average densities of the rock matrix and the organic matter we deduce that in most samples the microscopic kerogen evaluation accounted for at least 80% of... 

Partial specific volumes were calculated from density measurements on poloxamer solutions made using a digital density meter (Paar DMA 02C). 

Textural Parameters. Adsorption-desorption isotherms of N2 at 77K were determined in a Micromeritics ASAP 2010 with a micropore system. Prior to measurement, the samples were outgassed at 140 C for at least 16 h. The specific surface area was determined by the BET method, assuming that the area of a nitrogen molecule is 0.162 nm [12]. Micropore volume was calculated by the t-plot method using the Harkins and Jura [13] thickness. We used model isotherms calculated from density functional theory (DFT) to determine the pore size distributions and cumulative pore volume of the pillared samples by taking the adsorption branch of the experimental nitrogen isotherm, assuming slit-like pores [14]. 

The KBIs for the 1-propanol (l)/water (2) mixture are available in the literature,and there is agreement between the KBIs obtained in various calculations.In the present paper, the excesses (deficits) for the 1-propanol (l)/water (2) mixture have been calculated with eqn (13) by using the KBIs already calculated by us. The partial molar volumes for the 1-propanol (l)/water (2) mixture have been calculated from density data" and the isothermal compressibilities have been evaluated using the expression ... 

Drawing conclusions The density of water is equal to its mass divided by its volume. Calculate the density of water by using your data from step 11. Then, calculate the density of water by using your data from step 12. 

The molar volume can be calculated from density according to the relation... 

When a molecule is represented as an object with well-defined boundaries, geometric methods of analysis may be applied. Several steric parameters have been derived from the model in w hich atoms, hence molecules, are represented as geometric objects with surfaces and volumes. The boundary of an atom is usually determined by its van der Waals radius. Surface area and volume of groups and molecules can be estimated. Bondi,Hermann, and Pearlman are among those who have studied surface area and volume. Molar refractivity (MR), calculated from density and refractive index, has frequently been used to estimate the bulk or global volume of a molecule or group. A more recent trend is to use MR as a model for dispersion interactions. 

The polymerization is accompanied by approximately 6% shrinkage (calculated from densities of monomer and polymer at 25 °C). Upon heating the polymer solution in the presence of trifluoromethanesulfonic acid the substituted 1,3-dioxolane ring opens and linear polymer is formed. This is accompanied by a 9.7% expansion in volume. 

The corresponding H-NMR spectra are shown in Fig. 8.5. The volume changes during polymerizations, as calculated from densities of monomer and polymers, are given in the Table 8.11 47). 

Because the excess volume for this system was expected to be small (10), and any effect is second order (15), only a few determinations were deemed necessary. A standard pycnometric technique was used (16). The densities at 29°C of three samples of known mole fraction, in addition to the pure components, were found. The excess volumes calculated from these results are shown as Table I. For the accuracy required by the calculations, a value for VE of 1.0 cm3 mol 1, independent of composition over the range of x considered, was sufficient. The effect of error in VE is discussed later. Differentiation of Equation 12 then leads to... 

The volume calculated from the density data is slightly smaller than real lank volume. 

Wp (cm /g) is the total pore volume calculated from the true (1.12 cm /g) and apparent densities, (cm /g) is the total pore volume determined by mercury intrusion. 

The approximate crystallinity of a polymer sample can be calculated from density measurements. Based on the two-phase model of polymer behavior, the mass or volume fraction of crystallinity can be calculated by measuring the density of a polymer sample, if the densities of the amorphous material and of pure crystals are known, as indicated by the following equations ... 

Batchinski observed that zero-shear viscosity ( jo) of low-molecular-weight liquids at different T and P changes with the density, p rjooup [Batchinski, 1913]. Later, Doolittle correlated In rjo with redefined free volume, (po, also calculated from density [Doolittle, 1951a,b, 1952, 1954 Doolittle and Doolittle, 1957] ... 

FIGURE 11.9 Specific total, V, free Vf = hV, and occupied, Vqcc = (1 — h)V, volume of PC as a function of T at ambient P. h is the hole fraction calculated from V using the S-S equation of state. Open symbols, experimental data dots, S-S equation of state fits to the volume in the temperature range T>Tg-, stars, free volume calculated from Vf=N v,), where (Vf,) is the mean hole volume from PALS and is the specific hole density, assumed to be constant at N f = 0.67 X 10 g (corresponding to 0.81 nm at 300 K). (Adapted from Dlubek et al., [2007d].)... 

X-ray diffraction (XRD) results are provided in Table 111 in weight percent. Table IV provides results of Si content in volume percent from three different measurements, namely (1) calculation from density. (2) measured by XRD and converted from weight to volume percent and (3) measured by quantitative image analysis (QIA). In all cases, the amount of carbon in the starting preforms, with similar starting SIC weights, increases as the sample number increases. 

Tables 63 and 64 record the densities and volumes calculated from those densities of a few simple paraffin molecules. Column 4 gives the volumes calculated by the above formula from x-ray data for the crystalline state. Column 5 contains the quotient, which indicates how many times the molecular volume found for the liquid state is greater than that calculated for the crystalline state. The lower hydrocarbons are compared at 0 in Table 63 and the higher at 99° in Table 64.

Values of cb for various molalities were calculated from density data of Chemical Engineers Han ook (McGraw-Hill Book Company, Inc., New York, 1950). Partial molal volumes Vb were calculated from these density data by the method of tangent intercepts described by Lewis and Randall (loc, cit.f p. 39). Relative viscosities m/mb are available for NaCl solutions at 18°C. in International Critical Tables (Vol. V, p. 15). The accompanying tabulation summarizes the results of the various calculations, and Fig. 5.6 compares the calculated results with the experimental data as reported in International Critical Tables (Vol. V, p. 67). 

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