Propane coefficients

As an example of the quantitative testing of Eq. (5.47), consider the polymerization of diethylene glycol (BB) with adipic acid (AA) in the presence of 1,2,3-propane tricarboxylic acid (A3). The critical value of the branching coefficient is 0.50 for this system by Eq. (5.46). For an experiment in which r = 0.800 and p = 0.375, p = 0.953 by Eq. (5.47). The critical extent of reaction, determined by titration, in the polymerizing mixture at the point where bubbles fail to rise through it was found experimentally to be 0.9907. Calculating back from Eq. (5.45), the experimental value of p, is consistent with the value =0.578. 

Extraction from Aqueous Solutions Critical Fluid Technologies, Inc. has developed a continuous countercurrent extraction process based on a 0.5-oy 10-m column to extract residual organic solvents such as trichloroethylene, methylene chloride, benzene, and chloroform from industrial wastewater streams. Typical solvents include supercritical CO9 and near-critical propane. The economics of these processes are largely driven by the hydrophihcity of the product, which has a large influence on the distribution coefficient. For example, at 16°C, the partition coefficient between liquid CO9 and water is 0.4 for methanol, 1.8 for /i-butanol, and 31 for /i-heptanol. 

One molecule (or mole) of propane reacts with five molecules (or moles) of oxygen to produce three molecules (or moles) or carbon dioxide and four molecules (or moles) of water. These numbers are called stoichiometric coefficients (v.) of the reaction and are shown below each reactant and product in the equation. In a stoichiometrically balanced equation, the total number of atoms of each constituent element in the reactants must be the same as that in the products. Thus, there are three atoms of C, eight atoms of H, and ten atoms of O on either side of the equation. This indicates that the compositions expressed in gram-atoms of elements remain unaltered during a chemical reaction. This is a consequence of the principle of conservation of mass applied to an isolated reactive system. It is also true that the combined mass of reactants is always equal to the combined mass of products in a chemical reaction, but the same is not generally valid for the total number of moles. To achieve equality on a molar basis, the sum of the stoichiometric coefficients for the reactants must equal the sum of v. for the products. Definitions of certain terms bearing relevance to reactive systems will follow next. 

Fig. 13. Activity coefficients for the n-propane (2)-methane (3) system at 100°F. (O) Data of B. H. Sage and W. N. Lacey, Some Properties of the Lighter Hydrocarbons, Hydrogen Sulfide, and Carbon Dioxide. American Petroleum Institute, New York, 1955.

To take care of the three carbon atoms per propane molecule, we need three molecules of CO2. Thus, the carbon atoms are balanced by changing the stoichiometric coefficient of CO2 from 1 to 3. In this reaction the ratio of CO2 to propane is 3 1. Similarly, we need four molecules of water for the eight hydrogen atoms in one molecule of propane. Using this information, we modify the equation as follows ... 

Fig. 7.19. The hybrid-based MO coefficients (absolute value) in propane. [Shaded and unshaded areas correspond to different signs of AO coefficients (+lobe and — lobe)]...

Heat Release Rate From Fuel Gas. The fuel gas used in these tests was a mixture of natural gas supplied by the local gas company. This gas mixture contains approximately 90 percent methane and small fractions of ethane, propane, butane, C02, and nitrogen, as analyzed by Brenden and Chamberlain (6). Although composition of the gas changes with time, the changes were small in our case. A statistical sample of gross heat of combustion of fuel gas over several months showed a coefficient of variation of 0.7 percent. Also, the gross heat of combustion of natural gas reported by the gas company on the day of the test did not vary significantly from test to test. Thus, we assumed that the net heat of combustion was constant. 

FIGURE 8.19 Peak extinction coefficient versus equivalence ratio of fuel/oxygen stream mixture in propane and ethene opposed-jet diffusion flames. /w is the fuel injection parameter. The greater the extinction coefficient, the greater the soot mass. From Ref. [93]. 

Fig. 9. Comparison of dissociative sticking coefTicients of methane, ethane, propane, and n-butane on Ni(100) measured at high pressures with sticking coefficients predicted from molecular beam data. (From Ref 103.)...

For propane, n-pentane and n-hexane the differential heats of adsorption over FER dropped more rapidly, right after 1 molecule was adsorbed per Bronsted acid site. Similar results were obtained with TON. In contrast, with MOR and FAU the drop in the differential heats of adsorption for n-alkanes occurred at lower coverages, indicating that only a certain fraction of the Bronsted acid sites were accessible to the adsorbing alkane probe molecules. With MFI the drop did not occur until 2 molecules of n-alkane were adsorbed per Bronsted acid site, suggesting perhaps a higher stoichiometry of about two n-alkanes per Bronsted acid site. In the cases of i-butane and i-pentane the drop occurred around one alkane per Bronsted acid site. Finally, n-butane adsorption isotherms measured over TON framework type catalysts having three different A1 contents (Si/Al2 = 90, 104, 128) showed Henry coefficients to increase with increase in the A1 content [5], Based... 

Nowak et al. (63) presented a comparative study of the diffusivities of rigid models of methane, ethane, and propane in silicalite. (The details of the calculation are reported in the preceding section.) The calculated diffusion coefficients decreased as the length of the carbon chain increased, and the effect was found to be far more pronounced for ethane than propane. The calculated diffusivities, in units of 108 m2/s, were 0.62, 0.47, and 0.41 for methane, ethane, and propane, respectively. The ethane value is in satisfactory agreement with PFG-NMR measurements [0.38 (77), 0.3 (80), 0.4 (42) for silicalite. The value for propane, however, was calculated to be almost an order of magnitude larger than the NMR results of Briscoe et al. (80). [The agreement with the value of Caro et al. (71) is better, but still an overestimation.]... 

Nicholas et al. (67) have performed MD calculations of propane in sili-calite in which the propane molecule is given complete flexibility. The calculations, which have been detailed previously for methane diffusion, employed a large simulation box with multiple sets of adsorbates to ensure good statistics. The framework was kept fixed and data were collected over a 40-ps run. The results predict diffusion coefficients in very good agreement with the values of Caro et al. (71). The calculated values for a concentration of 4 and 12 propane molecules per silicalite unit cell are 0.12 and 0.005 X 10 8 m2/s, respectively. These values for propane are far lower than those of Nowak et al. (63), the reason for this is that Nicholas et al. used flexible adsorbate molecules, whereas Nowak et al. used rigid ones. 

The CB-MC method has been used to simulate the adsorption isotherms of various alkanes in silicalite (170, 171). Using potential parameters that were fitted to obtain good agreement with experimental Henry s law coefficients, Smit and Maesen (170,171) have simulated the adsorption isotherms of straight-chain alkanes in silicalite. Good agreement was obtained for ethane and propane in comparison with the different type-I curves measured experimentally. The overall agreement with experimental isotherms was found to be satisfactory with hexane and heptane, and a kink is seen... 

Fig. 6. Reaction rate coefficients for the combination of f-butyl radicals in Aj n-hexa-decane solvent V, n-dodecane solvent , n-decane solvent X, n-octane solvent 8 n-heptane solvent and of allyl radicals in propane ( ) and melhylallyl radicals in isobutane (O) plotted against the Smoluchowski—Stokes—Einstein rate coefficient, eqn. (30). The broken line is of unit slope. The solid line is a comparison of the steady-state (t-> >) Collins and Kimball rate coefficient [eqn. (26)] with the activation rate coefficient, feact = 1011 dm3 mol-1 s 1 and the diffusion-limited rate coefficient 4irRD replaced by eqn. (30). After Schuh and Fischer [40].

K. They noted a decay over timescales 95 and < 35 ns, respectively, which was attributed to geminate ion-pair recombination (see Fig. 33). The decay of the optical absorption is independent of the dose of radiation received and continues for about lps. Rather than displaying a dependence on time as eqn. (153), i.e. at f 3/2, the experimental results are more nearly represented by either at f 1 decay to an optical density about one tenth of the maximum or by a decay as t 1/2 to zero absorption. These effects may be the recombination of ions within a spur (or cluster of ion-pairs), which is more nearly like a homogeneous reaction. The range of electrons in propane at 100 K is 10 nm [334] and the extrapolated diffusion coefficient is 10 11 m2 s 1 [320]. The timescale of recombination is 10 ps. The locally greater concentration of ions within a spur probably leads to a faster rate of reaction and is consistent with the time-scale of the reaction observed. Baxendale et al. [395] observed the decay of the infrared optical absorption of the solvated electron in methylcyclo-hexane at 160 K. They noted that the faster decay occurring over < 50 ns was independent of dose and depended on time as t 1/2, i.e. the reaction rate decays as t 3/2, see eqn. (153). It was attributed to recombination of... 

The slow combustion reactions of acetone, methyl ethyl ketone, and diethyl ketone possess most of the features of hydrocarbon oxidation, but their mechanisms are simpler since the confusing effects of olefin formation are unimportant. Specifically, the low temperature combustion of acetone is simpler than that of propane, and the intermediate responsible for degenerate chain branching is methyl hydroperoxide. The Arrhenius parameters for its unimolecular decomposition can be derived by the theory previously developed by Knox. Analytical studies of the slow combustion of methyl ethyl ketone and diethyl ketone show many similarities to that of acetone. The reactions of methyl radicals with oxygen are considered in relation to their thermochemistry. Competition between them provides a simple explanation of the negative temperature coefficient and of cool flames. 

Figure 4 Temperature dependence of the experimental self-diffusion coefficient of propane molecules in NaX.

Use the Peng-Robinson equation of state to calculate the compositions, densities, and quantities (lb moles) of the equilibrium liquid and gas of the mixture given below at 160°F and 500 psia. Use binary interaction coefficients of 0.0 for methane-propane,... 

A system with clearly defined disperse (A) and continuous (B) component phases is afforded by copolymers of styrene (A) grafted onto a polydimethyl siloxane matrix (B)101 Lack of appreciable interaction between the components was indicated by gas solubility and Tg measurements. The permeability coefficient of propane and other paraffins over a composition range vA = 0 — 0.55 followed the trend described by Eqs. (30)—(33) (with PA = 0, in view of the fact that the polystyrene phase is practically impermeable). Of particular relevance to the present discussion is the close agreement with the Bruggeman, and definite deviation from the Bottcher, equations at higher vA (cf. Fig. 11). Corresponding block copolymer membranes with vA = 0.34 also fitted into this pattern, except in one case where the structure was found to be lamellar and P was considerably lower. 

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