Diffusion coefficients hydrogen transfer

Because the conditions for the reaction are the same as in Example 4.6, the pseudo first-order rate constant k will again be 16.8 s 1, and the effective diffusivity of hydrogen in the liquid filled pores of the catalyst Dt will be 0.11 x 10 8 m2/s. Also because the transfer coefficients kt and ks depend mainly on the physical properties of the system, the same values, namely, ki = 1.23 x 10"3 m/s and ks = 0.54 x 10-3 m/s, will be used even though the hydrodynamics of the three-phase fluidised-bed will be different and the particle size is larger. 

A study involving iron amalgams in acidic and alkaline media indicates a magnetic field effect on the Tafel slope, probably due to a complex interaction of the magnetic field with amalgam formation, diffusion, and hydrogen evolution. Experimental results obtained with cupric sulfate solutions show no magnetic field effect on the transfer coefficient... 

In contrast to the well studied molecular diffusion, proton diffusion is less well understood. Protons can move in the hydrogen-bonded network of water molecules by transfer in a hydrogen bond and a successive jump into another hydrogen bond by molecular rotation, as illustrated in Fig. 24.3. This diffusion processis oversimplified but well highlights the dominant proton motions involved. Although the model was proposed a half century ago [12], its process has eluded experimental investigation. The competitive molecular diffusion shades the protonic diffusion. The protonic diffusion coefficient is estimated to be the order of... 

The concentration gradients of the reducing agents caused by mass transfer can be flattened by adding a reducing gas with high diffusion coefficient such as hydrogen (Fig. 17). 

Substrate limitations have been documented and quantitatively described ( U, 2, 17 ). Dooley et al. (11) present an excellent description of modeling a reaction in macroreticular resin under conditions where diffusion coefficients are not constant. Their study was complicated by the fact that not all the intrinsic variables could be measured independently several intrinsic parameters were found by fitting the substrate transport with reaction model to the experimental data. Roucls and Ekerdt (16) studied olefin hydrogenation in a gel-form resin. They were able to measure the intrinsic kinetic parameters and the diffusion coefficient independently and demonstrate that the substrate transport with reaction model presented earlier is applicable to polymer-immobilized catalysts. Finally, Marconi and Ford (17) employed the same formalism discussed here to an immobilized phase transfer catalyst. The reaction was first-order and their study presents a very readable application of the principles as well as presents techniques for interpreting substrate limitations in trlphase systems. 

Design of hydrogen coolers must provide for a steady decrease in the heat-transfer coefficient as diffusion of the remaining water to a cold surface becomes more difficult. Because of the generally higher diffusion coefficients in hydrogen systems, the effect is less marked here than in the case of chlorine cooling. 

According to [59], at 25 °C the diffusion coefficient of protons in water is Dh+ = 9.28 10 cm /s, while the self-diffusion of water molecules is three times lower, = 2.8 10" cm /s. The hydrogen-bonded network, that restrains the self-diffusion of water molecules, paves the way for the rather fast proton transfer along the hydrogen bonds. Curiously, ordering water molecules within the network in itself does not accelerate proton transfer. Actually, according to recent data [60], the rate of proton diffusion in the... 

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