Enthalpy of Reaction at Temperatures

The enthalpies of reaction at temperature, T, are related to their values at the standard temperature. 

Several groups have determined values for Af//° (NiFz, cr) from enthalpies of reaction at temperatures between 500 K and 1000 K. Jellinek and Rudat [28JEL/RUD] investigated the reaction ... 

Combining these expressions the standard enthalpy of reaction at temperature Tis... 

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. 

Fuel Cell Efficiency The theoretical energy conversion efficiency of a fuel cell e° is given by the ratio of the free energy (Gibbs function) of the cell reaction at the cell s operating temperature AG, to the enthalpy of reaction at the standard state AH°, both quantities being based on a mole of fuel ... 

In the preceding sections we discussed methods of obtaining enthalpies of reaction at a fixed temperature (generally 298.15 K). In particular, we pointed out that it is possible to tabulate enthalpies of formation and bond enthalpies and to use these to calculate enthalpies of reaction. Such tables of enthalpies of formation are available for only a few standard temperatures. Frequently, however, it is necessary to know the enthalpy of a reaction at a temperature different from those available in a reference table. Therefore, we consider now the procedures that can be used to calculate the enthalpy of reaction (at constant pressure) at one temperature, from data at another temperature. 

Change in enthalpy Heat transfer from cold utility Heat transfer in exchanger Heat transfer from hot utility Heat available in nth interval Heat of mixing at temperature t Heat of reaction at temperature t Standard heat of combustion Standard enthalpy of formation Standard heat of mixing Standard heat of reaction... 

The heat of reaction at temperature T is given in terms of the enthalpy of each species at temperature T, that is,... 

To directly assess the performance of different theoretical techniques, we have chosen to present the barriers (AHt) and reaction enthalpies (AH) at 0 K and to exclude the zero-point vibrational energy. In order to make a meaningful comparison with experiment, the experimental activation energy and enthalpy of reaction must be back-corrected accordingly. We have accomplished these corrections by using zero-point vibrational energies and temperature corrections calculated at the B3-LYP/6-31G(d) level. This leads to an experimental vibrationless AHt at 0 K of 31.2 kj moT [60] and, depending on which experimental value is used [59-61], vibrationless enthalpies of reaction at 0 K (AH) of -6.9 kJ moT, -8.0 kJ mol, -11.6 kJ mol or -19.4 kJ mol are obtained [62]. 

Potter (1 ) investigated mass spectrometrlcally the equilibrium CaCl(g) + ZrCl (g) CaClgCg) + ZrCl Cg) in the temperature range 1163-1157 K. Ion intensities were measured 2.5 eV above threshold and they were used in the calculation of equilibrium constants. Using the reported equilibrium constants, the enthalpies of reaction at 298... 

The enthalpy of formation of ZrSi04(s) from its constituent oxides has been determined at 977 K by Ellison and Navrotsky [92ELL/NAV] using high temperature solution calorimetry. They determined an enthalpy of reaction at this temperature of -(27.9 1.9) kJ-moP. A value for the enthalpy of reaction at 298.15 K was then determined from this value and the heat capacities of ZrSi04(s), Zr02(s) and Si02(s) which, in turn, was used to calculate the enthalpy of formation. The enthalpy of formation determined in the study and its associated uncertainty are selected by this review ... 

The scatter in the experimental data is quite pronounced and the temperature range quite short, so these values have appreciable uncertainty. However, the derived enthalpy of reaction at 700 K, (208.3 + 10.5) kJ-mol overlaps, within the combined uncertainties, with that calculated for Reaction (A.37), (194.7 + 10.4) kJ-mol assuming the heat capacity of ThOl2(cr) is the mean of those of Th02(cr) and Thl4(cr). The data have, therefore, been used to provide an estimate of the entropy of ThOl2(cr) -see Section VI11.4.1.5. 

The reaction requires high temperatures ( 800 °C) and the use of catalysts. Calculate the standard enthalpy of reaction at 25 °C and determine whether it is exothermic or endothermic. 

For the calculation of the standard enthalpy of reaction at a temperature different from 25 "C (298.15 K), Kirchhoffs law can be applied ... 

This means that the standard enthalpy of reaction at another temperature can be calculated when the heat capacities Cp. in the standard state (liquid, solid, and hypothetical ideal gas) of the compounds involved are known. The temperature dependence of the heat capacities can be described, for example, by a polynomial of the following form ... 

Using these values, the standard enthalpy of reaction at any temperature can be determined. Thus, according to Eq. (12.9), the following value is obtained for the... 

As shown in Example 12.1, the absolute value of the enthalpy of reaction increases with increasing temperature. Therefore, the more precise calculation will lead to a smaller equilibrium constant and thus a smaller conversion than the calculation with a constant standard enthalpy of reaction at 25 C. Thus, according to Eq. (12.23), the following equilibrium constant is obtained for a temperature of450 C,... 

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