Hydrogen equilibrium concentration

Steam. Steam is a potential poison of nickel catalysts under extremely high steam concentrations and low hydrogen concentrations. This is apparent in Figure 11 where the equilibrium ratio of Ph2/Fh2o over Ni and over Ni(active) is plotted as a function of temperature for the following reactions ... 

The hydrogen concentration contours for 50 atm and 700°K (Figure 8) indicate that there is appreciable unreacted hydrogen after equilibrium is reached. It is clear that multiple reaction stages are required to approach pure methane. 

P the total pressure, aHj the mole fraction of hydrogen in the gas phase, and vHj the stoichiometric coefficient of hydrogen. It is assumed that the hydrogen concentration at the catalyst surface is in equilibrium with the hydrogen concentration in the liquid and is related to this through a Freundlich isotherm with the exponent a. The quantity Hj is related to co by stoichiometry, and Eg and Ag are related to - co because the reaction is accompanied by reduction of the gas-phase volume. The corresponding relationships are introduced into Eqs. (7)-(9), and these equations are solved by analog computation. 

Because 1 is several orders of magnitude larger than 2 or, we identify 1 as dominant. Notice, however, that the water equilibrium generates some hydroxide ions in the solution, so this equilibrium must be used to find the concentration of hydroxide ions. The third reaction involves a minor species, HCO3, as a reactant, so it cannot be the dominant equilibrium. However, just as the water equilibrium generates some hydroxide ions, the hydrogen carbonate equilibrium generates some carbonate anions, whose concentration must be determined. 

Expressions for 9 SM and H2 can be derived and related to rate (k) and equilibrium constants (K). The SI and S2 site balances are 9SM +9a + S, = 1 and //2 + S2 = 1 respectively 9sx, S2 are empty sites). Based on Henry s law, the gas-phase hydrogen pressure and the liquid-phase hydrogen concentration may be used interchangeably. The rate expression can be written as follows ... 

Before addition of the extra hydrogen, its concentration was 0.250 mol/L. After addition of the extra hydrogen, but before any equilibrium shift could take place, there would be 0.253 mol/L. The shift of the equilibrium would use up some but not all of the added hydrogen, and so the final hydrogen concentration must be above 0.250 mol/L and below 0.253 mol/L. Some nitrogen has been used up, and its final concentration must be less than its original concentration, 0.100 mol/L. Some additional ammonia has been formed, and so its final concentration has been increased over 0.200 mol/L. Notice that Le Chatelier s principle does not tell us how much of a shift there will be, but only qualitatively in which direction a shift will occur. 

Bech Nielsen et al. (1988) also made a channeling study of the 2H in B-2H complexes that was similar in principle to that just described but differed in details of technique and in some of the conclusions arrived at. Also, they did not investigate the position of the boron atoms. They used Si uniformly doped with a high (1 x 1019 B/cm3) boron concentration, rather than implanted boron. The surface was etched off after hydrogenation, but no SIMS data was presented to confirm the uniform hydrogen concentration assumed. The penetration depth of the H was given as —7000 A. The channeling measurements were performed at 30 K. For analysis of their data Bech Nielsen et al. used the same model, based on the assumption of statistical equilibrium (SE) of the channeled ions, already described in connection with the measurements of implanted deutrium... 

The final question we shall consider here has to do with the extrapolation of the solubility of hydrogen in silicon to lower temperatures. Extrapolation of a high-temperature Arrhenius line, e.g., from Fig. 11, would at best give an estimate of the equilibrium concentration of H°, or perhaps of all monatomic species, in intrinsic material the concentration of H2 complexes would not be properly allowed for, nor would the effects of Fermi-level shifts. Obviously the temperature dependence of the total dissolved hydrogen concentration in equilibrium with, say, H2 gas at one atmosphere, will depend on a number of parameters whose values are not yet adequately known the binding energy AE2 of two H° into H2 in the crystal, the locations of the hydrogen donor and acceptor levels eD, eA, respectively, etc. However, the uncertainties in such quantities are not so... 

It will be seen that, despite the rather considerable range of assumptions used for the various curves, the total dissolved hydrogen in equilibrium with gas at one atmosphere is very small, probably undetectable, at temperatures as low as 500 K. If AE2 is as low as 1.5 eV, the concentration of dissolved H2 always stays well below that of H°, as the n02 factor in (12) decreases faster with decreasing temperature than the factor exp(AE2/ r) increases for AE2 closer to 2.1 eV, H2 becomes strongly dominant at the lower temperatures. A AE2 appreciably larger than 2.1 eV would be hard to reconcile with the high temperature observations. The H° concentrations always decrease extremely rapidly at low temperatures. The possible... 

Case 1 in Figure 45.2 refers to a case where the reaction between S and H2 is very slow. In that case, the rate of hydrogen consumed by the reaction (i.e., the rate of the reaction) is small compared to the maximum rate of mass transfer. Thus, mass transfer feeds the liquid phase easily with dissolved hydrogen. The liquid-phase hydrogen concentration is very close to that at equilibrium given by the Henry s law ... 

Assuming a first-order rate law with respect to hydrogen, with a kinetic constant kc, the maximum rate of chemical reaction (mol s-1 mL3) is obtained when the hydrogen concentration reaches equilibrium (Ch,l=C ,i) and the corresponding maximum reaction flux ( m(mol s 1) results in Eq. (19). 

The boundary conditions require knowledge of the interface concentration of hydrogen ChjL to compute E (see below). For hydrogenations, the equilibrium concentration (ChjL= CfJ L) can be used, albeit with the assumption of no mass transfer resistance on the gas side. Otherwise, it must be determined using Eq. (4). The boundary conditions for the substrate S state that it is not transferred to the gas phase - that is, S is not vaporized. This assumption is most often... 

Situation 2 slow chemical reaction, Ho<0.3, = 1. The Hatta number is small, and thus the chemical reaction does not modify the mass transfer process and consequently, E 1. However, the chemical reaction is not so slow compared to the mass transfer rate. The hydrogen concentration in the bulk is smaller than the equilibrium concentration. The substrate concentration A is constant in the film and is almost that in the bulk. The consumption of H2 and A is negligible in the film and takes place in the bulk of the liquid. The reactor performances are obtained straightforwardly (see below). The mass transfer rate is obtained by /H LfCfJ.i-CH.L)-... 

The first reaction (Boudouard equilibrium) favors carbon formation at lower temperatures compared to POX. The hydrogen concentrations attained depend on the fuel used in POX but it never reaches the theoretical level [27],... 

In the case of BDPP with a bite angle of 90°, the high-pressure NMR and high-pressure IR studies showed the structures of the hydrido dicarbonyl diphosphine resting state as an axial-equatorial BPT. Similar behavior was observed for the furanoside diphosphines. Dinuclear rhodium species in equilibrium with the mononuclear pentacoordinate rhodium hydride carbonyl diphosphines have been found for these ligands. The position of this equilibrium depends on the hydrogen concentration and the ligands. The rate... 

Figure 2. Description of the initial and boundary conditions for the hydrogen diffusion problem in the pipeline. The parameter / denotes hydrogen flux and C,(P) is normal interstitial lattice site hydrogen concentration at the inner wall-surface of the pipeline in equilibrium with the hydrogen gas pressure P as it increases to 15 MPa in 1 sec. At time zero, the material is hydrogen free,...

Figure 3. Evolution of normalized NILS hydrogen concentration C, IC vs. normalized distance R lb ahead of the crack tip for crack size r/ = 1.9 mm (a) near crack tip solution, (b) solution over the entire uncracked ligament. The parameter b denotes the crack tip opening displacement which varies with time as the hydrogen pressure increases toward its final value of 15 MPa over 1 sec. The parameter C =2.659x10 H atoms/m ( = 3.142x10 H atoms per solvent atoms) denotes the hydrogen concentration on the inner wall-surface and crack faces in equilibrium with the hydrogen gas.

Figure 5. Description of (a) boundary conditions for the elastoplastic problem and (b) initial and boundary conditions for the hydrogen diffusion problem at the blunting crack tip in the MBL formulation. The parameter bCl denotes the crack tip opening displacement in the absence of hydrogen. The parameter C, (P) denotes NILS hydrogen concentration on the crack face in equilibrium with hydrogen gas pressure P. and / is hydrogen flux.

As in the full-field formulation, we assigned a zero flux boundary condition, i.e. j = 0 at the outer boundary of the domain as well as on the axis of symmetry ahead of the crack tip (Fig. 5b). Also, along the crack surface, we assumed the NILS hydrogen concentration CL to be in equilibrium... 

Figure 9. MBL formulation results plotted against normalized domain size L lb. under zero concentration boundary condition on the remote boundary while the crack faces are in equilibrium with 15 MPa hydrogen gas (a) non-dimensionalized effective time to steady state = >t lb (b) peak values of the normalized hydrogen concentration in NILS at / =/ (effective time to steady state).

Over platinum black, -hexane gives 2- and 3-methylpentanes, methylcyclopentane, and benzene. Actual concentrations are compared in Fig. 2 with equilibrium ones as a function of hydrogen pressure. Unreacted n-hexane is ignored since it would not be able to equilibrate with all its products. Realistic values are obtained if methylcyclopentane plus isomers are compared with the amount of benzene. These, however, correspond to much higher effective hydrogen concentrations than measured in the gas phase (31). 

Based on the Langmuir-Hinshelwood expression derived for a unimolecular reaction system (6) Rate =k Ks (substrate) /[I + Ks (substrate)], Table 3 shows boththe apparent kinetic rate and the substrate concentration were used to fit against the model. Results show that the initial rate is zero-order in substrate and first order in hydrogen concentration. In the case of the Schiff s base hydrogenation, limited aldehyde adsorption on the surface was assumed in this analysis. Table 3 shows a comparison of the adsorption equilibrium and the rate constant used for evaluating the catalytic surface. 

The chemical potential of hydrogen in the gas phase, at equilibrium with the dissolved hydrogen in the solid, is given by Equation 2 where gh2 is the standard (1 atm) chemical potential of gaseous hydrogen. At small hydrogen concentrations in the metal, mh is given by Equation 3, (II, 25) where the next-... 

Fig. 3.12. The rototranslational absorption spectrum of H2-He pairs at three temperatures 77.4 K ( ), 195 K (x), and 293 K ( ). The data shown represent the enhancement of the absorption due to the addition of helium to hydrogen gas, obtained in 32 mole percent equilibrium hydrogen concentration in helium by subtraction of the H2-H2 spectra after [37].

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