Heats of reactions

The heat of reaction, or more accurately, the enthalpy change during a chemical reaction, A, indicates the amount of energy being absorbed or released when a chemical transformation takes place at given operating atmosphere and temperature of 298 K. The standard molar heat of reaction of a chemical reaction (expressed in energy per mole extent) is denoted by It is calculated by 

Principles of Chemical Reactor Analysis and Design, Second Edition. By Uzi Mann Copyright 2009 John Wiley Sons, Inc. 

The heat of reaction is a function of temperature and pressure. Since enthalpy is a state quantity, we relate file heat of reaction at any temperature and the standard pressure of 1 atm, to the standard heat of reaction at 298 K by 

Example 5.1 Determine the heat of combustion of n-octane at 620°C and 1 atm. The heats of formations of the various species and their heat capacities are given below. Data The standard heats of formation of the species (at 298 K) are 

The specific molar heat capacities Cpj (assumed constant) are 

Both have chosen flammability, explosiveness and toxicity as hazardous properties of substances. Heikkila et al. (1996) have also included corrosiveness to the list because in corrosive environments the right choice of construction materials is essential to inherent safety. 

Viscosity has not been found to be a meaningful. The hot spot effect in poorly mixed viscous reactors can be included in the heat of reaction parameter. New phase generation and catalysts have not been chosen either because both parameters are considered by hazardous properties of those substances (chemical interaction, explosiveness etc.). This applies also to waste products parameter. 

The chosen meaningful parameters are the following reaction heat, flammability, explosiveness, toxicity, corrosiveness, chemical interaction, inventory, process temperature and pressure, equipment safety and safe process structure (see Table 5). This does not mean that other factors affecting the inherent safety of a process are meaningless. On the contrary they should be considered more detailed in further design stages. 

From Table 6 it can be seen how the selected parameters have a connection to the basic principles of inherent safety. For instance the subindices of equipment safety and safe process structure contain several characteristics of inherent safety such as limitation of effects or tolerance to maloperation. It is practical to include several characteristics into few parameters, since the inherent safety principles are both very broad and overlapping. The philosophy behind them cannot be described just by one process parameter. The selected parameters are discussed in more detail on the following pages. 

Principles of Inherent Safety (Kletz, 1991) pns (Edwards and Lawrence, 1993) ISI (Hcikldlactal., 1996) 

It is possible to calculate a heat of reaction for a high-energy system by assuming what the reaction products will be, and then nsing available thermodynamic tables of 

Decomposition of the starting materials into their constituent elements 

Subsequent reaction of these elements to form the desired products 

The net heat change associated with the overall reaction can then be calculated frtma  

Consider the following reaction, balanced using the oxidation numbers or Pyro Valence method  

For the choice of a suitable reactor, the heat of reaction under standard conditions ArH is, among others, of decisive importance. Since the ArH generally can not be measured directly in a calorimeter (industrially relevant reactions do not proceed with 100% yield), they must be determined via the experimentally readily accessible heats of combustion of the reactants AcH . 

The enthalpies of formation of the reactants i are calculated from the heats of combustion AcH i by using the Hess equation (Equation 3.1.1-1) [Yaws 1988], and the reaction enthalpy ArH calculated therefrom (Equation 3.1.1-2) is then often the difference of large numbers (see also Example 3.1.1-1), so that it is subject to large errors and should be treated with caution  

to minimize the risk of scale-up, it is often unavoidable to perform an (expensive) investigation of the reaction in a pilot plant under adiabatic conditions, which normally can not be achieved in small laboratory reactors (this should be checked). 

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The enthalpy of formation of benzene is required, that is, the enthalpy of reaction (3.1.1-3). 

For a hydrogen fuel cell, the overall reaction (Equation 1.13) is the same as tiie reaction of hydrogen combustion, which is an exothermic process. 

The heat or enthalpy of a chemical reaction is the difference between tiie heats of formation of products and reactants. For the above equation, the heat or entiialpy 

The heat of formation of liquid water is -286 kJ/mol at 25 °C and heat of formation of elements is by definition equal to zero. Therefore, 

The negative sign of the enthalpy means that this is an exothermic reaction. The fuel cell reaction can now be written as 

This equation is valid at 25 °C only, meaning that both the reactant gases and the product water are at 25 °C. At 25 °C and atmospheric pressure water is in liquid form [1]. 

The heat associated with the combustion of an energetic material such as black powder is called the heat of reaction. The heat of explosion is the heat of reaction associated with the rapid decomposition of such a material in an inert atmosphere. 

Assuming the reaction of black powder given in equation (2.8) is at constant pressure if only pressure-volume work is considered, the enthalpy change for the reaction at the temperature concerned is equal to the sum of the enthalpies of the products minus the sum of the enthalpies of the reactants [equation (2.17)], 

If the reaction is a standard state reaction where the starting materials in their standard states react to give products in their standard states, and the standard heats of formation of the elements are assumed 

For example, the enthalpy of formation of CO2 from combustion of the black powder constituent, charcoal, is given by reaction (2.19)  

Normally, the standard state is the most stable state at one atmosphere pressure and at the given temperature. Most tabular data, as used for the calculation of reaction temperatures, are given at 0 °C or 298 K. The overall calculation for the heat of reaction of black powder at different temperatures is simplified by using tabulated data of the enthalpy function. Hr — for the reaction products, since no enthalpy measurements can be made in the sense of an absolute quantity. 

If the reaction is a standard state reaction where the starting materials in their standard states react to give products in their standard states, and the standard heats of formation (A// 7) of the elements are assumed to be zero at any given temperature, then the standard heat of reaction, A//7-(reaction), IS cxprcssed as in equation (2.18)  

In contrast to this is the law of Hep The law of He6 states that the heat of reaction is independent of the reaction path. The law of He6 can be regarded as a precursor of the first law of thermodynamics. 

The mass is constant. However, this is only true in a nonrelativistic situation. The equation of continuity expresses the conservation of mass. In relativity theory the mass m increases with its velocity v by 

In our consideration of the chlorination of methane, we have so far been concerned chiefly with the particles involved-molecules and atoms- and the changes that they undergo. As with any reaction, however, it is important to consider also the energy changes involved, since these changes determine to a large extent how fast the reaction will go, and, in fact, whether it will take place at all. 

When heat is liberated, the heat content (enthalpy), //, of the molecules themselves must decrease the change in heat content. A//, is therefore given a negative sign. (In the case of an endothermic reaction, where heat is absorbed, the increase in heat content of the molecules is indicated by a positive AH.) 

ProUcQi2.1 Calculate AH for the corresponding reaction of methane with  

The value of —25 kcal that we have just calculated is the nettkH for the overall reaction. A more useful picture of the reaction is given by the A/f s of the individual steps. These are calculated below  

Problem 2.2 Calculate for the corresponding steps in the reaction of methane with (a) bromine, (b) iodine, (c) fluorine. 

Consider enthalpy changes that accompany chemical reactions. The enthalpy of reaction or heat of reaction is defined as the difference between the enthalpies of the products and the enthalpies of the reactants  

The enthalpy of formation, which we have discussed in the previous section, offers an easy way to overcome this difficulty. We now introduce Hess s Law. Recall that enthalpy is a state function, and hence the enthalpy change depends on only the initial and fmal states. Hess s law is basically the same as stated above, but expressed in a different way Hess s law states that the enthalpy change for a chemical reaction is the same whether it takes place in one or several stages. Consider the combustion of methane again.  

Weighted sum of Weighted sum of the enthalpies of the enthalpies of formation of the formation of the 

This equation applies to a system undergoing a chemical reaction at constant pressure and temperature. 

Consider a general reaction which occurs at a constant pressure  

Most of the chemical reactions performed in the fine chemicals industry are exothermal, meaning that thermal energy is released during the reaction. It is obvious that the amount of energy released is directly linked to the potential damage in the case of an incident. For this reason, the heat of reaction is one of the key data, which allow assessment of the risks linked to a chemical reaction at the industrial scale. 

The unit of energy (J) is related to other units as follows  

The latter, the specific heat of reaction, is practical for safety purposes, because most of the calorimeters directly deliver the specific heat of reaction in kj kg 1. Further, since it is a specific entity, it can easily be scaled to the intended process conditions. Both heat of reaction and molar enthalpy are related by 

Obviously, the heat of the reaction depends on the concentration of reactant (C). By convention, exothermal reactions have negative enthalpies, whereas endothermic reactions have positive enthalpies.11 Some typical values of reaction enthalpies are given in Table 2.1 [1], 

Reaction enthalpies also may be obtained from enthalpies of formation (AHjj, given in tables of thermodynamic properties [2, 3]  

So far we have considered enthalpy changes for simple physical processes such as temperature changes and phase transitions. But the importance of chemistry to the energy economy arises from the fact that there are enthalpy changes in chemical reactions as well. This enthalpy change is commonly referred to as the heat of reaction. Because many reactions are carried out under constant pressure conditions, this term is sensible, even if slightly imprecise. 

Thus far our discussion on thermochemistry has focused on physical processes 

The combustion of natural gas, methane, to produce heat can be summarized in the following reaction  

Energy involved in the combustion of methane, CH. In the combustion process, the chemical potential energy of the reactants is higher than the products. The difference in potential energy is the heat involved in the reaction 

The first law of thermodynamics simply says that energy cannot be created or destroyed. With respect to a chemical system, the internal energy changes if energy flows into or out of the system as heat is applied and/or if work is done on or by the system. The work referred to in this case is the PV work defined earlier, and it simply means that the system expands or contracts. The first law of thermodynamics can be modified for processes that take place under constant pressure conditions. Because reactions are generally carried out in open systems in which the pressure is constant, these conditions are of greater interest than constant volume processes. Under constant pressure conditions Equation 3 can be rewritten as 

Written as Equation 4, q is the heat exchange at constant pressure and PAV is the work done. It is important to understand the significance of the mathematical signs in Equation 4, and how they relate to the change in internal energy. When q is posi- 

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Allow vaporization of liquid in the reactor so that it can be condensed and refluxed back to the reactor as a means of removing the heat of reaction... 

The problem with the fiowsheet shown in Fig. 10.5 is that the ferric chloride catalyst is carried from the reactor with the product. This is separated by washing. If a reactor design can be found that prevents the ferric chloride leaving the reactor, the effluent problems created by the washing and neutralization are avoided. Because the ferric chloride is nonvolatile, one way to do this would be to allow the heat of reaction to raise the reaction mixture to the boiling point and remove the product as a vapor, leaving the ferric chloride in the reactor. Unfortunately, if the reaction mixture is allowed to boil, there are two problems ... 

As shown in Fig. 10.6, the vapor from the reactor flows into the bottom of a distillation column, and high-purity dichloroethane is withdrawn as a sidestream several trays from the column top. The design shown in Fig. 10.6 is elegant in that the heat of reaction is conserved to run the separation and no washing of the reactor... 

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable fall for endothermic reactors, then this is the option normally chosen. If this is the case, then the feed stream to the reactor requires heating and the efiluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) and a hot stream (the reactor efiluent). The heat of reaction appears as elevated temperature of the efiluent stream in the case of exothermic reaction or reduced temperature in the case of endothermic reaction. 

LOW RATE OF HEAT TRANSFER AND/OR HIGH HEAT OF REACTION... 

Figure 13.1a shows two possible thermal profiles for exothermic plug-fiow reactors. If the rate of heat removal is low and/or the heat of reaction is high, then the temperature of the reacting stream will increase along the length of the reactor. If the rate of heat removal is high and/or the heat of reaction is low, then the temperature will fall. Under conditions between the two profiles shown in Fig. 13.1a, a maximum can occur in the temperature at an intermediate point between the reactor inlet and exit. 

If indirect heat transfer is used with a large temperature difference to promote high rates of cooling, then the cooling fluid (e.g., boiling water) is fixed by process requirements. In this case, the heat of reaction is not available at the temperature of the reactor effluent. Rather, the heat of reaction becomes available at the temperature of the quench fluid. Thus the feed stream to the reactor is a cold stream, the quench fluid is a hot stream, and the reactor effluent after the quench is also a hot stream. 

Figure 13.5 shows a flowsheet for the manufacture of phthalic anhydride by the oxidation of o-xylene. Air and o-xylene are heated and mixed in a Venturi, where the o-xylene vaporizes. The reaction mixture enters a tubular catalytic reactor. The heat of reaction is removed from the reactor by recirculation of molten salt. The temperature control in the reactor would be diflficult to maintain by methods other than molten salt. 

The appropriate placement of reactors, as far as heat integration is concerned, is that exothermic reactors should be integrated above the pinch and endothermic reactors below the pinch. Care should be taken when reactor feeds are preheated by heat of reaction within the reactor for exothermic reactions. This can constitute cross-pinch heat transfer. The feeds should be preheated to pinch temperature by heat recovery before being fed to the reactor. 

Using this equation it is possible to calculate heats of reaction from the variation of AG with temperature. 

Figure C3.5.1. (a) Vibrational energy catalyses chemical reactions. The reactant R is activated by taking up the enthalpy of activation j //Trom the bath. That energy plus the heat of reaction is returned to the bath after barrier...

Free energy is related to two other energy quantities, the enthalpy (the heat of reaction measured at constant pressure) and the entropy. S. an energy term most simply visualised as a measure of the disorder of the system, the relationship for a reaction taking place under standard conditions being... 

The representation of a chemical reaction should include the connection table of all participating species starting materials, reagents, solvents, catalysts, products) as well as Information on reaction conditions (temperature, concentration, time, etc.) and observations (yield, reaction rates, heat of reaction, etc.). However, reactions are only Insuffclently represented by the structure of their starting materials and products,... 

The knowledge base is essentially two-fold on one hand it consists of a series of procedures for calculating all-important physicochemical effects such as heats of reaction, bond dissociation energies, charge distribution, inductive, resonance, and polarizability effects (.see Section 7.1). The other part of the knowledge base defines the reaction types on which the EROS system can work. 

Heats of reaction Heats of reaction can be obtained as differences between the beats of formation of the products and those of the starting materials of a reaction. In EROS, heats of reaction arc calculated on the basis of an additivity scheme as presented in Section 7.1. With such an evaluation, reactions under thermodynamic control can be selected preferentially (Figure 10.3-10). 

The evaluation of chemical reactions can be performed to various levels of sophistication heats of reaction allow for a consideration of the thermodynamics of a reaction, whereas reaction rates consider its kinetic aspects. 

Reactions in porous catalyst pellets are Invariably accompanied by thermal effects associated with the heat of reaction. Particularly In the case of exothermic reactions these may have a marked influence on the solutions, and hence on the effectiveness factor, leading to effectiveness factors greater than unity and, In certain circumstances, multiple steady state solutions with given boundary conditions [78]. These phenomena have attracted a great deal of interest and attention in recent years, and an excellent account of our present state of knowledge has been given by Arls [45]. 

For the preparation of phenol, the aqueous solution should be heated carefully to 50-55°, at which temperature the reaction proceeds smoothly above this temperature, how ever, the reaction may rapidly become veiy vigorous, and the heat of reaction will then cause a marked rise in the temperature and the production of a large amount of tarry byproducts. 

Mix 1 g. of the nitro compound with 4 g, of sodium dichromate and 10 ml. of water in a 50 ml. flask, then attach a reflux condenser to the flask. Add slowly and with shaking 7 ml. of concentrated sulphuric acid. The reaction usually starts at once if it does not, heat the flask gently to initiate the reaction. When the heat of reaction subsides, boil the mixture, cautiously at first, under reflux for 20-30 minutes. Allow to cool, dilute with 30 ml. of water, and filter oflF the precipitated acid. Purify the crude acid by extraction with sodium carbonate solution, precipitation with dUute mineral acid, and recrystaUisation from hot water, benzene, etc. 

Semiempirical methods are parameterized to reproduce various results. Most often, geometry and energy (usually the heat of formation) are used. Some researchers have extended this by including dipole moments, heats of reaction, and ionization potentials in the parameterization set. A few methods have been parameterized to reproduce a specific property, such as electronic spectra or NMR chemical shifts. Semiempirical calculations can be used to compute properties other than those in the parameterization set. 

By allowing compounds to react in a calorime ter It IS possible to measure the heat evolved in an exothermic reaction or the heat absorbed in an en dothermic reaction Thousands of reactions have been studied to produce a rich library of thermo chemical data These data take the form of heats of reaction and correspond to the value of the enthalpy change AH° for a particular reaction of a particular substance... 

Heat of formation (AH ) the enthalpy change for formation of a compound directly from the ele ments is one type of heat of reaction In cases such as the formation of CO2 or H2O from the combustion of carbon or hydrogen respectively the heat of forma tion of a substance can be measured directly In most... 

Equations (1) and (2) are the heats of formation of carbon dioxide and water respectively Equation (3) is the reverse of the combustion of methane and so the heat of reaction is equal to the heat of combustion but opposite in sign The molar heat of formation of a substance is the enthalpy change for formation of one mole of the substance from the elements For methane AH = —75 kJ/mol... 

The heats of formation of most organic com pounds are derived from heats of reaction by arith metic manipulations similar to that shown Chemists find a table of AH values to be convenient because it replaces many separate tables of AH° values for indi vidual reaction types and permits AH° to be calcu lated for any reaction real or imaginary for which the heats of formation of reactants and products are available It is more appropriate for our purposes however to connect thermochemical data to chemi cal processes as directly as possible and therefore we will cite heats of particular reactions such as heats of combustion and heats of hydrogenation rather than heats of formation... 

You have seen that measurements of heats of reaction such as heats of combustion can pro vide quantitative information concerning the relative stability of constitutional isomers (Section 2 18) and stereoisomers (Section 3 11) The box in Section 2 18 described how heats of reaction can be manipulated arithmetically to generate heats of formation (AH ) for many molecules The following material shows how two different sources of thermo chemical information heats of formation and bond dissociation energies (see Table 4 3) can reveal whether a particular reaction is exothermic or en dothermic and by how much... 

A similar analysis for fluorination of methane gives AH° = -426 kJ for its heat of reaction Fluori nation of methane is about four times as exothermic as chlorination A reaction this exothermic if it also occurs at a rapid rate can proceed with explosive violence... 

Although it is not universally true that the activation energies of reactions parallel their heats of reaction, this is approximately true for the kind of addition reaction we are discussing. Accordingly, we can estimate E = k AH, with k an appropriate proportionality constant. If we consider the difference between two activation energies by combining this idea with Eq. (7.21), the contribution of the nonstabilized reference reaction drops out of Eq. (7.21) and we obtain... 

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