The Variation of Reaction Enthalpy with Temperature

We need to know how to predict the reaction enthaipy of a biochemical reaction at 

Suppose we want to know the enthalpy of a particular reaction at body temperature, 37°C, but have data available for 25 C, or suppose we want to know whether the oxidation of glucose is more exothermic when it takes place inside an Arctic fish that inhabits water at 0 C than when it takes place at mammalian body temperatures. In precise work, every attempt would be made to measure the reaction enthalpy at the temperature of interest, but it is useful to have a rapid way of estimating the sign and even a moderately reliable numerical value. 

Values of standard molar constant-pressure heat capacities for a number of substances are given in the Resource section. Because eqn 1.24 applies only when the heat capacities are constant over the range of temperature of interest, its use is restricted to small temperature differences (of no more than 100 K or so). 

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 

It follows that for each reactant and product (assuming that no phase transition takes place in the temperature range of interest) 

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The Variation of Reaction Enthalpy with Temperature Temperature dependence of reaction enthalpy... 

The molar heat capacities are assumed to remain a constant over the temperature range T, -y Tj. The variation of heat capacities with temperature must also be taken into account when the enthalpies are measured over a wide range of temperatures. Alternatively, for the reaction A -> B, AH = H - H ... 

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. 

Table 2.5 shows the thermodynamic behavior of the water ionization reaction. The variation of log Kjy and AG (molal scale for ions, mole fraction scale for water) with temperature at a fixed pressure of 1 atm and the variation of these quantities with pressure at 25°C are given. These data can be used to obtain the enthalpy change of reaction, AH, and the volume change of reaction, AV. ... 

The enthalpies of reaction vary with temperature. The variation of AH with temperature is given by KirchhofTs equation. 

The modified Arrhenius method yields more accurate results for Ea than the linear plot because it does not include the assumption that this parameter is constant with the temperature. Nevertheless, the linear plot is widely adopted because for many reactions, the variation of Ea with T is small. Also, linear plots are more suitable than nonlinear plots to handle low-precision data. In either case, the procedure to derive the activation enthalpies and the reaction enthalpies is as described. 

The variation of the association equilibrium constant, with reciprocal temperature is shown in Figure 6. These data yield a value of = -29.8 kcal mol for the enthalpy change in reaction (4), and AA = -26 cal mol K for the corresponding entropy change. As discussed previously, a combination of the... 

The enthalpy change for this polymerization is AWp = —6.5 Real mor. The polymerization reaction in this problem is finished at a fixed steam pressure (1 atm). The equilibrium concentration of H2O in the polymer melt varies with temperature and steam pressure in this case. Tlte enthalpy of vaporization of H2O is about 8 Real mol . Compare the limiting values of number average molecular weight of the polyamide produced at 280 and 250°C final polymerization temperatures. Hint Recall that the variation of an equilibrium constant K with temperature is given by r/(ln K)/d /T) = —AH/R, where AH is the enthalpy change of the particular process and R is the universal gas constant. Calculate Ki and the equilibrium concentration of H2O in the melt at 250°C and use Eq.(10-8).]... 

Enthalpies of dissociation may be determined from measurements of the variation of the equilibrium pressure of the gaseous product with reaction temperature [60], In the study of the kinetics of these reactions (Chapters 8 and 12) consideration must be given to the possible influence of the reverse reaction on the rate measurements [68], Kinetic parameters should be measured at very low pressures of HjO or CO2 in the reaction vessel [45], At higher pressures, equilibria may be established within the pores of the solid product. This is given as the explanation for the frequent observation that the value of the enthalpy of dissociation of a particular carbonate is close to the value of the activation energy measured for evolution of COj [45]. 

Using typical waste material analyses, calculation has been made of the variation of HF partial pressure with H20/02 ratio for various N2/02 concentrations and selected combustion temperatures. The results are illustrated in Fig. 11.4a,b. The calculated enthalpy change associated with the combustion reaction in each case is also shown in Fig. 11.5 for a temperature of 1400 K. With the aid of such information, the most... 

Measurement of variation in rate constants with temperature allow determination of the activation parameters (activation enthalpy, A H, and activation entropy, A S ) applying in the reaction, which assist in elucidating the mechanism. 

Since A<5max showed no significant variation with temperature and pressure, enthalpy AH and entropy AS of reaction could be easily determined by variable-temperature single-point analyses and the volume of reaction AV by variable-pressure H-NMR studies. 

In this monograph, the kinetics of carbonate decompositions have been considered in several sections concerning the formation of oversaturated vapour and nucleation (Sect. 2.4), the structure of the solid product (Sect. 2.6), the influence of the reaction mode and stoichiometry on the molar enthalpy (Sect. 5.4), the experimental estimation of the self-cooling (Sect. 6.3), the T-S effect (Sect. 7.3), the variation of the enthalpy of decomposition with temperature (Sect. 8.2), the compensation effect (Chapter 12), and the determination of the absolute rates of decomposition of single crystals and powders in a vacuum and in air (Sects. 15.1 and 15.5). 

Determine the equilibrium composition that is achieved at 300 bar and 700 K when the initial mole ratio of hydrogen to carbon monoxide is 2. You may use standard enthalpy and Gibbs free energy of formation data. For purposes of this problem you should not neglect the variation of the standard heat of reaction with temperature. You may assume ideal solution behavior but not ideal gas behavior. You may also use a generalized fugacity coefficient chart based on the principle of corresponding states as well as the heat capacity data listed below. 

Making use of I law of thermodynamics, Kirchhoff in 1858 deduced mathematical expressions to define the variation of heat of reaction with temperature. The enthalpies of reaction i.e., AH generally vary with temperature. The exact influence of temperature can be worked out as follows ... 

Studies of how the intensities of bands vary as a function of concentration or pressure have been important in determining the identities of reaction products (e.g. Xc2 from XeF" and elemental xenon (Section 12.2.2)). Variations as a function of temperature have been used to estimate the enthalpy changes of various reactions, such as the dissociation of digallane (Ga2Hs) into two monogaUane molecules (GaHa) [17]. An alternative approach has been to trap vapors of equilibrium mixtures of molecules with different conformations or different structures held at different temperatures in cold matrices (Section 2.8.1). Data from IR spectra have then been used to determine equilibrium constants and associated thermodynamic properties for systems such as ds-FC(0)0F trani-FC(0)OF [18]. 

It was shown in Chapter 4 that the rate of reaction is a function of temperature and concentration. The application of the subsequent equations developed were simplest for isothermal conditions since is then generally solely a function of concentration. If nonisothermal conditions exist, another equation must be developed to describe any temperature variations with position and time in a reactor. For example, in adiabatic operation, the enthalpy (heat) effect accompanying the reaction can be completely absorbed by the system and result in temperature changes in the reactor. As noted earlier, in an exothermic reaction, the temperature increases, which in turn increases the rate of reaction, which in turn increases the conversion for a given interval of time. The conversion, therefore, would be higher than that obtained under isothermal conditions. When the reaction is endothermic, the decrease in temperature of the system results in a lower conversion than that associated with the isothermal case. If the endothermic enthalpy of reaction is large, the reaction may essentially stop due to the sharp decrease in temperature. 

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