Condensation absolute rate

The observation of condensation products at 30°C may seem to contradict statements made earlier regarding our ability to separate the methylolation and condensation reactions by holding reaction temperatures below 70°C. Flowever, there is no conflict. The differences in the situations are primarily matters of absolute rate. The relative rates are still similar for methylolation and condensation. No... 

By comparing Eqs. (71) and (72) to the non-phase-change equations in Section II,A,2, it can be seen that the only additional parameters to be evaluated are rv and rcl, the absolute rates of vaporization and condensation at the gas-liquid interface. The methods for evaluating all parameters in these model equations are given in Section III,D,2. 

The absolute rates of vaporization and condensation are evaluated by using the rate expressions discussed in Section III,B. The net rate of phase change at the bubble interface or equivalently the rate of bubble growth, has been widely studied for single bubbles in stationary systems. Bankoff (B2) has reviewed the results of these studies. Ruckenstein (R2) has analyzed bubble growth in flowing systems. 

The absolute rates of vaporization and condensation are evaluated from the rate expressions given in Section III,B. In the past, the rate of mass transfer (which is the net rate of phase change) has not been calculated from an understanding of the physics of the phase-change process at the interface. The rate is generally evaluated by applying some simplifying assumptions to the process, rather than from an expression in terms of the dependent variables of the model equations. 

From the design viewpoint, Eq. (78) could be coupled with Eq. (71) to obtain an approximation of the system performance and if the liquid temperature profile can be estimated, the same procedure can be followed with Eq. (80). However, in general the design engineer needs to use analytical expressions for the absolute rates of vaporization and condensation, so that with a knowledge of the rate terms and the other parameters, Eqs. (71) and (72) could be solved for the temperature and mass flow-rate profiles. 

This section describes the phase change process for a single component on a molecular level, with both vaporization and condensation occurring simultaneously. Molecules escape from the liquid surface and enter the bulk vapor phase, whereas other molecules leave the bulk vapor phase by becoming attached to the liquid surface. Analytical expressions are developed for the absolute rates of condensation and vaporization in one-component systems. The net rate of phase change, which is defined as the difference between the absolute rates of vaporization and condensation, represents the rate of mass... 

An expression for the absolute rate of condensation can be developed readily if the simple kinetic theory of gases and the ideal gas law are applied (S2) ... 

Ec is a condensation coefficient. Schrage (S2) has shown that the absolute rate of vaporization is given by... 

The assumptions inherent in the derivation of the Hertz-Knudsen equation are (1) the vapor phase does not have a net motion (2) the bulk liquid temperature and corresponding vapor pressure determine the absolute rate of vaporization (3) the bulk vapor phase temperature and pressure determine the absolute rate of condensation (4) the gas-liquid interface is stationary and (5) the vapor phase acts as an ideal gas. The first assumption is rigorously valid only at equilibrium. For nonequilibrium conditions there will be a net motion of the vapor phase due to mass transfer across the vapor-liquid interface. The derivation of the expression for the absolute rate of condensation has been modified by Schrage (S2) to account for net motion in the vapor phase. The modified expression is... 

This review focuses on the kinetics of reactions of the silicon, germanium, and tin hydrides with radicals. In the past two decades, progress in determining the absolute kinetics of radical reactions in general has been rapid. The quantitation of kinetics of radical reactions involving the Group 14 metal hydrides in condensed phase has been particularly noteworthy, progressing from a few absolute rate constants available before 1980 to a considerable body of data we summarize here. 

Rates and Activation Parameters. The first condensed-phase absolute rate measurement for a carbene-alkene addition was reported by Closs and Rabinow in 1976 flash lamp photolysis of diphenyldiazomethane generated (triplet) diphenylcarbene, which added to butadiene (in benzene) with k =... 

If we assume a uniform homogeneous adsorbing surface, then, by writing down the equations for the rate of condensation and rate of evaporation of two gases which are simultaneously adsorbed, it may be shown that the relative amounts of each taken up by the adsorbent should be independent of the absolute pressure of the gases, and dependent only on the relative pressures of the two. Indications that this condition is not always fulfilled have been interpreted by assuming ... 

W. F. K. Wynne-Jones and H. Eyring, /. Chem. Phys., 3, 492 (1935). The Absolute Rate of Reactions in Condensed Phases. 

Fnel when the exposure time is greater than 10 5 sec, and the gas phase is saturated. From this discussion it can be concluded that the net rate of phase change, that is, the rate of mass transfer, can be calculated from either Eq. (65) or Eq. (66) with an equal degree of accuracy. However, the absolute rates of vaporization and condensation can only be calculated from the rate expressions based on the molecular interchange process. It is shown later in this chapter that the absolute rates must be determined to describe accurately the energy transfer that accompanies phase change. 

This type of operation has been applied to the distillation of materials that have very low vapor pressures at the maximum operating temperature. The available pressure drops in such cases would be too low to obtain practical production rates in conventional equipment, but by operating such that the rate of distillation is approximately equal to the absolute evaporation rate of the liquid reasonable capacities can be obtained. The most common method of obtaining the molecular distillation conditions is to carry out the operation at a high vacuum (0.01 mm. Hg or less) and to place the condensing surface so that it is parallel to the evaporating surface and in close proximity to it. The condenser is operated at a low temperature to limit the reevaporation. In order to obtain satisfactory absolute rates of evaporation, it has been found that as an approximate rule the temperature should not be lower than 100°C. below the temperature at which the vapor pressure of the substance being evaporated is 1 to 5 mm. Hg abs. 

If the boiling point changes very slowly or only slightly, in practice, the absolute rates of heat release by the reaction and by condensation are equal. 

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