Exothermic versus Endothermic Reactions

Another way of visualizing the optimal trajectory for the exothermic reversible reaction is to consider isothermal reaction rates at increasing temperatures. At T the equilibrium conversion is high but the rate is low, at T2 the rate is higher but the equihbrium conversion is lower, at the rate has increased further and the equihbrium conversion is even lower, and at a high temperature T4 the initial rate is very high but the equihbririm conversion is very low. 

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These gas-phase fuel processing reactions have significantly different operating temperatures and thermal requirements (exothermic versus endothermic), so that thermal matching of the various gas streams through heat exchangers is an engineering requirement. 

Energy relationships for reactions can be represented by energy diagrams, in which energy is plotted versus the reaction progress. The concepts of exothermic and endothermic reactions and activation energy are clearly represented by such diagrams. 

For cases where AH0 is essentially independent of temperature, plots of in Ka versus 1/T are linear with slope —(AH°/R). For cases where the heat capacity term in equation 2.2.7 is appreciable, this equation must be substituted in either equation 2.5.2 or equation 2.5.3 in order to determine the temperature dependence of the equilibrium constant. For exothermic reactions (AH0 negative) the equilibrium constant decreases with increasing temperature, while for endothermic reactions the equilibrium constant increases with increasing temperature. 

Figure Z-3 Plot of energy of reactants and products in a chemical reaction versus the reaction coordinate. The activation energy for the forward reaction is f, for the back reaction E, and the heat of the reaction is A Hr = Ef — Et,. The curve at the left is for an endothermic reaction (Ef > E, ), while the curve at the right is for an exothermic reaction ( j < E ).

Reaction Coordinate — Fig. The profile of energy versus reaction coordinate in ACT (a) Exothermic reaction (b) Endothermic reaction. 

Figure 4.4 Relative heat production and heat withdrawal rates versus dimensionless pellet temperature 0p A) exothermic reactions, 0p, 0t and An > 0 B) endothermic reactions, 0p, 0t and An < 0 ( ) stable operating point (o) unstable operating point.

Eigure 10.16 displays the logarithm of the rate constant versus AGrxn behavior using Eqs. (10.36) and (10.37) for an example PT reaction (T = 300 K coq = 300 cm 1, Vf = 25 kcal moTi, 8 kcal moTi, mg= 20 amu, AcOf = 3200 cm , ficOffi = 2700 cm h and = 28 A i). Contributions from individual transitions (wp - Up) are also indicated. In particular. Fig. 10.16 describes the dominance of the 0-0 transitions near AG n the increased contributions from the 0-1 transition for exothermic reactions and from the 1-0 transition for endothermic reactions, as discussed above. Indeed, the rate constants for excited proton vibrational transitions will dominate for more asymmetric reactions. These aspects have an important influence on activation free energy behavior the full rate constant continuously increases going from endo- to exothermic reactions due to the increased contributions of O-Wp transitions as the reaction becomes more exothermic, while, the drop in rate constant with increased reaction endothermicity is decreased with contributions from Wp-O transitions. 

Sketch a potential energy versus reaction progress plot for an endothermic reaction and for an exothermic reaction. Show AA and in both plots. When concentrations and temperatures are equal, would you expect the rate of the forward reaction to be equal to, greater than, or less than the rate of the reverse reaction if the reaction is exothermic Endothermic ... 

PROBLEM 8.21 Draw Energy versus Reaction progress diagrams for El and E2 reactions that are overall (a) exothermic, (b) endothermic. Use a tertiary iodide as a sample substrate molecule. 

Differential thermoanalysis involves recording the temperature difference between an inert compound and the sample during heating. Such differences occur if reactions take place which either release (exothermic effect) or consume (endothermic effect) energy. These effects are recorded as peaks on a plot of the temperature difference versus the temperature. Such thermal effects are associated with the loss of adsorbed H2O and structural OH as in TGA and also with phase transformations. 

It is interesting to note that the exothermic reversible reaction A B is identical to the same endothermic reversible reaction B A. This can be seen by plotting X versus T and noting that the r = 0 equihbrium hue separates these two reactions. In the reaction A B the rate in the upper portion where r < 0 is exactly the reaction B A. We defined all rates as positive quantities, but if we write the reaction as its reverse, both r and AZ/y reverse signs. This is plotted in Figure 5-19. 

Figure 5-19 Plot of X versus 7" for an exothermic reversible reaction A B. The upper portion of this curve where r <0 can be regarded as the endothermic reversible reactions tfi A if the sign of r is reversed or if X is replaced by 1 - X...

Equation 16-7 not only shows the simple way that K, depends on temperature, it also shows a simple way to determine the enthalpy change for a reaction. By determining the value of e at several different temperatures, and then plotting log Ke versus 1 IT, we should get a straight line whose slope is -AE/2.3.R. If the reaction is exothermic LH is negative), the slope will be positive if the reaction is endothermic (A/f is positive), the slope will be negative (Figure 16-1). Equation 16-7 applies to all chemical equilibria and is independent of the concentration units used either Kp or < can be use(j equally... 

Equation 13 l-22b suggests that the logarithm of the equilibrium constant should be a linear function of the reciprocal of the absolute temperature if the heat of reaction is independent of temperature and, presumably, an almost linear function of l/T even if Arxnff° is a function of temperature. (Compare this behavior with that of the vapor pressure of a pure substance in Sec. 7.7, especially Eq. 7.7-6.) Consequently, it is common practice to plot the logarithm of the equilibrium constant versus the reciprocal of temperature. Figure 13.-1-2 gives the equilibrium constants for a number of reactions as a function of temperature plotted in this way. (Can you identify those reactions that are endothermic and those that are exothermic )... 

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