Methane calculations

Bond dissociation energies for a selection of substituted methanes, calculated at a range of levels [23], are compared with experimental values [37] in Tables 6.9 and 6.10. Also listed are mean absolute deviations (MADs) and mean deviations (MDs) from experimental values [e.g. MAD(Exp.)] and from CBS-RAD [e.g. MD(CBS-RAD)]. 

Differential heats of adsorption for methane calculated with the Clapeyron equation from isotherms at 0°, 30° and 50°C. are given in Table III. The... 

Brinkman and coworkers81 obtained a value of around 30 kcal mol 1 from a similar gas-phase study for the same proton affinity relative to methane. Calculations at the 6-311+G(d,p) level gave a value of 25 kcal mol 1 (for H3SiCH2-). The proton affinities of (H3Si)2CH- and (H3Si)3C- relative to methane were calculated to be 47 and 66 kcal mol-1, respectively. The experimental proton affinity of (Me3Si)2CH- was found to be approximately 43 kcal mol-1. 

A large carcerand has a cavity volume of 120 A3. If the molecular volume of methane is 28.5 A3, calculate the occupancy factor, p, for a 1 1 methane carceplex of this host. What host volume would result in an occupancy factor of 0.67, equivalent to solid methane Calculate the notional pressure of one molecule of methane in a cavity of this size. Do you think that such a carceplex is likely to form ... 

Using the adjusted parameters Pab given in Table 2.1, we studied the optimal geometry structures of several simplest molecules. It turned out that the H-H bond length is larger by 0.01 A than the experimental value. The intemuclear separations C-H in methane, calculated by the SLG-MINDO/3 method, coincide with the experiment up to 0.001 A. Meanwhile the calculated C-C bondlength in ethane turns out to be 1.512 A. This is much smaller than the experimental value of 1.536 A. It has to be noticed, however, that the SCF-MINDO/3 method yields for the C-C bond in ethane... 

Fig. 7. History match of cases A-G and M and N with Darcy flow permeabilities of the rock salt seal for methane calculated plotted against the maximum depths reached by the seal.

Both the C-C and C-H bond activation branches of the potential energy surface for the reaction between Fe and ethane (calculations by B3LYP method) are characterized by a low barrier for the first step (the insertion of the Fc into a C-C or C-H bond) [55]. The second step is the rate determining one. In the C-C bond activation this is a [1,3]-H shift leading to a complex between Fe=CH2 and methane. Calculations using high-accuracy quantum chemical methods (B3LYP and PCI-80) for the endothermic reaction... 

It is desired to compute the global emissions of carbon that resulted from oil and gas production in 1986. Worldwide oil production in 1986 was 5.518 x 10 barrels day and worldwide gas production in the same year was 6.22 x lO ft yr (Katz and Lee, 1990). For oil a density of 0.85 g cm can be assumed. Assume that oil has an average composition of Ck)H22- A barrel has volume of 0.16 m Assume that the gas produced is entirely methane. Calculate global emissions from each in g(C)yr- . 

The degree of dispersion D of the the catalyst was foimd to be 42 % by means of chemisorption measurements with H2. At 10 bar and 300 °C a catalyst turnover number of 0.16 s was determined for methane. Calculate the rate of formation of methane in mols g(cat.) (metal + support). 

For a feed containing 4 mol of sulfur per mole methane, calculate the composition of the product if 90% conversion of methane and 70% conversion of sulfur are achieved. 

The outline of the chapter is the following We start, in Sect. 6.2, by giving a technical overview on how to solve the Kohn-Sham equations. The next section is devoted to p>seudo-potentials, an essential ingredient of many DFT calculations. In Sect. 6.4 we present our first test case, namely atoms, before we proceed to some plane-wave calculations in Sect. 6.5. The final example, methane calculated using a real-space implementation, is presented in Sect. 6.6. We will use atomic rniits throughout this chapter, except when explicitly stated otherwise. 

At the end of one week, a gaseous mixture is produced which analyzes 25 mol% methane. Calculate the reaction rate constant for this gas phase reaction. Use the conversion variable a rather than X or C in the solution. 

Pure acetone reacts isothermally to form ketene and methane at 2 atm and 650°C. The percent conversion of acetone is 70%. Calculate the reactor exit molar flow rate of acetone, ketone, and methane. Calculate the heat added or removed from the reactor. As a basis assume 100 kmol/h of pure acetone. Note that 1 mol of acetone reacts to form 1 mol of ketene and 1 mole of methane. 

Lasaga AC, Gibbs GV (1990) Ab initio quantum-methanical calculations of surface reactions - a new era In Stumm W (ed) Aquatic chemical kinetics. Wiley-Interscience, New York, pp 259-291... 

Figure 6 Free energy of particle insertion for methane calculated using a staged FEP method the free-energy change is shown for both the forward (X = 0 1) and reverse (X = 1 0) processes and for the average (data taken from Jorgensen, Blake, and Buckner. ).

Figure 7 The free energy of solvation of methane calculated using the staged insertion method of Kofke and Cummings.Each point represents the cumulative free energy calculated from all stages up to the value of the coupling parameter X. Taken from Arthur and Haymet. ...

In our study, the polarizability tensor of methane calculated from Gaussian 94 (22) is isotropic within the numerical accuracy of the calculation. Therefore the formula and calculations could be simplified. However, for most guest molecules in clathrate hydrates that are not as symmetric as methane, this derivation gives a general approach to characterize the induced dipole-dipole interaction. 

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