Enthalpy change from temperature dependence

The temperature dependence of reaction enthalpies can be determined from the heat capacity of the reactants and products. When a substance is heated from T to T2 at a particular pressurep, assuming no phase transition is taking place, its molar enthalpy change from AHm (T]) to AHm (T2) is... 

Enthalpy changes per mol of proton are given as calculated from temperature dependence or as measured microcalorimetrically. 

Anion Binding. This discussion illustrates how valuable information on enthalpy changes of surface reactions (either from temperature dependence or from direct calorimetric measurements) are. Zeltner et al. (1986) have studied calorimetrically the surface complex formation of phosphate and salicylate on goethite. They show that these reactions are exothermic (at pH = 4) with AHadS values at low coverage ( 10 %) of ca. -24 kJ mol 1, they argue tentatively that these values indicate biden-tate surface complex formation. They also show that -AH decreases with increasing surface coverage. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

FIGURE 8.5 Because enthalpy is a state function, the enthalpy change from solid to vapor does not depend on the path taken between the two states. Therefore, at a constant temperature,... 

The enthalpies, KH, of the homolytic cleavage of the central Si-Si bond in disilane dimers a can be calculated from temperature-dependent ESR experiments, using Eq. 3, in which C is the concentration of the radical, T is the absolute temperature and A is a. constant. The change in the concentration of the radicals as a function of temperature could be followed by EPR as shown in Fig. 6a for radical 3b. The concentrations of the thermally generated radicals (2b and 3b) were determined by calibration of the height of the EPR signal of the silyl radicals in comparison with a 3 X 10 M toluene solution of TEMPO (2,2,6,6-tetramethyl-piperidinooxy). 

The 1960s brought two major advances in the discipline of ion energetics and stmcture. The development of high-pressure mass spectrometer ion sources led by Kebarle and co-workers allowed the measurement of equilibrium constants for gas-phase ionic systems at well-specified temperatures and, from temperature-dependent studies, the enthalpy and entropy changes associated with gas phase equilibria. These concepts provided the foundation for current studies of molecular recognition in the gas phase. 

This free energy change, dG thus corresponds to the hypothetical transition from hypercoil to expanded coil at zero charge. Values for dG are reported in Table III along with values of dH° and dS° obtained from temperature dependence studies. The behavior of the entropy and enthalpy terms is typical of processes controlled by... 

The end result of computing enthalpies and entropies from Eqs. (2-28) and (2-29) seem to yield data dependent on the T selected. However, it is important to notice that most computations involving enthalpy and entropy actually involve changes in these quantities. For example, suppose we want to determine the enthalpy change from a temperature Ti to another higher temperature, Ja- Then,... 

Figure 1.4. Temperature dependence of the change in Gihhs energy, enthalpy and entropy upon transfer of ethane and butane from the gas phase to water. The data refer to transfer from the vapour phase at 0.101 MPa to a hypothetical solution of unit mole fraction and are taken from ref. 125.

Enthalpy changes for biochemical processes can be determined experimentally by measuring the heat absorbed (or given off) by the process in a calorimeter (Figure 3.2). Alternatively, for any process B at equilibrium, the standard-state enthalpy change for the process can be determined from the temperature dependence of the equilibrium constant ... 

The Arrhenius activation energy,3 obtained from the temperature dependence of the three-halves-order rate constant, is Ea = 201 kJ mol-1. This is considerably less than the standard enthalpy change for the homolysis of acetaldehyde, determined by the usual thermodynamic methods. That is, reaction (8-5) has AH = 345 kJ mol-1. At first glance, this disparity makes it seem as if dissociation of acetaldehyde could not be a predecessor step. Actually, however, the agreement is excellent when properly interpreted. 

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

The binding enthalpy change (AH) could be determined either from the plots of the temperature dependence of the binding constant according to the van t Hoff relationship ... 

All partitioning properties change with temperature. The partition coefficients, vapor pressure, KAW and KqA, are more sensitive to temperature variation because of the large enthalpy change associated with transfer to the vapor phase. The simplest general expression theoretically based temperature dependence correlation is derived from the integrated Clausius-Clapeyron equation, or van t Hoff form expressing the effect of temperature on an equilibrium constant Kp,... 

The equilibrium concentration of the ions A- and B- participating in the equlibrium can be directly observed by mass spectrometry. Thus, the free-energy change can be derived from the equilibrium constant, since the concentrations of the neutral species are known in advance. Similarly, by measuring the temperature dependence of the equilibrium constants, the associated enthalpy and entropy can be obtained from van t Hoff plots. By measuring a series of interconnecting equlibria, an appropriate scale can be established. The primary standard in such work has frequently been SO2 whose electron affinity is well established by electron photodetachment36. 

From the definition of the heat of reaction, Qp will depend on the temperature T at which the reaction and product enthalpies are evaluated. The heat of reaction at one temperature T0 can be related to that at another temperature 7. Consider the reaction configuration shown in Fig. 1.1. According to the First Faw of Thermodynamics, the heat changes that proceed from reactants at temperature T() to products at temperature 7), by either path A or path B must be the same. Path A raises the reactants from temperature T0 to 7, and reacts at 7). Path B reacts at T0 and raises the products from T0 to 7). This energy equality, which relates the heats of reaction at the two different temperatures, is written as... 

From left to right, the reaction is exothermic. Therefore, the enthalpy change, AH, is negative. If the enthalpy change was the only condition that determined whether a reaction is favourable, then the synthesis reaction would take place. The synthesis reaction does take place—but only at relatively moderate temperatures. Above 400 C, the reverse reaction is favourable. The decomposition of HgO(s) occurs. Thus, the direction in which this reaction proceeds depends on temperature. 

Because of this relationship between (TT — and p-j x.. the former quantity frequently is referred to as the Joule-Thomson enthalpy. The pressure coefficient of this Joule-Thomson enthalpy change can be calculated from the known values of the Joule-Thomson coefficient and the heat capacity of the gas. Similarly, as (H — is a derived function of the fugacity, knowledge of the temperature dependence of the latter can be used to calculate the Joule-Thomson coefficient. As the fugacity and the Joule-Thomson coefficient are both measures of the deviation of a gas from ideahty, it is not surprising that they are related. 

Since the ROM of (3.44b) is just a mathematical expression, of course, a question arises as to what the underlying physical mechanism is that could be responsible for the ROM dependence of decomposition temperature of the NaBH constituent on the content of MgH A similar question was raised for the case of the (MgH + LiAIH ) composite. The first physical model of interest is the one proposed by Vajo et al. [196-198]. According to this model the enthalpy change of LiBH during decomposition is reduced by the formation of an intermediate compound MgB from the free Mg obtained due to the decomposition of the MgH constituent. This model is presented graphically for the thermodynamic destabilization of LiBH by MgH in Fig. 3.25b. By analogy, the reaction of (3.43) can be adapted to the NaBH and MgH system in the following form... 

This equation can be derived from potential theory. The entropy and enthalpy changes as functions of the loading state are the prime differentiators for various sorbent/sorbate pairs. These loading dependencies are indicated by the form of the functions AS(x) and AH(x). Here the dependencies are written strictly as functions of the loading (x) only. There may some modest temperature dependency as well. The heat and entropy changes with temperature tend to be small hence the universal form tends to be linear in reciprocal temperature over a wide range of temperatures. 

The overall enthalpy and entropy changes for the distribution reaction (i.e., transfer of the metal complex from the aqueous to the organic phase) can be obtained from the temperature dependence of A r according to... 

---