Enthalpy of reaction calculation

Tab. 2.10. Volume of reaction, AV, van der Waals volumes of reaction AVw, enthalpies, entropies, and Gibbs enthalpy of reaction calculated for the hypothetical cyclizations of 1-alkenes to cycloalkanes by means of the corresponding thermodynamic parameters [76].

The average enthalpy of reaction for 0 to 45°C was recalculated, and found to be 5.3 kJ-mof. This value is accepted for 25°C, and an uncertainty of 2.0 kJ-mol is assigned, in part by considering separately the average enthalpies of reaction calculated from the association constants for the four highest temperatures (7.5 kJ-moF ) and for the four lowest temperatures (3.3 kJ mol ). 

The average enthalpy of reaction, calculated from the equally weighted values for the temperature range 15 to 40°C, is 6kJ mol, in excellent agreement with the value obtained from the data of Katayama [73KAT]. An uncertainty of + 2.5 kJ mof is estimated in the present review. 

Tables of average standard bond enthalpies make the assumption that the standard enthalpy of a bond is independent of the molecule in which it exists. This is only roushly true. Since standard bond enthalpies vary from one compound to another, the use of avaage standara bond enthalpies gives only approximate values for standard enthalpies of reaction calculated from them. Experimental methods are used to obtain standard enthalpies of reaction whenever possible. Calculations bwd on average standard bond enthalpies are used only for reaaiona which cannot ce studied experimentally —for example, the reactions of a substance which has not been isolated in a pure state.

The applicability of the resulting thermod)mamic functions is further exemplified by the calculations of equilibria in gas-phase reactions involving LaF (Hildenbrand and Lau, 1995) and LaCl (Chervonnyi and Chervonnaya, 2004b) molecules. Available experimental values of Kp for these reactions make it possible to trace changes in the enthalpies of reactions calculated by the third or second law (ArH°(0, III law) and ArH°(0, II law), respectively), as well as to compare the enthalpies of atomization derived from these values (AatH°(0, III law) and AatH° (0, II law), respectively) depending on the thermod)mamic functions used in the calculations. The results are summarized in Tables 65 and 66. 

This can be attained by comparison of the enthalpies of reactions calculated by the second and third laws, II law) and A,.H°... 

The solubility of lanthanum, neodymium and gadolinium hydroxide has been studied over an extensive temperature range, with data available for neodymium hydroxide available from 0 to 300 °C. All three solubility constants vary linearly with respect to the inverse of absolute temperature (Figure 8.8). The enthalpies of reaction calculated from the linear relationships are all within 10% indicating a similar functionality of the solubilities as a function of temperature as would be expected. The calculated enthalpy of reactions are -137.2 3.8, -139.8 1.7 and -129.5 4.4 kj mol for lanthanum, neodymium and gadolinium hydroxide, respectively. 

Similar to both Al2(OH)2 and AljfOH), the stability constants reported for A1j3(OH)32 from measurements conducted in l.Omolkg" KCl also vary linearly with respect to the inverse of absolute temperature (Figure 13.9). The enthalpy of reaction calculated from this relationship is... 

If one knows the enthalpy of fomiation at 298 K of all the constituents of a chemical reaction, one knows the enthalpy of reaction, The calculation rests on the... 

Many cliciiiical reactions evolve or absorb heat. When applying energy balances (consenatioit law for energy) in tccluiical calculations the heat (enthalpy) of reaction is often indicated in mole units so that tliey can be directly applied to demonstrate its chemical change. To simplify the presentation that follows, examine the equation ... 

Enthalpy of reaction and standard entlialpy of reaction are not always employed in engineering reaction/combustioii calculations. The two other terms tliat hai C been used are tlie gross (or liighcr) heating value and tlie net (or lower) heating value. These arc discussed later in this Section. 

EXAMPLE e.ll Using standard enthalpies of formation to calculate a standard enthalpy of reaction... 

A note on good practice Enthalpies of formation are expressed in kilojoules per mole and enthalpies of reaction in kilojoules for the reaction as written. Note how the stoichiometric coefficients are interpreted as numbers of moles, and that an unwritten coefficient of 1 for urea is included as 1 mol in the calculation. 

Draw the Lewis structure for the hypothetical molecule N6, consisting of a six-membered ring of nitrogen atoms. Using bond enthalpies, calculate the enthalpy of reaction for the decomposition of N6 to N2(g). Do you expect N6 to be a stable molecule ... 

Table 3 contains the enthalpies, zero point energies, entropies and free enthalpies of the activation and reaction steps (3)—(5). The enthalpies are the pure differences of the enthalpies of formation calculated by MINDO/3 at T = 298 K in the gas phase. The free enthalpies were calculated with the help of enthalpies corrected by the zero point energies and of the entropies given in Table 3. 

The addition of a 2-methyl-2-penten-4-yl radical to the QDI (based on p-phenylene diamines [PPDs] thus producing the corresponding PPD radical) is highly exothermic. The reaction not only stabilizes the relatively unstable alkenyl radical, but also results in the aromatization of the diimino-cylcohexadienyl ring. The enthalpy of reaction for this reaction is calculated (using MOPAC/AMl Hamiltonian ) to be about —40 kcal/mol. 

Applying the calculation formula given by the CHETAH programme for C4 by replacing AH by AH, which is the enthalpy of reaction defined previously as IR , and apply the same classification criteria as with CHETAH ... 

Standard heat data are usually compiled at 298 K, and to calculate the heat of reaction at an arbitrary temperature, the temperature dependency of enthalpies of reaction species have to be considered. These are generally dependent on temperature as follows... 

There are two important relationships in thermochemistry which are very useful in the calculation of enthalpies of reactions. These are known as Hess s law and Kirchoff s equation. 

The standard enthalpy of reaction for the dissolution of ammonium nitrate in water can be calculated using the enthalpies of formation for reactants and products ... 

Assuming that we start at 298 K, the final T will be around 270 K or —3°C or 25°F. Brrr Our calculation has also involved a number of other assumptions, including that we have assumed a temperature-independent enthalpy of reaction and a temperature-independent heat capacity for the water. We have also assumed that the water does not freeze (would release some heat). Nevertheless, the calculation gives a fairly reasonable estimate of the temperature drop that provides the cooling therapy of an instant ice pack. 

Practically, all the hydrocarbons have BDE of C—H bonds higher than 300 kJ mol-1, and this method of calculation can be used for them. The enthalpy of reaction was calculated as AH= D(R—H)—220 (kJ mol-1). The weakest bonds participate in this reaction. The pre-exponential factor depends on the reaction enthalpy value for the reactions with high enthalpy [18]. 

The parabolic model is, in essence, empirical because the parameter a is calculated from spectroscopic fa and v ) and atomic (/q and /q) data, while the parameter bre (or Ee0) is found from the experimental activation energies E(E= RT a(A/k)), where A is the pre-exponential factor typical of the chosen group of reactions, and k is the rate constant. The enthalpy of reaction is calculated by Equation (4.6). The calculations showed that = const, for structurally similar reactions. The values of a and bre for reactions of different types are given in Table 4.16. 

Table 25. An additional correction of APV = RTAn = 0.6 kcal mol-1 is made for die reaction itself. Connectivity is to the leftmost atom in Y. Calculated from the enthalpies of formation tabulated in References 13 and 224. cFrom Reference 234. From Reference 21. eNot calculated. f From enthalpy of formation calculated in Reference 229. Enthalpy of formation of C2H3 from References 226 and 227. Calculated value from Reference 228. 1 Calculated value from Reference 92. Calculated enthalpy of formation from Reference 219. Calculated value from Reference 233. ...

Enthalpies of reaction can be calculated from enthalpy of formation data. 

Enthalpies of reaction can also be calculated from combustion data. 

The enthalpy of reaction that is most needed is the not the enthalpy of any specific reaction, desired or undesired, but rather the global or macro enthalpy of reaction at various conditions, including different temperatures. This term is defined as the heat evolved by the reaction system in which reactants are converted into products and by-products by one or more reactions. The global enthalpy of reaction is difficult to calculate, but relatively easy to measure by experiment. Any such experiment must simulate the conditions which exist in the process under study (i.e., concentrations, temperatures, and pressures). The experimental values will, of course, include the heat evolved from the desired reaction(s) and from all of the undesired reactions that happen to occur under the selected conditions. 

Two sources to obtain this necessary information are the use of data bases and through experimental determinations. Enthalpies of reaction, for example, can be estimated by computer programs such as CHETAH [26, 27] as outlined in Chapter 2. The required cooling capacity for the desired reactor can depend on the reactant addition rate. The effect of the addition rate can be calculated by using models assuming different reaction orders and reaction rates. However, in practice, reactions do not generally follow the optimum route, which makes experimental verification of data and the determination of potential constraints necessary. 

Credible cases are identified when the probability of decomposition is low. Energy calculations of known or proposed chemical reactions and side reactions are carried out to determine a more likely level of energy release than the worst-case scenario. Therefore, it is necessary to define the most energetic reactions. Enthalpies of reaction are calculated, followed by calculations of the adiabatic temperature rise of the system and the corresponding pressure rise. 

---