Water diffusion, activation energy

Baxendale and Wardman (1973) note that the reaction of es with neutrals, such as acetone and CC14, in n-propanol is diffusion-controlled over the entire liquid phase. The values calculated from the Stokes-Einstein relation, k = 8jtRT/3jj, where 7] is the viscosity, agree well with measurement. Similarly, Fowles (1971) finds that the reaction of es with acid in alcohols is diffusion-controlled, given adequately by the Debye equation, which is not true in water. The activation energy of this reaction should be equal to that of the equivalent conductivity of es + ROH2+, which agrees well with the observation of Fowles (1971). 

In water. The two principle controlling factors for gas diffusion processes in liquids are the gas mass and its activation energy for diffusion. The diffusion activation energy in turn is controlled by the extent of interaction of the gas molecule or atom with the liquid phase. For noble gases, because they are monatomic and have a stable electron shell, there is little interaction with water and the rate of diffusion is almost entirely controlled by their respective masses. This is in contrast with species such as CO2 and CH4 where interaction occurs with water molecules through induced dipole-dipole moments. Because this is in addition to mass, these species diffuse significantly more slowly in water than noble gases of similar mass (Table 5, Fig. 11). 

The most complete study of noble gas diffusion rates in water remains the experimental determination by Jahne et al. (1987). In this work the diffusion coefficient in water was determined for systems between 0 and 35°C and the results expressed in terms of the diffusion constant, A (cm /s), and diffusion activation energy, Ea (Kj/Mol) (Table 5), to provide a temperature dependent expression for the determination of the gas diffusion coefficient, D (cm /s), at variable temperature following... 

The dependence of the rate of cure on temperature is thus controlled by three heats, which are the heat of evaporation of water, the activation energy for diffusion, and the heat of solution of water in the cured material. 

Diffusion of the molecular gases can be compHcated by reactions with the glass network, especially at the sites of stmctural defects. The diffusion coefficient of water, for example, shows a distinct break around 550°C (110). Above 550°C, the activation energy is approximately 80 kj /mol (19 kcal/mol), but below 550°C, it is only 40 kJ/mol (9.5 kcal/mol). Proposed explanations for the difference cite the fact that the reaction between water and the sihca network to form hydroxyls is not in equiUbrium at the lower temperatures. 

Endotliermic Decompositions These decompositions are mostly reversible. The most investigated substances have been hydrates and hydroxides, which give off water, and carbonates, which give off CO9. Dehydration is analogous to evaporation, and its rate depends on the moisture content of the gas. Activation energies are nearly the same as reaction enthalpies. As the reaction proceeds in the particle, the rate of reaction is impeded hy resistance to diffusion of the water through the already formed product. A particular substance may have sever hydrates. Which one is present will depend on the... 

Fig. 13. Plot of variations of activation energy ( /kJ mole"1) with water vapour pressure (PHjO/Torr) for dehydration of calcium sulphate. Data from Ball et al. [281,590, 591] who discuss the significance of these kinetic parameters. Dehydrations of CaS04 2 H2O, nucleation ( ), boundary (o) and diffusion (e) control Q-CaSC>4 5 H2O, diffusion control, below (X) and above (+) 415 K j3-CaS04 5 H20, diffusion control ( ).

R is the gas constant Dq and activation energy Eu are constants derived from an Arrhenius plot for diffusion coefficients applying at different temperatures, and solubility coefficient was obtained from a separate permeation test at TiK. Suitable testing using a specially constmcted permeation cell water-cooled at one end provided good validation data. 

Pure PHEMA gel is sufficiently physically cross-linked by entanglements that it swells in water without dissolving, even without covalent cross-links. Its water sorption kinetics are Fickian over a broad temperature range. As the temperature increases, the diffusion coefficient of the sorption process rises from a value of 3.2 X 10 8 cm2/s at 4°C to 5.6 x 10 7 cm2/s at 88°C according to an Arrhenius rate law with an activation energy of 6.1 kcal/mol. At 5°C, the sample becomes completely rubbery at 60% of the equilibrium solvent uptake (q = 1.67). This transition drops steadily as Tg is approached ( 90°C), so that at 88°C the sample becomes entirely rubbery with less than 30% of the equilibrium uptake (q = 1.51) (data cited here are from Ref. 138). 

Cell membranes or synthetic lipid vesicles with normal low permeability to water will, if reconstituted with AQP1, absorb water, swell and burst upon exposure to hypo-osmotic solutions. The water permeability of membranes containing AQP 1 can be about 100 times greater than that of membranes without aquaporins. The water permeability conferred by AQP1 (about 3 billion water molecules per subunit per second) is reversibly inhibited by Hg2+, exhibits low activation energy and is not accompanied by ionic currents or translocation of any other solutes, ions or protons. Thus, the movement of water through aquaporins is an example of facilitated diffusion, in this case driven by osmotic gradients. 

Of potentially greater significance is surface hydration which occurs concurrently with alkali diffusion at relatively low temperature. The average activation energy of water diffusion in obsidian can be estimated at 75kJ between 95° and 245°C (25). A nuclear resonance hydration profile of obsidian at 25°C has yielded a diffusion coefficient of 5xlO-20 cm2-s 1... 

The temperature dependence of the reaction was studied, and the activation energy of the reaction was calculated to be approximately 100 kj mol The exponent n was found to lie in the range 1-2, which is consistent with a 2D diffusion controlled reaction mechanism with deceleratory nucleation. The rate of reaction increases markedly with the amount of water added to the LDH with very small amounts of water added, the deintercalation process does not go to completion. This effect is a result of the LiCl being leached into solution. An equilibrium exists between the LDH and gibbsite/LiCl in solution. The greater [LiCl], the further to the LDH side this lies. 

Takamatsu et al. studied the diffusion of water into the acid as well as mono-, di-, and trivalent salt forms of 1155 and 1200 EW samples."pj e gravimetric uptakes of membranes immersed in distilled liquid water versus time were determined. Three approximate diffusion formulas were applied to the data, and all yielded essentially the same result. The log D versus 1/7 plots, over the range 20—81 °C, yielded activation energies of 4.9 and 13.0 kcal/mol for the acid and K+ forms, respectively. Diffusion coefficients of various mineral cations that permeated from aqueous electrolytes were considerably smaller than that of water. Also, log Z7was seen to be proportional to the quantity q a, where q is the charge of the cation and a is the center-to-center distance between the cation and fixed anion in a contact ion pair. 

In many cases, redox reactions that are favorable from a thermodynamic point of view may not actually take place sometimes, the activation energy barriers for such reactions are too high to allow fast transformation, according to the preferred thermodynamic considerations. For example, the complete oxidation of any organic molecule to carbon dioxide and water is thermodynamically favorable. However, such oxidation is not favorable kinetically, which implies that organic molecules— including all forms of living species—are not oxidized immediately this fact explains the ability to sustain life. The reason for this difference between kinetic and thermodynamic considerations, for redox reactions, is partly because redox reactions are relatively slow compared to other reactions and partly due to the fact that, in many cases, reactions are poorly coupled because of slow species diffusion... 

However, the activation energies are invariably small and generally fall in the range 6-30 kJ moH with the majority around 15 kJ moHh The latter observation led Hart and Anbar [67] to suggest that reaction (31) has an activation energy associated with reorientation of the solvent shell to facilitate transfer of the electron, and that this reorientation energy is the same as that required for e q to diffuse in water. The corollary to this argument is that the... 

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