ineering ng & E P l r a o c i c e m s e s Journal of h T C e f c h o Gargurevich, J Chem Eng Process Technol 2016, 7:2 l ISSN: 2157-7048 n a o n l o r g u y o J Chemical Engineering & Process Technology DOI: 10.4172/2157-7048.1000287 ReviewResearch Article Article OpenOpen Access Access Chemical Reaction Thermodynamics and Reaction Rate Theory Ivan A Gargurevich* Chemical Engineering Consultant, Combustion and Process Technologies, 32593 Cedar Spring Court, Wildomar, CA 92595, USA Abstract Chemical reactor modeling requires the formulation of Heat, Mass, and Chemical Species balances and depending on reactor configuration Computational Fluid Dynamic (CFD) to account for mixing effects. Thermochemical properties such as the species enthalpy have to be considered to account for heat of chemical reactions when conducting an overall or finite energy balance. To properly calculate the heat of reaction due to a reversible reaction, knowledge of the forward and reverse rate coefficients is required. Similarly, the species balance requires knowledge of the net rates of chemical reactions within the reactor to account for composition changes and the equilibrium constant is needed. Keywords: Thermodynamics; Chemical kinetics reactor, the net rate of formation for a given species has to be estimated. Consider I- elementary reversible (or irreversible) chemical reactions Reaction Thermodynamics [2] involving K chemical species that can be represented in the There are some fundamental thermochemical relations that are following general form K K relevant in the mathematical treatment of the chemical reactor. For ⇔ ∑γ'"Ʀi χ k ∑ γƦi χ k (i=1, 2, 3 …. I) (8) an ideal gas, if the natural elements are taken as reference, the specific k= 1 k= 1 enthalpy for the kth species can be written as follows th Where χ k is the chemical symbol for the k species. The production T th 000 rate r k of the k species can be written in terms of the rate-of-progress (T)= (25) + HHk ∆ f ,k ∫ cp,k dT (1) variables q for all reactions involving the kth species 25 i I Where standard conditions are at 1.0 atmosphere of pressure, = (k=1,2,....K) (9) r k ∑γ Ʀiq i 0 (25) i−1 DH fk, is the species heat of formation at 25°C, and Cp,k is the specific heat at constant pressure. The standard heat of reaction at temperature Where T can then be written as [1], T =- (10) 00 0 nnki ki n ki ()T =+(25) "' rxn ååk f, k k pk, (2) DnHH nò c dT and qi for the ith reaction is given by the difference of the forward kk25 th and reverse rates as Where νk is the stoichiometric coefficient for the k species ki ki participating in the reaction and it is negative for reactants. =-[]nn `[] (11) q i kkfiÕÕXXkkfr Similarly, the standard entropy change for a chemical reaction is th given by equation Where [Xk] is the molar concentration of the k species and kfi, and T 0 00 k ., are the forward and reverse rate constants of the ith reaction. ()T =+(25) c pk, ri DnSSrxn ååkkk nò dT (3) kk25 T In summary, the mathematical treatment of chemical reactor design 0 th Where S k is the absolute entropy for the k species in the chemical requires knowledge of thermodynamic properties such as species reaction at 25°C. heat of formation, heat capacity, entropy, and kinetic coefficients The properties given by equations (2) and (3) are important because for chemical reactions. If experimental or estimated values for these from them the standard free energy for the reaction at temperature T properties were not available in the literature, it becomes necessary to can be obtained as follows make sound estimates by methods described in the sections that follow this introduction. 00=-0 (4) DGSrxn()TTDDHTrxn ()rxn () T Estimation of Thermochemical Properties and the equilibrium constant for the reaction can then be estimated by The emphasis on this section will be illustrating methods that equation (5) [1] 0 =- DG rxn()T RTln K activity (5) Furthermore, if the forward rate coefficient k of a chemical reaction *Corresponding author: Ivan A Gargurevich, Chemical Engineering Consultant, f Combustion and Process Technologies, 32593 Cedar Spring Court, Wildomar, CA is known, the reverse rate coefficientr k is calculated as follows (by the 92595, USA, Tel: 9516759455; E-mail: [email protected] principle of microscopic reversibility) Dn Received February 10, 2016; Accepted March 06, 2016; Published March 31, = 2016 KKactivity C()RT (6) Citation: Gargurevich IA. (2016) Chemical Reaction Thermodynamics and = k f K C (7) Reaction Rate Theory. J Chem Eng Process Technol 7: 287. doi:10.4172/2157- k r 7048.1000287 Where Kc is the reaction equilibrium constant in concentration units. Copyright: © 2016 Gargurevich IA . This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted To account for the change in species concentrations within the use, distribution, and reproduction in any medium, provided the original author and source are credited. J Chem Eng Process Technol ISSN: 2157-7048 JCEPT, an open access journal Volume 7 • Issue 2 • 1000287 Citation: Gargurevich IA (2016) Chemical Reaction Thermodynamics and Reaction Rate Theory. J Chem Eng Process Technol 7: 287. doi:10.4172/2157-7048.1000287 Page 2 of 11 can be used to estimate the thermochemistry of Polycyclic Aromatic number of optical isomers, the total symmetry number, and electronic Hydrocarbons (PAH) in order to be able to model mathematically degeneracies, respectively. The symmetry number σ is the total experiments conducted dealing with toxic trace components in simple number of independent permutations of identical atoms or groups in a hydrocarbon fuels. The discussion is not meant to cover all of the molecule that can be arrived by simple rotations. Both the internal (σint) theoretical aspects (only the main results are presented), but enough and external (σext) symmetries must be considered in establishing the references are given to make it possible for the reader to find more total symmetry number or extensive treatment of methods used for estimating thermochemistry. σ=(σint) × (σext) Conventional methods: additivity Group values of hydrocarbons and halogen-containing compounds There are three important thermochemical properties of stable for estimating heat capacity, intrinsic entropy, and heats of formation molecules that are required input in the mathematical models of can be found in Benson [4]. Total symmetry number for common reactors: heat of formation, absolute entropy, and specific heat. molecules can be found in Senkan [3]. The properties calculated by Conventional methods of estimating thermochemical properties group additivity often need to be corrected for next-nearest-neighbor include methods that are highly empirical in nature, such as those interactions such as cis, trans or gauche interactions, as well as based on various forms of additivity principles, as well as those that are nongroup interactions such as corrections due to ring-strain in cyclic based on the use of statistical mechanical calculations [3]. Statistical molecules. Values for these corrections can be found in Benson [4]. mechanics Figure 1 however is of no use in estimating the heat of formation of molecules. The discussion that follows is expended on the Group Additivity and PAH works of Benson, Senkan and Golden [3-5]. Group additivity has been used successfully to estimate the There are empirical methods based on additivity principles. The thermodynamic properties of PAH by Stein and Benson (Figure 2), first level in the hierarchy of additivity methods is the bond additivity. Stein and Fahr and Wang [6-8]. More recently group additivity was In this approach, the molecular properties can be considered as being used to estimate the properties of fullerene precursors by Pope et made up of additive contributions from the individual bonds in the al. [9] who used groups developed by Moiseeva [10] to estimate the properties of PAH containing 5-carbon rings such as fluoranthene. molecule. For example, the heat of formation of CH3C1 [3] at 298 °K can be calculated as follows: Figure 2 shows the various groups existing in a PAH and the group additivity values taken from Stein and Benson. Stein and Benson [6] ΔHf (298)=3ΔHf (C-H)+ΔHf (C-C1)=3(-3.8)+(-7.4)=-18.8 kcal/mol show that the average difference between predicted and measured heats Where the bond contributions C-H and C-Cl can be found in of formation for eleven PAH including pyrene, for example is <2 kcal/ Benson [4]. (A similar procedure would be used to estimate the heat mol, with the only exception being perylene for which the error was 6.7 capacity and absolute entropy). This estimate is within 5% of the kcal/mol and may be due to the inability of group additivity to account experimentally measured value of -19.6 k cal/mol. It has been found for “destabilization” of aromatic systems due to the presence of rings that bond additivity rules reproduce experimental heat capacity and that contain only exo-type bonds. The average error for estimates of entropy values within ± 1 cal/mol-K on the average, but the error is entropy and heat capacity was less than 1 cal/mol-K. greater for heavily branched compounds. Values of heat formation are They also found that the average error in the estimated values for generally estimated to be within ± 2 kcal/mol but again are subject to the heats of formation of substituted naphthalenes was about 1.2 k cal/ large errors in heavily branched compounds. Bond additivity methods mol. cannot be employed to distinguish differences in properties of isomers such as n- butane and isobutene, for example.