Standard enthalpy change variation with temperature

There is considerable variation in the heat of reaction data employed in different articles in the literature that deals with this reaction. Cited values differ by more than an order of magnitude. If we utilize heat of combustion data for naphthalene and phthalic anhydride and correct for the fact that water will be a gas instead of a liquid at the conditions of interest, we find that for the first reaction (equation 13.2.3) the standard enthalpy change will be approximately — 429 kcal/g mole for the second reaction it will be approximately — 760 kcal/g mole. These values will be used as appropriate for the temperature range of interest. Any variation of these parameters with temperature may be neglected. 

Knowledge of these changes in standard Gibbs energy and enthalpy allows one to calculate the equilibrium composition and its variation with temperature. 

At first, we observe that no data are provided about the molar heat capacities of the components or about their variations with temperature. Consequently, we assume that the standard enthalpies and entropies do not vary with temperature between two state changes. 

Equation (3.16.6) can now be used to show how G/RT varies with temperature by numerical solution of the transcendental equation (3.13.14). This variation is not of particularly great interest. Rather more to the point is a study of the enthalpy changes with temperature. Proceeding by standard methodology, one obtains the enthalpy as H - — T2[d(G/T)/3T]. Here one must be careful to recognize that for RT/w < 1/2, x" - x"(T) is an implicit function of temperature. Accordingly, the differentiation process yields... 

The variation of AW , the change in standard state enthalpy by the process, with temperature can be calculated from the heat capacity of the species involved in the process. ... 

More interesting for practical applications is the approach of Pompe et al. [22] where two GC thermodynamic parameters (standard-state changes of enthalpy, AH°, and of entropy, AS°) are estimated. Since these parameters can be used to describe the variation of retention with temperature (see Section 3.2.2), estimations of retention can be extended to other temperature conditions, including programmed temperature. 

The enthalpy change AH° is known in standard conditions. The variation of the equilibrium constant with temperature can also be determined by differentiating Equation 2.11 ... 

To derive Kirchhoffs law, we consider the variation of the enthalpy with temperature. We begin by rewriting eqn 1.14b to calculate the change in the standard molar enthalpy of each reactant and product as the temperature of... 

Bakeeva, Pashinkin, Bakeev, and Buketov [73BAK/PAS] measured the selenium dioxide pressure over gold selenite in the interval 489 to 599 K by the dew point method. The pressure was calculated from the dew point temperature by the relationship for the saturated vapour pressure in [69SON/NOV]. The data in the deposited VlNITl document (No. 4959-72) have been recalculated with the relationship selected by the review. The enthalpy and entropy changes obtained from the temperature variation of the equilibrium constant are A //° ((V.123), 544 K) = (576.8 13.0) kJ-mol and A,S° ((V.123), 544 K) = (899.4 + 24.0) J-K -mor. The uncertainties are entered here as twice the standard deviations from the least-squares calculation. 

Much has been written about the relative merits of standard free energies, enthalpies and entropies as fundamental properties to elucidate chemical processes (see, for example, Taft, 1956 Leffler and Grunwald, 1963 Hepler, 1963 Larsen and Hepler, 1969 Wells, 1968 Exner, 1964a, b Hammett, 1970 Bell, 1973). In our opinion this question can only be answered in terms of the use to which the data will be put. Since AG°, AH° and AS° at room temperature all contain kinetic energy (partition function) terms, none of these properties corresponds exactly to the potential energy. Physical organic chemists are not put off much by this fact since they are usually more concerned with how properties change in response to systematic variation of molecular structure or solvent than they arc in particular properties of individual compounds. 

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