Zero order reaction point energy

Stahl and Parliment126, too, examined higher temperature reactions. They studied the glucose-proline system (0.2 M in each) in a continuous-flow reactor either at different times (0.25-5.0 min) at 200 °C or for 1.0 min at different temperatures (160-220 °C). The main volatile components identified at 200 °C after 0.25 min were only three 2-acetyltetrahydropyridine, 5-acetyl-2,3-dihydro-l//-pyrrolizine, and maltoxazine (see Scheme 5.3, p. 66). After 2 min the pyrrolizine dominated. The kinetics for each of the three compounds was pseudo-zero order. The activation energy of the pyrrolizine was 188 kJ (45 kcal) mol-1, much higher, as expected, than those of the other two compounds [25-63 kJ (6-15 kcal) mol-1]. The low value for maltoxazine fits with its presence in malted barley and its formation in aqueous glu-cose-Pro and maltose-Pro systems at boiling point.127... 

Zero-order rate equation, 34 Zero-order reaction, 17 Zero-point vibrational energy, 294, 299... 

Studies on the thermal degradation of PE samples with different molecular masses in the isothermal regime at different temperatures have shown that the kinetic curves have linear plots up to 70% weight loss (Figure 1.2), which point to a zero-order reaction. The activation energy of thermal degradation increases with the molecular mass of the polymer from 192.3 kj/mol (molecular mass 11,000) up to 276.3 kj/mol (molecular mass 23,000) [2]. 

First, we perform an optimization of the transition structure for the reaction, yielding the planar structure at the left. A frequency calculation on the optimized structure confirms that it is a first-order saddle point and hence a transition structure, having a zero-point corrected energy of -113.67941 hartrees. The frequency calculation also prepares for the IRC computation to follow. 

Table 3 shows that the small activation enthalpies of the reactions (3) and (4) are clearly affected by the zero point energy corrections. But the relative order of the activation enthalpies remains the same with or without the corrections. The activation entropies have great negative values, which is of mechanistic interest (see part 4.3.1). However, because of their similarity, when comparing the three reactions to one another they have only small importance, e.g. for estimation of copolymerization parameters (see part 4.3.2). 

Fig. 16 (a) R (D + RX) and P (D,+ + R + X ) zero-order potential energy surfaces. Rc and Pc are the caged systems, (b) Projection of the steepest descent paths on the X-Y plane J, transition state of the photoinduced reaction j, transition state of the ground state reaction W, point where the photoinduced reaction path crosses the intersection between the R and P zero-order surfaces R ., caged reactant system, (c) Oscillatory descent from W to J on the upper first-order potential energy surface obtained from the R and P zero-order surfaces. 

The minimum on the intersection parabola is the saddle point corresponding to the transition state of the dark reaction, denoted J in Figs 16b and 16c. The first-order potential energy surfaces involve an upper surface associating the portions of the R and P zero-order potential energy surfaces situated above the intersection parabola and a lower surface associating the portions of the R and P zero-order potential energy surfaces situated below the intersection parabola. 

MICHAELIS-MENTEN EQUATION FIRST-ORDER REACTION ZERO POINT ENERGY HOOKE S LAW SPRING KINETIC ISOTOPE EFFECTS Zeroth law of thermodynamics, THERMODYNAMICS, LAWS OF ZETA... 

Si and Su are the slopes of the zero-order potential energy surfaces at the intersection (Si = —Sn for an exchange reaction), and v is the velocity with which the point representing the system moves through the intersection region. For typical conditions it is found that p 1 for interactions EIfII of more than 0.5 kcal mol"1 (50). Under these conditions the reactions will be adiabatic, and the square root relation is expected to hold provided EitU is not too large. However, for small EltJ1 ... 

The problem of specifying a collision between two such molecules is complicated by the range of the attractive forces. If we think about it in detail, we will find, as in the case of gases, that for each physical process of interest (i.e., pressure, viscosity, diffusion, etc.), there will be a different definition of a collision. From the point of view of a chemical reaction, no generalization is possible, but we may say for purposes of convenience, as a zero-order approximation, that a pair of molecules will be considered in a state of collision so long as their potential energy of interaction is of the order of magnitude of fcT. 

Figure 3 Plots of free energy of zero-order precursor and successor states versus reaction coordinate, for electron-transfer reactions / (A+- B) — r(A- B+). (a) AG° > 0 (b) AG° = 0 (c) 0 > AG° > —X (d) AG° < —X. The upward-pointing arrows in (a), (b), and (c) indicate intervalence charge-transfer transitions the downward-pointing arrow in (d) indicates a possible fluorescent transition from the precursor state / (A+- -B)...

Fig. 11. Reaction coordinate diagram for ECL system involving rubrene (A) and 9,10-diphenylan-thracene (B). Potential energy curves are presented in the zero-order approximation, without removing the degeneracy at the crossing points of the potential energy curves. Broken lines represent the vibronically excited triplet state.

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