Heat of reaction equations

When chemical equations are combined by addition, the standard heats of reaction may also be added to give, the standard heat of the resulting reaction. This is possible because enthalpy is a property, and changes in it are independent of path. In particular, formation equations and standard heats of formation may always be combined to produce any desired equation (not itself a formation equation) and its accompanying standard heat of reaction. Equations written for this purpose often include an indication of the physical state of each reactant and product, i.e., the letter g, l, or s is placed in parentheses after the chemical formula to show whether it is a gas, a liquid, or a solid. This might seem unnecessary since a pure chemical species at a particular temperature and 1 bar or l(atm) can usually exist only in one physical state. However, fictitious states are often assumed as a matter of convenience. 

An examination of the chemical equations for the three equilibria given above shows that, as written, reaction (1) is equivalent to reaction (2) minus reaction (3). Consequently, if standard free energy equations are written out in a manner similar to that used for thermochemical (heat of reaction) equations in 12d, etc., they can be added and subtracted in an analogous manner. 

A fermenter is cooled through the heat exchange area in order to remove the metabolic heat and maintain the set point temperature. The total heat of reaction, can be calculated from heats of reactions (Equations 6.1-6.3) ... 

We can use this value and the value for Qal to calculate the heat of reaction (Equation 5.24) ... 

In Chapter 9 we will see that a quantity called the standard AG of a reaction can be obtained by measuring the equilibrium concentrations of the reactants and products. If the equilibrium concentrations (hence AG) are measured at various temperatures, the data on the variation of AG with T can be used to obtain AH, which is the heat of reaction. Equations (5.2.13) and (5.2.14) are versions of the Gibbs-Helmholtz equation. 

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

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... 

Equations 17—20 result from contact between hot metal and slag, and the sulfur and carbon come dissolved in the hot metal. Likewise, the manganese, siUcon, and phosphoms which are produced are dissolved into the hot metal. The heats of solution for these elements in some cases depend on concentration, and are not included in the heats of reaction Hsted above. The ratio of the concentration of the oxide (or element for sulfur) in the slag to the concentration of the element in the hot metal is the partition ratio, and is primarily a function of slag chemistry and temperature. 

The heat of reaction AH is given in joules per gram mole of ammonia formed. Equation 22 ignores the heat of mixing which must be taken into account for apphcation to industrial situations (21,22). The heat evolved in synthesis at 370—540°C is approximately 54,430 kj/mol (23, 400 Btu/lb-mol). 

Two variables of primary importance, which are interdependent, are reaction temperature and ch1orine propy1ene ratio. Propylene is typically used ia excess to act as a diluent and heat sink, thus minimising by-products (eqs.2 and 3). Since higher temperatures favor the desired reaction, standard practice generally involves preheat of the reactor feeds to at least 200°C prior to combination. The heat of reaction is then responsible for further increases in the reaction temperature toward 510°C. The chlorine propylene ratio is adjusted so that, for given preheat temperatures, the desired ultimate reaction temperature is maintained. For example, at a chlorine propylene molar ratio of 0.315, feed temperatures of 200°C (propylene) and 50°C (chlorine) produce an ultimate reaction temperature of approximately 500°C (10). Increases in preheat temperature toward the ultimate reactor temperature, eg, in attempts to decrease yield of equation 1, must be compensated for in reduced chlorine propylene ratio, which reduces the fraction of propylene converted and, thus aHyl chloride quantity produced. A suitable economic optimum combination of preheat temperature and chlorine propylene ratio can be readily deterrnined for individual cases. 

The preceding equation assumes the reaction is completely quenched immediately after the relief point is reached. This behavior is closely approximated if the reaction stops in the quench pool and the reactor empties quickly and thoroughly. If the reaction continues in the quench pool, the temperature Tr should be increased to the maximum adiabatic exotherm temperature. An equation is presented by CCPS (AIChE-CCPS, 1997) that includes the heat of reaction. In some cases, an experiment is necessary to confirm that the reaction indeed stops in the quench pool. 

Temperature gradient normal to flow. In exothermic reactions, the heat generation rate is q=(-AHr)r. This must be removed to maintain steady-state. For endothermic reactions this much heat must be added. Here the equations deal with exothermic reactions as examples. A criterion can be derived for the temperature difference needed for heat transfer from the catalyst particles to the reacting, flowing fluid. For this, inside heat balance can be measured (Berty 1974) directly, with Pt resistance thermometers. Since this is expensive and complicated, here again the heat generation rate is calculated from the rate of reaction that is derived from the outside material balance, and multiplied by the heat of reaction. 

The implicit Crank-Nicholson integration method was used to solve the equation. Radial temperature and concentrations were calculated using the Thomas algorithm (Lapidus 1962, Carnahan et al,1969). This program allowed the use of either ideal or non-ideal gas laws. For cases using real gas assumptions, heat capacity and heat of reactions were made temperature dependent. 

To make the necessary thermodynamic calculations, plausible reaction equations are written and balanced for production of the stated molar flows of all reactor products. Given the heat of reaction for each applicable reaction, the overall heat of reaction can be determined and compared to that claimed. However, often the individual heats of reaction are not all readily available. Those that are not available can be determined from heats of combustion by combining combustion equations in such a way as to obtain the desired reaction equations by difference. It is a worthwhile exercise to verify this basic part of the process. 

A recent article reported equations to help calculate the heat of reaction for proposed organic chemical reactions. In that article, enthalpy equations were given for 700 major organic compounds. 

When HI is less dian H die reaction is exodiermic and A// is negative, i.e. temperature increases. When HI is greater dian H die reaction is endodiermic and die temperature falls. The heat of reaction is usually expressed in die equation as A//, e.g. 

Chemical reactions obey the rules of chemical kinetics (see Chapter 2) and chemical thermodynamics, if they occur slowly and do not exhibit a significant heat of reaction in the homogeneous system (microkinetics). Thermodynamics, as reviewed in Chapter 3, has an essential role in the scale-up of reactors. It shows the form that rate equations must take in the limiting case where a reaction has attained equilibrium. Consistency is required thermodynamically before a rate equation achieves success over tlie entire range of conversion. Generally, chemical reactions do not depend on the theory of similarity rules. However, most industrial reactions occur under heterogeneous systems (e.g., liquid/solid, gas/solid, liquid/gas, and liquid/liquid), thereby generating enormous heat of reaction. Therefore, mass and heat transfer processes (macrokinetics) that are scale-dependent often accompany the chemical reaction. The path of such chemical reactions will be... 

All of tlie recoimnended heat flax equations in API 520 and NFPA Codes tliat are used to design relief valve assmne tliat tlie liquids are not self-reactive or subject to runaway reaction. If tliis situation arises, it is necessary to include tlie heat of reaction and tlie rate of tlie reaction into account in sizing the relief device. 

Heat of combustion, 113 Heat of hydrogenation, 186 table of, 187 Heat of reaction, 154 Helicase, DNA replication and, 1106 Hell-Volhard-Zelinskii reaction, 849 amino acid synthesis and. 1025 mechanism of, 849 Heme, biosynthesis of, 966 structure of, 946 Hemiacetal, 717 Hemiketal, 717 Hemithioacetal, 1148 Henderson-Hasselbalch equation,... 

Now suppose we measure the heat of reaction of hydrogen and oxygen in a calorimeter like that shown in Figure 7-2. This experiment has been performed many times 68.3 kcal of heat, Q%, are produced for every mole of water formed. The equation for this reaction is... 

Comparing equations (9), (10), and (11), we see that is just the ionization energy of F (g). By usual practice, however, the reverse of reaction (11) is usually considered. Of course the heat of reaction (12) is just the negative of that of reaction (II) ... 

Two thermocouples, Em at x = 0 and Ex at a distance x, permit the monitoring of the atomic hydrogen concentration change along the side-tube. The atoms recombining on the thermocouple tip covered by the active catalyst evolve the heat of reaction and thus the thermoelectric power becomes a relative measure of the concentration of atoms in the gas phase. Finally, one obtains for the direct use in an experimental work the following equation... 

Rule To find any proposed heat of reaction write down the chemical equations of the component reactions so that each symbol appears equally often on both sides of the sign of equality. If the heats of reaction (with proper signs) have been inserted, the unknown heat of reaction being denoted by x then the latter... 

For the dependence of the heat of reaction at constant volume, we have Kirchhoff s equation ( 58) ... 

These equations enable one to calculate the heat of reaction at any temperature from its value at one temperature... 

We thus arrive at the same equation as for a homogeneous gas reaction, except that the heat of reaction refers to all the phases, gaseous and condensed. 

Nernst, in his Theoretische Chemie, devoted a whole chapter to a critical examination of the rule of Thomsen and Berthelot, and he concluded that in many cases the heat of reaction certainly does correspond very closely with the maximum work, AT, which latter magnitude he took from van t Hoff as a measure of the chemical affinity. Whilst pointing out that it very often gives results wholly incompatible with experience, and cannot therefore be indiscriminately applied, Nernst showed that the rule nevertheless holds good in too many cases to be wholly false in an appropriate metaphor he claimed that it contains a genuine kernel of truth which has not yet been shelled from its enclosing hull. This labour of emancipation was partially effected in the newer work of the same author, Applications of Thermodynamics to Chemistry, 1907, which is an attempt to place the rule of Berthelot on a scientific basis, and to determine under what conditions its use is legitimate. He points out that the equation ... 

For the manufacturing of sulfosuccinic acid esters, which belong to a special class of surfactants, maleic acid anhydride is needed. Maleic acid anhydride is an important intermediate chemical of the chemical industry. Its worldwide output amounts to about 800,000 tons (1990) [64]. Maleic acid is produced by catalytic vapor phase oxidation process of benzene or n-C4 hydrocarbons in fixed bed or fluidized bed reactors according the following reaction equations. The heat of reaction of the exothermic oxidation processes is very high. 

The design equations for a CSTR do not require that the reacting mixture has constant physical properties or that operating conditions such as temperature and pressure be the same for the inlet and outlet environments. It is required, however, that these variables be known. Pressure in a CSTR is usually determined or controlled independently of the extent of reaction. Temperatures can also be set arbitrarily in small, laboratory equipment because of excellent heat transfer at the small scale. It is sometimes possible to predetermine the temperature in industrial-scale reactors for example, if the heat of reaction is small or if the contents are boiling. This chapter considers the case where both Pout and Tout are known. Density and Q ut wiU not be known if they depend on composition. A steady-state material balance gives... 

The reaction rates in Equation (5.17) are positive and apply to the reaction. That is, they are the rates of production of (possibly hypothetical) components having stoichiometric coefficients of -bl. Similarly, the heats of reaction are per mole of the same component. Some care is needed in using literature values. See Section 7.2.1. 

Example 6.6 Suppose the reactions in Equation (6.1) are exothermic rather than endothermic. Specihcally, reverse the sign on the heat of reaction terms... 

Heats of Reaction. Chemical reactions absorb or liberate energy, usually in the form of heat. The heat of reaction, h.Hn, is defined as the amount of energy absorbed or liberated if the reaction goes to completion at a fixed temperature and pressure. When > 0, energy is absorbed and the reaction is said to be endothermic. When /sHr < 0, energy is liberated and the reaction is said to be exothermic. The magnitude of Is.Hr depends on the temperature and pressure of the reaction and on the phases (e.g., gas, liquid, solid) of the various components. It also depends on an arbitrary constant multiplier in the stoichiometric equation. 

These equations differ by constant factors, but aU the heats of reaction become equal when expressed in joules per mole of water formed, —241,818. They are also equal when expressed in joules per mole of oxygen formed, 4-483,636, or in joules per mole of hydrogen formed, 4-241,818. Any of... 

The heats of reaction associated with stoichiometric equations are additive just as the equations themselves are additive. Some authors illustrate this fact by treating the evolved heat as a product of the reaction. Thus, they write... 

The stoichiometry and heats of reaction in Equations (7.21) and (7.22) are algebraically summed to give... 

It does not matter that there is no known catalyst that can accomplish the reaction in Equation (7.21) directly. Heats of reaction, including heats of formation, depend on conditions before and after the reaction but not on the specific reaction path. Thus, one might imagine a very complicated chemistry that starts at standard conditions, goes through an arbitrary trajectory of temperature and pressure, returns to standard conditions, and has Equation (7.21) as its overall effect. A77. =-1-147,360 J/mol of styrene formed is the net heat effect associated with this overall reaction. 

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