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The Activation Energy

The rate-limiting step can usually be described as an energy barrier the system must cross. [Pg.23]

The rate constants, k+ and A - and the equilibrium constant, K, are thus related by [Pg.24]

Experimentally, E is found by plotting measured values of In k against /T and computing the slope of the best-fit straight line through the data points (slope = E/R ). After E has been obtained, A may be calculated from equation (58) and the measured values of /c. Often E can be determined within a few percent however, difficulties in measuring the absolute value of the reaction-rate constant often produce uncertainties in A that exceed a factor of 2. If the reaction were not an elementary step then E obtained in this way would be called an overall activation energy. [Pg.585]

For the sake of simplicity, the theoretical basis of equation (58) will be considered only for homogeneous reactions in ideal gas mixtures, although the principal concepts presented require only small modifications to be applied to other homogeneous reactions and to heterogeneous processes. [Pg.585]

At the molecular level, a homogeneous reaction in an ideal gas involves a collision between two or three appropriate reactant molecules. [Pg.585]

FIGURE B.5. Schematic illustration of potential-energy surface. [Pg.586]

The Boltzmann energy-distribution law states that the probability that a molecule possesses energy E is proportional to More-elaborate [Pg.587]

Quantum mechanics Quasi-classical mechanics Assumptions [Pg.213]

Based on the theoretical descriptions of Chapters 2, 4, and 6, the pre-exponential factor of a bimolecular reaction A + B — products is expected to be related to the collision frequency, i.e., the number of collisions per unit time and per unit volume. [Pg.213]

The pre-exponential factor of a bimolecular reaction is related to the reaction cross-section (see Problem 2.3). A relation that is fairly easy to interpret can be obtained within the framework of transition-state theory. Combining Eqs (6.9) and (6.54), we can write the expression for the rate constant in a form that gives the relation to the (hard-sphere) collision frequency  [Pg.213]

Here the partition functions refer to internal degrees of freedom (subscript int for internal), QAB = 8i 2(ii,d2)kBT/ h2, that is, a rotational partition function where A and B are considered as point masses separated by the distance d, and Z = itd2 v) is related to the (hard-sphere) collision frequency Zab defined in Eq. (4.16), that is, Zab = Z[A][B.  [Pg.213]

Within transition-state theory, Eq. (8.2) is an exact expression for the rate constant. We observe that the pre-exponential factor deviates from the simple interpretation, as being related to the collision frequency Zab via Z, due to the presence of internal degrees of freedom. Typically, the calculated value of Z is of the order of 1011 dm3 mol-1 s 1 10 16 m3 molecule-1 s 1 (see Example 4.1). The magnitude of the partition functions in Eq. (8.2) is typically small compared to this number. Thus, if we neglect the internal degrees of freedom of the reactants and the activated complex, except for rotational degrees of freedom of the activated complex (AB), and assume that the associated partition function can be approximated by QAB, we will get a pre-exponential factor given by Z. [Pg.213]


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.)... 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.)...
The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... [Pg.722]

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 ... [Pg.742]

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... [Pg.311]

The activation energy, is defined as tlie minimum additional energy above the zero-point energy that is needed for a system to pass from the initial to the final state in a chemical reaction. In tenns of equation (A2.4.132). the energy of the initial reactants at v = v is given by... [Pg.605]

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... [Pg.605]

There are two main applications for such real-time analysis. The first is the detemiination of the chemical reaction kinetics. Wlien the sample temperature is ramped linearly with time, the data of thickness of fomied phase together with ramped temperature allows calculation of the complete reaction kinetics (that is, both the activation energy and tlie pre-exponential factor) from a single sample [6], instead of having to perfomi many different temperature ramps as is the usual case in differential themial analysis [7, 8, 9, 10 and H]. The second application is in detemiining the... [Pg.1835]

After 60 minutes of aimealing, all the Pt has reacted to fonn Pt2Si. Almost immediately thereafter the reaction between Pt2Si and Si to fonn PtSi starts and after a fiirther 60 minutes all the Pt2Si has reacted, resulting in a stable PtSi film on Si. The data of silicide thickness versus ramped temperature can be plotted in reduced fonn in an Arrhenius-like plot to give the activation energy [6, 14] ... [Pg.1836]

With the aid of (B1.25.4), it is possible to detennine the activation energy of desorption (usually equal to the adsorption energy) and the preexponential factor of desorption [21, 24]. Attractive or repulsive interactions between the adsorbate molecules make the desorption parameters and v dependent on coverage [22]- hr the case of TPRS one obtains infonnation on surface reactions if the latter is rate detennming for the desorption. [Pg.1863]

Hawkins J M, Nambu M and Meyer A 1994 Resolution and configurational stability of the chiral fullerenes C-g, C g, and Cg. A limit for the activation energy of the Stone-Wales transformation J. Am. Chem. Soc. 116 7642-5... [Pg.2425]

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. [Pg.58]

The electronic partition function of the transition state is expressed in terms of the activation energy (the energy of the transition state relative to the electronic energy of the reactants) E as ... [Pg.514]

To a first approximation, the activation energy can be obtained by subtracting the energies of the reactants and transition structure. The hard-sphere theory gives an intuitive description of reaction mechanisms however, the predicted rate constants are quite poor for many reactions. [Pg.166]

Examining transition state theory, one notes that the assumptions of Maxwell-Boltzmann statistics are not completely correct because some of the molecules reaching the activation energy will react, lose excess vibrational energy, and not be able to go back to reactants. Also, some molecules that have reacted may go back to reactants again. [Pg.166]

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 ... [Pg.159]

The rates of reaction of phenacyl bromide with thiosemicarbazide and its phenylated derivative were determined by conductivity measurements in ethanol (517). The reaction is second order up to 85% completion. The activation energies are 10.5 to 11.3 kcal/mole with the phenyl thiosemicarbazide and 8.5 to 9.3 kcal/mole for the unsubstituted derivatives. [Pg.256]


See other pages where The Activation Energy is mentioned: [Pg.14]    [Pg.41]    [Pg.310]    [Pg.214]    [Pg.287]    [Pg.334]    [Pg.475]    [Pg.698]    [Pg.704]    [Pg.708]    [Pg.712]    [Pg.726]    [Pg.607]    [Pg.946]    [Pg.947]    [Pg.953]    [Pg.1019]    [Pg.1863]    [Pg.1868]    [Pg.2722]    [Pg.2724]    [Pg.2729]    [Pg.2888]    [Pg.2913]    [Pg.626]    [Pg.318]    [Pg.62]    [Pg.168]    [Pg.164]    [Pg.165]    [Pg.166]    [Pg.166]    [Pg.210]    [Pg.232]    [Pg.108]   


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Activation Energies and the Effect of Temperature

Activation Energy and Pre-Exponential Factors in the Reaction Rate Constant Expression

Activation Energy and the Temperature Dependence of Rates

Activation Energy of the Reverse Reaction

Activation energies of the relaxation process

Activation energy for the glass

Activation energy for the glass transition

Activation energy of the

Activation energy of the electrode reaction

Activation energy of the elementary step

Activation energy of the viscous flow

Activation energy values of the

Apparent activation energies and kinetic isotope effects using the reaction order approach

Calculation of the Activation Energy

Calculation of the Activation Energy by Iterative Procedure

Chemisorption measure the rate and activation energy of adsorption

Determination of the Activation Energy

Determining the Activation Energy

Effect of the Activation Energy

Empirical estimates of the activation energy

Energy transfer in the activation step

Excess Gibbs energy and the activity coefficient

Free volume and activation energy for movement in the glass

Lower the Activation Energy

Lowering the activation energy

Relaxation Activation Energy of Polymers in the Glass Transition Region

Speed up Reactions by Lowering the Free Energy of Activation

Temperature-dependent electron tunneling. Methods of determining the activation energy

The Activation Energy of Catalysed Reactions

The Electron Transfer Activation Energy and Solvent Reorganisation Term

The activation energy for conduction

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