Equilibrium constant endothermic reaction

For each reaction in a surface chemistry mechanism, one must provide a temperature dependent reaction probability or a rate constant for the reaction in both the forward and reverse directions. (The user may specify that a reaction is irreversible or has no temperature dependence, which are special cases of the general statement above.) To simulate the heat consumption or release at a surface due to heterogeneous reactions, the (temperature-dependent) endothermicity or exothermicity of each reaction must also be provided. In developing a surface reaction mechanism, one may choose to specify independently the forward and reverse rate constants for each reaction. An alternative would be to specify the change in free energy (as a function of temperature) for each reaction, and compute the reverse rate constant via the reaction equilibrium constant. 

The reaction is highly endothermic and conversion is limited in extent by equilibrium. The reaction equilibrium constant is defined as ... 

Because the reaction is endothermic, the equilibrium constant increases with increasing temperature, but still, even at 3000° and ordinary pressures, there is no appreciable dissociation. The great strength of the NsN bond is principally responsible for the chemical inertness of N2 and for the fact that most simple nitrogen compounds are endothermic even though they may contain strong bonds. Thus E(NssN) 6E(N—N) whereas E(C C) 2.5E(C—C). 

Radical substitution reactions by iodine are not practical because the abstraction of hydrogen from hydrocarbons by iodine is endothermic, even for stable radicals. The enthalpy of the overall reaction is also slightly endothermic. Thus, because of both the kinetic problem excluding a chain reaction and an unfavorable equilibrium constant for substitution, iodination cannot proceed by a radical-chain mechanism. 

This reaction is fast it reaches equilibrium quickly. The reaction is also reversible, highly endothermic, and the equilibrium constant is quite large (6 X 10 500°C). 

Reactions 1 and 3 are highly exothermic and therefore have equilibrium constants that decrease rapidly with temperature. Reaction 2 is moderately exothermic, and consequently its equilibrium constant shows a moderate decrease with temperature. Reaction 4 is moderately endothermic, and its equilibrium constant increases with increasing temperature. The relationship between temperature and equilibrium constant for these four reactions is depicted in Figure 1 where carbon is assumed to be graphite. Thermodynamic data were taken from Refs. 1 and 2. 

We can see from Table 9.2 that the equilibrium constant depends on the temperature. For an exothermic reaction, the formation of products is found experimentally to be favored by lowering the temperature. Conversely, for an endothermic reaction, the products are favored by an increase in temperature. 

Cyclohexane (C) and methylcyclopentane (M) are isomers with the chemical formula C6H12. The equilibrium constant for the rearrangement C M in solution is 0.140 at 25°C. (a) A solution of 0.0200 mol-L 1 cyclohexane and 0.100 mol-I. 1 methylcyclopentane is prepared. Is the system at equilibrium If not, will it will form more reactants or more products (b) What are the concentrations of cyclohexane and methylcyclohexane at equilibrium (c) If the temperature is raised to 50.°C, the concentration of cyclohexane becomes 0.100 mol-L 1 when equilibrium is reestablished. Calculate the new equilibrium constant, (d) Is the reaction exothermic or endothermic at 25°C Explain your conclusion. 

L-mol 1 -min 1 and the rate constant for the reverse reaction is 392 L-mol 1 -min. The activation energy for the forward reaction is 39.7 kj-mol 1 and that of the reverse reaction is 25.4 kj-mol" (a) What is the equilibrium constant for the reaction (b) Is the reaction exothermic or endothermic (c) What will be the effect of raising the temperature on the rate constants and the equilibrium constant ... 

Experimental studies on how temperature affects equilibria reveal a consistent pattern. The equilibrium constant of any exothermic reaction decreases with increasing temperature, whereas the equilibrium constant of any endothermic reaction increases with increasing temperature. We can use two equations for A G °, Equations and, to provide a thermod3mamic explanation for this behavior AG = -RT x Teq AG° — AH°-TAS°... 

The ionization of water is so important in the study of aqueous equilibria that the equilibrium constant is given the special symbol, Kw. It can be seen that, Kw, like all equilibrium constants, depends on temperature. Since Kw is larger (the forward reaction is encouraged) at higher temperatures, the forward reaction must consume heat, so the ionization of water must be endothermic. 

Figure 6.4a shows the behavior of an endothermic reaction as a plot of equilibrium conversion against temperature. The plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as illustrated in Examples 6.1 and 6.2. If it is assumed that the reactor is operated adiabatically, a heat balance can be carried out to show the change in temperature with reaction conversion. If the mean molar heat capacity of the reactants and products are assumed constant, then for a given starting temperature for the reaction Ttn, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.4a. As the conversion increases, the temperature decreases because of the reaction endotherm. If the reaction could proceed as far as equilibrium, then it would reach the equilibrium temperature TE. Figure 6.4b shows how equilibrium conversion can be increased by dividing the reaction into stages and reheating the reactants...

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. 

When one of the aromatic groups of the triarylmethyl free radical is replaced by an alkyl group, a decrease in stability due to a loss of resonance stabilization is to be expected. The paramagnetism and reactions associated with these less stable radicals will therefore appear only when the ethane is heated well above room temperature, the dissociation being endothermic. The rate of formation, but not the equilibrium constant, is experimentally accessible for these radicals since the radical once formed is subject to rearrangement, cleavage, and disproportionation reactions ... 

This behavior can be shown graphically by constructing the rD-7 -/A relation from equation 5.3-16, in which kp kr, and Keq depend on T. This is a surface in three-dimensional space, but Figure 5.2 shows the relation in two-dimensional contour form, both for an exothermic reaction and an endothermic reaction, with /A as a function of T and ( rA) (as a parameter). The full line in each case represents equilibrium conversion. Two constant-rate ( -rA) contours are shown in each case (note the direction of increase in (- rA) in each case). As expected, each rate contour exhibits a maximum for the exothermic case, but not for the endothermic case. 

There is an important difference in this behavior between an exothermic reaction and an endothermic reaction. Fran equation 3.1-5, the van t Hoff equator, the equilibrium constant (Keq) decreases with increasing T for an exothermic reaction, and increases for an endothermic reaction. The behavior of f eq(T) corresponds to this. 

Heat effects accompanying chemical reaction influence equilibrium constants and compositions as well as rates of reaction. The enthalpy change of reaction, AHr, is the difference between the enthalpies of formation of the participants. It is positive for endothermic reactions and negative for exothermic ones. This convention is the opposite of that for heats of reaction, so care should be exercised in applications of this quantity. Enthalpies of formation are empirical data, most often known at a standard temperature, frequently at 298 K. The Gibbs energies of formation, AGfl likewise are empirical data. 

In Figure 2.4, data for the equilibrium constants of esterification/hydrolysis and transesterification/glycolysis from different publications [21-24] are compared. In addition, the equilibrium constant data for the reaction TPA + 2EG BHET + 2W, as calculated by a Gibbs reactor model included in the commercial process simulator Chemcad, are also shown. The equilibrium constants for the respective reactions show the same tendency, although the correspondence is not as good as required for a reliable rigorous modelling of the esterification process. The thermodynamic data, as well as the dependency of the equilibrium constants on temperature, indicate that the esterification reactions of the model compounds are moderately endothermic. The transesterification process is a moderately exothermic reaction. 

The related formation equilibrium constant should have a small value if it is zero no XZ would form if, on the other hand, it is very large the stable XZ would not re-decompose and no X re-deposition could be obtained. Notice that if the synthesis of XZ is endothermic, the equilibrium will be displaced to the right with increasing temperature (the opposite is true if the reaction corresponds to an exothermic formation of XZ). Therefore, in order to have the transport of X, (synthesis of the intermediate at one end of the tube and re-decomposition with deposition of X at the other end) this must be placed at the hot end if the formation of XZ is endothermic (or the cold end, if exothermic). 

A change in temperature, however, does force a change in the equilibrium constant. Most chemical reactions exchange heat with the surroundings. A reaction that gives offbeat is classified as exothermic, whereas a reaction that requires the input of heat is said to be endothermic. (See Table 13-2.) A simple example of an endothermic reaction is the vaporization of water ... 

Please realize that the effect of temperature on the equilibrium constant depends on which of the two opposing reactions is exothermic and on which is endothermic. You must have information on the heat of a reaction before you can apply Le Chateliers principle to judge how temperature alters the equilibrium. 

Note that reaction 2.16 is endothermic (the plus sign for AH° means that heat is taken into the system), whereas reactions 2.14 and 2.15 are exothermic (the reactions give out heat to the surroundings). Many heats of formation or of reaction can be measured by calorimetry (i.e., by recording the temperature rise of a thermally insulated apparatus of known heat capacity when the reaction of interest is carried out in it) or can be obtained from other AH data, as shown for the water-gas reaction. If we know AH° and also know the standard entropy change (AS°) for a given reaction, we can calculate its equilibrium constant (K°) from a combination of Eqs. 2.9... 

The equilibrium constant of an endothermic reaction (AH° =+) increases if the temperature is raised. 

The equilibrium constant for the reaction between methanol on surface sites and internal sites, K, is the most complex in its temperature and acetylation dependence. In some coals temperature dependences shift about from exothermic to endothermic reactions, and no overall pattern for high rank and low rank coals seems to exist. 

We see that the reaction is endothermic, in keeping with the fact that the equilibrium constant increases with increasing temperature... 

The principle ofLe Chatelier summarizes the conclusions that may be drawn from the illustrative examples in this chapter "Whenever a stress is placed on a system at equilibrium, the equilibrium position shifts in such a way as to relieve that stress." If the stress is an increase in the partial pressure (concentration) of one component, the equilibrium shifts toward the opposite side in order to use up part of the increase. If the stress is an increase in the total pressure, the stress may be partially relieved by a shift toward the side with the smaller number of gaseous moles if there are the same number of gaseous moles on each side, no shift will occur, and no stress will be relieved. If the stress is an increase in temperature, the stress is partly relieved because, for an endothermic reaction, the equilibrium constant increases and the equilibrium shifts to the right for an exothermic reaction, the equilibrium constant decreases and the equilibrium shifts to the left. A catalyst places no stress on the system and causes no shift in the equilibrium position. 

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