Enthalpy of reaction calculation from

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 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... 

Equation 2.26 is also used to evaluate the uncertainty of a standard enthalpy of formation, calculated from a reaction enthalpy. Consider, for instance, a selected value for the standard enthalpy of combustion of ferrocene, A CH° [Fe(r 5-C5H5)2, cr] = —5891.5 4.2 kJ mol-1 [31],... 

Disproportionation reaction 7 might be expected to be thermoneutral in the gas phase and perhaps less so in the liquid phase where there is the possibility of hydrogen-bonding. Only for gas phase dimethyl peroxide is the prediction true, where the reaction enthalpy is —0.2 kJmoD. The liquid phase enthalpy of reaction is the incredible —61.5 kJmoD. Of course, we have expressed some doubt about the accuracy of the enthalpy of formation of methyl hydroperoxide. For teri-butyl cumyl peroxide, the prediction for thermoneutrality is in error by about 6 kJmor in the gas phase and by ca 9 kJmoD for the liquid. The enthalpy of reaction deviation from prediction increases slightly for tert-butyl peroxide — 14kJmol for the gas phase, which is virtually the same result as in the liquid phase, — 19kJmol . The reaction enthalpy is calculated to be far from neutrality for 2-fert-butylperoxy-2-methylhex-5-en-3-yne. The enthalpies of reaction are —86.1 kJmoD (g) and —91.5 kJmol (Iq). This same species showed discrepant behavior for reaction 6. Nevertheless, still assuming thermoneutrality for conversion of diethyl peroxide to ethyl hydroperoxide in reaction 7, the derived enthalpies of formation for ethyl hydroperoxide are —206 kJmoD (Iq) and —164 kJmoD (g). The liquid phase estimated value for ethyl hydroperoxide is much more reasonable than the experimentally determined value and is consistent with the other n-alkyl hydroperoxide values, either derived or accurately determined experimentally. 

The final temperature can be calculated from the initial temperature T0, from the specific enthalpy of reaction, and from the specific heat capacity or from the adiabatic temperature rise ... 

Both second and third law values of the enthalpy of reaction were determined using two different detection techniques, electrometer analogue and ion counting for Reaction (V.57) whereas only the former was used for Reaction (V.58). For Reaction (V.57), the third law reaction data were significantly more consistent than the second law values and, as such, were selected by [78KLE/CUB]. The values selected for the enthalpy of reaction were (136.4 4.6) and (332.6 4.6) kJ-moP for Reactions (V.57) and (V.58), respectively. The enthalpy of formation calculated from the two reactions, utilising the enthalpy of formation of Zrl4(g) and the selected auxiliary enthalpy of... 

A,G ((A.43), 298.15 K) = (28.14 0.89) kJ-mol and A,// ((A.43), 298.15 K) = (116.4 10.9) kJ-mol. If the heat of vaporisation is calculated from the enthalpy of solution measurements, and the accepted values for the enthalpies of formation of H20(1, g), A,//" ((A.43), 298.15 K) = (110.4 1.3) kJ-mol. The enthalpy of reaction value from the vapour pressure measurements agrees with the value from calorimetry within the combined uncertainties, though the uncertainty is much lower for the value from calorimetry. Unfortunately, the method used to measure the water vapour pressure does not allow unambiguous identification of the lower hydrate. 

Enthalpies of formation were derived from enthalpies of reaction measured for reactions of NF3 with various partners in bomb calorimeters and enthalpies of formation of the various reactants from the literature. The following table lists the studied reactions along with the enthalpies of reaction and enthalpies of formation calculated from each reaction. 

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. 

The enthalpies of atomization calculated from the enthalpies of reaction determined by the third law aie given in the fourth and sixth columns analogous data calculated from the enthalpies of reaction determined by the second law are listed in the fifth and seventh columns. 

The standard free energies, enthalpies, and entropies calculated from the experimental data for the reaction 4Me + Hj = 2Me2H (where Me = Pd or Ni), at 1 atm of hydrogen pressure and 298°K. 

Section 6.11, when we calculated the enthalpy change for an overall physical process as the sum of the enthalpy changes for a series of two individual steps. The same rule applied to chemical reactions is known as Hess s law the overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction can be divided. Hess s law applies even if the intermediate reactions or the overall reaction cannot actually be carried out. Provided that the equation for each step balances and the individual equations add up to the equation for the reaction of interest, a reaction enthalpy can be calculated from any convenient sequence of reactions (Fig. 6.30). 

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. 

We can calculate an enthalpy of reaction with bond enthalpies by assuming the reaction consists of two steps first, bonds break, and then different bonds form. This approach can be simplified further if we consider the reaction consists only of reactive fragments, and the products form from these fragments. The majority of the molecule can remain completely unchanged, e.g. we only need to consider the hydroxyl of the alcohol and the carboxyl of the acid during a simple esterification reaction. 

Enthalpies of reaction can also be calculated from individual enthalpies of formation (or heats of formation), AHf, for the reactants and products. Because the temperature, pressure, and state of the substance will cause these enthalpies to vary, it is common to use a standard state convention. For gases, the standard state is 1 atm pressure. For a substance in an aqueous solution, the standard state is 1 molar concentration. And for a pure substance (compound or element), the standard state is the most stable form at 1 atm pressure and 25°C. A degree symbol to the right of the H indicates a standard state, AH°. The standard enthalpy of formation of a substance (AHf) is the change in enthalpy when 1 mol of the substance is formed from its elements when all substances are in their standard states. These values are then tabulated and can be used in determining A//°rxn. 

In summary, the standard enthalpy of formation of a pure substance at 298.15 K is the enthalpy of the reaction where 1 mol of that substance in its standard state is formed from its elements in their standard reference states, all at 298.15 K. A standard reaction enthalpy can be calculated from the values of AfH° for reactants and products by using equation 2.7 (Hess s law) ... 

Could we have avoided the convention of A II° = 0 for the elements in their standard reference states Although this assumption brings no trouble, because we always deal with energy or enthalpy changes, it is interesting to point out that in principle we could use Einstein s relationship E = me2 to calculate the absolute energy content of each molecule in reaction 2.2 and derive ArH° from the obtained AE. However, this would mean that each molar mass would have to be known with tremendous accuracy—well beyond what is available today. In fact, the enthalpy of reaction 2.2, -492.5 kJ mol-1 (see following discussion) leads to Am = AE/c2 of approximately -5.5 x 10-9 g mol-1. Hence, for practical purposes, Lavoisier s mass conservation law is still valid. 

Note that Ar// ]0 and Ar// 98 are both standard enthalpies of reaction, albeit at different temperatures. Their difference is given in terms of the enthalpies AH( 1), AH(2), AH (3), and AH(4), which represent the heat required to raise the temperature of each reactant and product from 298.15 K to 310 K and can be calculated from the general equation 2.10. 

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