Heat Capacity and Heat of Reaction

Chapter 7 has two goals. The first is to show how reaction rate expressions, SI a, b,..., T), are obtained from experimental data. The second is to review the thermodynamic underpinnings for calculating reaction equilibria, heats of reactions and heat capacities needed for the rigorous design of chemical reactors. 

We try to make calculations come out in round numbers so in many problems the feed concentrations are 2 moles/bter, conversions are 90%, reactor volumes 100 liters, and feed temperatures 300 or 400 K. We further assume that all heats of reaction and heat capacities are independent of temperature, pressure, and composition. We sometimes even assume the ideal gas constant R=2 cal/mole K, just because it makes it easier to remember than 1.98... . ... 

Effects of Reaction Parameters An unusual feature of Equation (15) is that it does not appear to involve the heat of reaction and heat capacity. This is because they were algebraically eliminated by combining the Frank-Kamenetskii relation,... 

Problem Taking the equilibrium constant (K/) for the JN2 + fH2 P NH8 equilibrium to be 0.00655 at 450 C (Table XXII), and utilizing the heat of reaction and heat capacity data in 12k, derive a general expression for the variation of the equilibrium constant with temperature. Determine the value of K/ at 327 C. 

Using the heats of reaction and heat capacities given in Example 5-2, determine the, conversion of chlorine to allyl chloride expected for a range of sizes of reactors (i.e., reactor volumes). 

Calorimetric techniques, and liquid phase calorimetry in particular, are promising methods to study catalytic reactions [39]. Notably, the use of a differential reaction calorimeter (DRC) makes it possible to determine the most important thermodynamic data such as the heat of reaction and heat capacity of the system [40-42]. 

C02 capture performance of different MOFs will be comprehensively reviewed in terms of their capacity, selectivity, heat of reaction, and major challenges facing researchers, and some ideas to approach these challenges will also be provided. The next section is dedicated to review the most recent studies of C02 capture and separation on MOFs, and we will mainly target the works published in the last four years. 

Assuming that we start at 298 K, the final T will be around 270 K or —3°C or 25°F. Brrr Our calculation has also involved a number of other assumptions, including that we have assumed a temperature-independent enthalpy of reaction and a temperature-independent heat capacity for the water. We have also assumed that the water does not freeze (would release some heat). Nevertheless, the calculation gives a fairly reasonable estimate of the temperature drop that provides the cooling therapy of an instant ice pack. 

ENTHALPY, ENTHALPY OF REACTION, AND HEAT CAPACITY TABLE 4.7. Enthalpy Change on Binding PALA to ATCase... 

We can calculate AH from thermal data alone, that is, from calorimetric measurements of enthalpies of reaction and heat capacities. It would be advantageous if we could also compute AS from thermal data alone, for then we could calculate AG or Ay without using equilibrium data. The requirement of measurements for an equilibrium state or the need for a reversible reaction thus could be avoided. The thermal-data method would be of particular advantage for reactions for which AG or AT is very large (either positive or negative) because equilibrium measurements are most difficult in these cases. 

The enthalpy of reaction and specific heat capacity of the reactants may be assumed to be constant during the process. 

Principles of the adiabatic reactor method have been discussed elsewhere [67,68], Under adiabatic conditions, assuming constant heat capacity, constant heat of reaction, and homogeneous reaction, temperature rise data yields fractional conversion, X [68] ... 

The critical points are the thermal conductivity and heat capacity of the formaldehyde crystal at the low temperature. If these parameters are low enough relative to the rate of reaction and heat release, the reaction may not be occurring at low temperatures. 

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 ... 

For a numerical base case, the kinetic and process parameters given in Table 2.1 are selected. Reactors with several design values of conversion and over a range of temperatures are sized. The purpose is to see the effect of these parameters on the size of the reactor and its heat transfer area. The effects of changes in the base case parameters, such as feed flowrate, heat of reaction, and overall heat transfer coefficient, will also be explored. Densities and heat capacities are assumed to be constant. 

The FDS5 pyrolysis model is used here to qualitatively illustrate the complexity associated with material property estimation. Each condensed-phase species (i.e., virgin wood, char, ash, etc.) must be characterized in terms of its bulk density, thermal properties (thermal conductivity and specific heat capacity, both of which are usually temperature-dependent), emissivity, and in-depth radiation absorption coefficient. Similarly, each condensed-phase reaction must be quantified through specification of its kinetic triplet (preexponential factor, activation energy, reaction order), heat of reaction, and the reactant/product species. For a simple charring material with temperature-invariant thermal properties that degrades by a single-step first order reaction, this amounts to -11 parameters that must be specified (two kinetic parameters, one heat of reaction, two thermal conductivities, two specific heat capacities, two emissivities, and two in-depth radiation absorption coefficients). 

There are relatively few chemical reactions capable of heating matter to temperatures greater than 3000°K. Table II contains a list of some of these reactions and the theoretical flame temperatures attainable. These reactions have two characteristics in common (1) high exothermic heats of reaction and (2) stable molecular products with low heat capacities, since dissociation consumes energy and results in additional products which must be heated to the flame temperature. 

In the summation the specific heats of the substances which are produced with evolution of heat are reckoned positive. The temperature coefficient of the heat of reaction is therefore equal to the change in the heat capacity of the system, consequent on the reaction. The heat of reaction increases with temperature when the substances formed in the reaction have a smaller heat capacity than the substances which disappear in the reverse case it decreases with temperature. For endothermic reactions in which Q is negative, an increase in Q means a diminution in the numerical value of the heat of reaction, and conversely. 

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