Activation energy for

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

It was noted in Section XVII-1 that chemisorption may become slow at low temperatures so that even though it is favored thermodynamically, the only process actually observed may be that of physical adsorption. Such slowness implies an activation energy for chemisorption, and the nature of this effect has been much discussed. 

Fig. XVIII-15. Oxygen atom diffusion on a W(IOO) surface (a) variation of the activation energy for diffusion with d and (b) variation of o- (From Ref. 136. Reprinted with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

Calculate also the activation energy for the reaction, again in kcal/mol, assuming that the Coulomb repulsion maximizes at 3 -y 10 cm separation of the nuclear centers. Assuming a successful cold-fusion device, how many fusions per second would generate one horsepower (1 hp) if the conversion of heat into work were 10% efficient ... 

Temperature progranuned desorption (TPD), also called thenual desorption spectroscopy (TDS), provides infonuation about the surface chemistry such as surface coverage and the activation energy for desorption [49]. TPD is discussed in detail in section B 1.25. In TPD, a clean surface is first exposed to a gaseous... 

In our simple model, the expression in A2.4.135 corresponds to the activation energy for a redox process in which only the interaction between the central ion and the ligands in the primary solvation shell is considered, and this only in the fonn of the totally synnnetrical vibration. In reality, the rate of the electron transfer reaction is also infiuenced by the motion of molecules in the outer solvation shell, as well as by other... 

Colgan E G 1995 Activation energy for Pt2Si and PtSi formation measured over a wide range of ramp rates J. Mater. Res. 10 1953... 

Nachtigaii P, Jordan K D, Smith A and Jdnsson H 1996 investigation of the reiiabiiity of density functionai methods reaction and activation energies for Si-Si bond cieavage and H2 eiimination from siianes J. Chem. Phys. 104 148... 

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

Similar difficulties arise in the nitrations of 2-chloro-4-nitroaniline and /)-nitroaniline. Consideration of the rate profiles and orientation of nitration ( 8.2.5) these compounds suggests that nitration involves the free bases. However, the concentrations of the latter are so small as to imply that if they are involved reaction between the amines and the nitronium ion must occur upon encounter that being so, the observed activation energies appear to be too high. The activation energy for the simple nitration of the free base in the case of/>-nitroaniline was calculated from the following equation ... 

The activation energy for cyclohexane ring inversion is 45 kJ/mol (10 8 kcal/mol) It IS a very rapid process with a half life of about 10 s at 25°C... 

Proton transfers from strong acids to water and alcohols rank among the most rapid chemical processes and occur almost as fast as the molecules collide with one another Thus the height of the energy barrier the activation energy for proton transfer must be quite low... 

The activation energy for this step is small and bond formation between a posi tive ion and a negative ion occurs rapidly... 

The SnI mechanism is generally accepted to be correct for the reaction of tertiary and secondary alcohols with hydrogen halides It is almost certainly not correct for methyl alcohol and primary alcohols because methyl and primary carbocations are believed to be much too unstable and the activation energies for their formation much too high for them to be reasonably involved The next section describes how methyl and primary alcohols are converted to their corresponding halides by a mechanism related to but different from S l... 

The activation energy for ro tation about a typical carbon-carbon double bond IS very high—on the order of 250 kj/mol (about 60 kcal/ mol) This quantity may be taken as a measure of the ir bond contribution to the to tal C=C bond strength of 605 kJ/mol (144 5 kcal/mol) in ethylene and compares closely with the value esti mated by manipulation of thermochemical data on page 191... 

Figure 10 12 shows the interaction between the HOMO of one ethylene molecule and the LUMO of another In particular notice that two of the carbons that are to become ct bonded to each other m the product experience an antibondmg interaction during the cycloaddition process This raises the activation energy for cycloaddition and leads the reaction to be classified as a symmetry forbidden reaction Reaction were it to occur would take place slowly and by a mechanism m which the two new ct bonds are formed m separate steps rather than by way of a concerted process involving a sm gle transition state... 

Figure 12 11 compares the energy profile for nitration of benzene with those for attack at the ortho meta and para positions of (trifluoromethyl)benzene The presence of the electron withdrawing trifluoromethyl group raises the activation energy for attack at all the ring positions but the increase is least for attack at the meta position... 

One reason for the low reactivity of pyridine is that its nitrogen atom because it IS more electronegative than a CH in benzene causes the rr electrons to be held more tightly and raises the activation energy for attack by an electrophile Another is that the nitrogen of pyridine is protonated in sulfuric acid and the resulting pyndinium ion is even more deactivated than pyndine itself... 

Shape of potential energy diagram is identical with that for ethane (Figure 3 4) Activation energy for rotation about the C—C bond is higher than that of ethane lower than that of butane... 

These are the only differences between the MNDO and AMI functional form. Dewar s group regenerated AMI parameters for the elements H, B, C, N, 0, F, Al, Si, P, S, Cl, Zn, Ge, Br, and Sn and found that the main gains in AMI over MNDO were the ability to reproduce hydrogen bonds and the promise of better activation energies for reactions. AMI does not significantly change the computation time compared with MNDO. 

Table 6.2 Rate Constants (at Temperature Given) and Activation Energies for Some Initiator Decomposition Reactions...

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