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Process Engineering Guide: GBHE-PEG-RXT-804

Physical Properties and Thermochemistry for Reactor Technology Information contained in this publication or as otherwise supplied to Users is believed to be accurate and correct at time of going to press, and is given in good faith, but it is for the User to satisfy itself of the suitability of the information for its own particular purpose. GBHE gives no warranty as to the fitness of this information for any particular purpose and any implied warranty or condition (statutory or otherwise) is excluded except to the extent that exclusion is prevented by law. GBHE accepts no liability resulting from reliance on this information. Freedom under Patent, Copyright and Designs cannot be assumed.



Process Engineering Guide: Physical Properties and Thermochemistry for Reactor Technology

CONTENTS SECTION 0 INTRODUCTION/PURPOSE 3 1 SCOPE 3 2 FIELD OF APPLICATION 3 3 DEFINITIONS 3 4 PHYSICAL PROPERTIES 3 4.1 Form of Equations 3 4.2 The Physical Property System: “The VAULT” 4 4.3 Physical Property Programs 5 4.4 Physical Property Estimation 5 4.5 Sources of Expertise 5 5 INTERFACING COMPUTER PROGRAMS TO THE

GBHE VAULT PHYSICAL PROPERTIES PACKAGE 7

5.1 Preparation of the Physical Property Data 6



6 THERMOCHEMISTRY 6

6.1 Hess's Law 8 6.2 Standard States 8 6.3 Heats of Formation 8 6.4 Determination of Heats of Reaction 9 7 CALCULATION OF HEATS OF REACTION 9 7.1 Analogous Reactions 9 7.2 Heat of Formation Data Compilations 10 7.3 Estimation of Standard Heats of Formation 10 7.4 Heats of Neutralization 13 7.5 Temperature Effect on Heat of Reaction 14 8 HEATS OF SOLUTION, DILUTION AND MIXING 14 8.1 Calculation of Heats of Solution / Dilution from

Literature Data 15 8.2 Estimation of Heats of Solution and Mixing 16 8.3 Integral and Differential Heats 18 9 EXPERIMENTAL DETERMINATION OF THERMOCHEMICAL PARAMETERS 19 9.1 Isoperibol Calorimetry for Heats of Reaction and Solution 19 9.2 Heat Flow Calorimetry 19 9.3 Adiabatic Calorimeter 20 9.4 Differential Scanning Calorimetry 20

10 COMPUTER CALCULATION OF ENTHALPY OR TEMPERATURE 20 11 BIBLIOGRAPHY 22



FIGURES 1 REACTION POTENTIAL ENERGY DIAGRAM 7 2 INTEGRAL AND DIFFERENTIAL HEATS OF SOLUTION 18



0 INTRODUCTION/PURPOSE The need for reliable physical property data has long been recognized. In pre-computer days, this was in the form of tabulations and graphs. Computers demanded that the form in which the data were supplied had to be adapted. This required not only accuracy, but robustness and ease of machine evaluation. 1 SCOPE This Guide provides background to the sources, correlations and uses of physico-chemical data used in reactor technology. 2 FIELD OF APPLICATION This Guide applies to process engineers in GBH Enterprises world-wide. 3 DEFINITIONS For the purposes of this Guide, no special definitions apply. With the exception of proper nouns and titles, terms with initial capital letters which appear in this Guide and are not defined above, are defined in the Glossary of Engineering Terms 4 PHYSICAL PROPERTIES A list of physical properties in which process engineers have been interested for application to reactor design is given in Ref. [22], Tables 4-1 and 4-4. Considerable development has taken place aimed at handling physical property information in computer programs, but the current state of the art in GBHE is that property values for pure materials or mixtures, (process streams are rarely pure materials) under the conditions relevant to some point in the process, are generated by correlating equations embodied in commercially available programs.



4.1 Form of Equations There is a wide range of correlation forms which has been used to calculate a given physical property. Different forms may be appropriate to different process conditions. It is beyond the scope of this introductory note to give comprehensive advice on the criteria for selection of the appropriate correlation forms to use in a particular application. If this advice is needed, please consult GBHE All the correlation forms have common characteristics. They are generally in two parts: (a) Constant terms (the Ai below) which are characteristic of a pure material.

These constants may be arbitrary (i.e. merely the values required to make the correlation fit measured data) or the values of other fixed properties of the pure material (e.g. critical properties, acentric factors). More rarely, interaction parameters (1 or 2) specific to certain correlations but characteristic of a binary mixture of materials may be available.

(b) Terms characteristic of the particular conditions in the process application,

namely terms in pressure P, temperature T and composition xi. Within this broad statement, there are subtleties. For the simple transport properties, the approach is commonly to calculate the property Zi of the pure materials at the relevant temperature and pressure, and then average these to form the mixture property Zm in a way related to the concentrations in the mixture; i.e.: Zi = f1 (Ai, P, T) Zm = f2 (Zi, xi) Function f2 is known as a "mixing rule". For some of the more complex correlations for thermodynamic properties, e.g. equations of state, the procedure might be to calculate correlation coefficients for the mixture Am, e.g.: Am = f3 (Ai, xi, P, T) Zm = f4 (Am, Ai, xi, P, T)



For more details, see Ref. [22], especially Section 4.4.9. 4.2 The Physical Property Vault System The system is in two parts: 4.2.1 The Vault The Vault is a store of correlation constants, and fixed properties for pure materials, together with interaction parameters for binary pairs, i.e. the Ai. Each set is qualified by other stored information, e.g. component name, temperature and pressure ranges over which the correlation gives a specified reliability and is numerically robust, references, accessibility restrictions, etc. 4.2.2 PROGRAMS Programs are available, given the Ai, calculate the physical property at specified application conditions of temperature, pressure and composition, i.e. which evaluate the functions f. Programs for carrying out complex thermodynamic calculations, like phase equilibria and splits, are also available. 5 INTERFACING CHEMCAD TO THE GBHE VAULT AND

PHYSICAL PROPERTY PACKAGE

CHEMCAD can be interfaced to the GBHE VAULT, so making available to them the store of constants and the software for using these constants to produce physical property data. 5.1 Preparation of the Physical Property Data - CHEMCAD This is a computer file containing information about the identity of the compounds relevant to the application, together with physical property, calculation method selection and numerical coefficient data.



6 THERMOCHEMISTRY Thermochemistry is the study of the relationship of heat or energy changes to chemical reaction processes. Because chemical reactions may involve reactants or products in any phase it is convenient to regard thermochemistry as embracing also the heat changes associated with physical processes (such as solution, dilution and phase transitions) and other associated properties. Heat is an important quantity - it is expensive to generate and if not adequately Controlled leads to loss of efficiency and/or potentially hazardous consequences. Chemical reactions are accompanied by energy changes resulting from the breaking and formation of chemical bonds in the molecules. If the chemical internal energy of the reaction system decreases, there is a corresponding gain in some other form of energy, manifested most frequently by evolution of heat, and vice versa. This is illustrated diagrammatically in Figure 1.

FIGURE 1 REACTION POTENTIAL ENERGY DIAGRAM

EF – Activation energy of forward reaction; ER – Activation energy of reverse reaction; ΔH – Heat of reaction.



The activation energy is related to the intermediate transition state and is an important parameter in reaction kinetics. This Clause deals with heats of reaction and associated processes. The development of the concepts of heat Q, internal energy E, and enthalpy H are well documented (Refs. [1] and [2]). The heat of reaction ΔH is the difference between the energy or heat content of the reactants and products in their specified states at constant temperature; it is thus the heat evolved or absorbed under stated isothermal conditions. The physical states of the reactants and products must be defined for ΔH to be meaningful. Most reactions take place at constant pressure and, for practical purposes, the term 'heat of reaction' means the enthalpy increment, i.e:

where ΔV is the difference in molar volume between reactants and products at constant pressure P. All thermochemical literature and data are based on determination of enthalpy and ΔH. Where a reaction takes place in a constant volume, no external work is done and Q = ΔE. It follows that where a reaction involves solid and liquid phases only, ΔV is likely to be small, in which case ΔH is approximately equal to ΔE. While most industrial reactors operate at constant pressure, so that the enthalpy increment is the true heat of reaction, the user must be aware of special situations (e.g. pressurization of a (partially) closed reactor in an emergency situation) in which ΔE would be the true heat of reaction. 6.1 Hess's Law It is a fundamental principle of thermochemistry that a process heat change is independent of the reaction path; the overall heat is determined only by the nature and state of the initial reactants and final products. This is stated in Hess's Law which is the basis of many thermochemical property calculations. Thus, for the overall process A D:



the overall heat is ΔH = ΔH1 + ΔH2 + ΔH3 6.2 Standard States Because a heat of reaction depends upon the state and conditions of the reactants and products, the concept of standard states is introduced to allow the comparison and combination of values. The following terms are used: (a) Standard states exist for a substance for all three states of matter; for a

gas it is the ideal gas at one atmosphere pressure, and in condensed phases it is the pure substance under a pressure of 1 atm, at a specified temperature. It is a thermodynamic convention to use 25°C (298.15 K) as the standard datum temperature.

(b) The reference state of a substance is the state (phase) that is physically

stable at a specified temperature and a pressure of 1 atm. Though not immediately apparent, it is possible for a substance to be in a standard state but not its reference state and vice versa. The two terms are sometimes confused but a substance can only have one reference state at a given temperature whereas it has three notional standard states. Thus, a substance has property values corresponding to all three standard states at 25°C.

Thermodynamic properties for substances in their standard states are denoted by the superscript symbol, e.g. ΔH°, ΔS°. If reactants and products of a reaction are in their standard states, the ΔH is then called the standard heat of reaction ΔH°. This is the value normally obtained by direct calculation; in practice the term standard is frequently dropped.



6.3 Heats of Formation The heat of formation of a compound is the heat of the notional reaction in which the compound is formed from its elements. Where the compound and elements are in their standard states the quantity is termed the standard heat (enthalpy) of formation, symbolized in literature as ΔfH° (current practice) or, until ca 1980, as ΔH°f. In this Guide it is ca 1980, as H°f. The value of the heat of formation of a compound in each standard state at 25°C is the quantity normally given in data tables. It follows from the definition that the standard heat of formation at 25°C of elements in their reference state is zero. 6.4 Determination of Heats of Reaction Heats of reaction may be obtained for many reactions by either experimental Calorimetry or by calculation from literature data. The choice between the two is dependent on the balance of many factors: (a) Experiment

(1) Measures actual overall process and therefore may lessen uncertainty - provided the extent of reaction is accurately known,

(2) The result may be subject to error due to heat losses or inadequate

calibration,

(3) An experimental result may not be readily applicable to an apparently similar process unless correctly reduced to a standard form,

(4) Must be used where data cannot be satisfactorily estimated.

(b) Calculation

(1) It is essential that a balanced reaction equation can be written, (2) Usually faster if heat of formation data are known or can be readily

estimated.



(3) Essential where required reaction conditions cannot be reproduced in the calorimeter or where insufficient material is available,

(4) Avoids use of toxic/hazardous substances,

(5) Does not allow for unknown side-reactions,

(6) May require use of other parameters that are unknown or introduce

greater uncertainty. 7 CALCULATION OF HEATS OF REACTION The necessary precondition for calculation of a heat of reaction is knowledge of the overall process, viz. a balanced chemical equation and knowledge of the states of all reactants and products. It can be readily shown from Hess's Law that the standard heat of reaction may then be calculated from the relation:

Equation (2) is the basis of heat of reaction calculations from literature data. It follows that the difficult task is generally to obtain the appropriate heats of formation and methods of obtaining them are discussed in this section. In many instances it will be difficult or confusing to attempt to encompass the whole process within the one equation and it may be preferable to express it in a series of equations; the overall ΔH is then the sum of the separate step heats. 7.1 Analogous Reactions The heats of formation should ideally relate to the exact compounds used. As the heat of reaction is determined largely by the molecular changes, i.e. bonds broken and created, at the reactive centre, however, a good approximation to the heat of reaction may often be obtained using simpler molecules without substituent’s remote from the reactive centre, e.g. benzene derivatives instead of polycyclics. This concept is the basis of the group contribution schemes for heats of formation (see below) but it is important to note that even remote groups may contribute to the heat if significant steriochemical changes occur, i.e. if the spatial interactions of substituent’s change.



Use of an analogous reaction is thus a question of compromise; it may allow calculation of an otherwise unattainable heat of reaction but the additional uncertainty introduced must be carefully assessed. Examples of analogous compounds are sodium salts for potassium salts, or mono-substituted rings for polysubstituted, short alkyl chain for longer. 7.2 Heat of Formation Data Compilations 7.2.1 Organic Compounds There are many compilations of heat of formation data. Those by Cox and Pilcher (Ref. [1]), Pedley and Rylance (Ref. [3]) and Pedley. Naylor and Kirby (Ref. [4]) are comprehensive and include only critically assessed data. Of these, Ref. [4] is the most recent and thus contains the most extensive data and is the recommended source for fine organic chemicals. A more limited range of organic data (mainly C1 and C2), considered good quality, is published by the US National bureau of Standards (Ref. [5]); a valuable feature is heats of formation in different strengths of solution for some compounds. This is one of the few authoritative sources of solution data. There are other sources covering a wide range of compounds (e.g. Ref.[2]). Some traditional data compilations are conveniently available but contain a restricted list of compounds only or data values that may not be up-to-date (Ref.6,7 and 8]). It may be noted, however, the 71st edition of (Ref. [8]) contains data from (Ref. [5]). 7.2.2 Inorganic Compounds Inorganic data are widely available in the US National Bureau of Standards and JANAF publications (Ref.[5 and 9]). Data for many compounds are very precise and reliable. Other less specialized sources also contain most of the more common compounds (Ref.[6.7 and 8]). The most comprehensive source of solution data is (Ref. [5]).



7.3 Estimation of Standard Heats of Formation There are several different methods for estimating heats of formation of organic compounds, most being based on “group contributions”; i.e. the empirical allocation of numerical values to molecular fragments or substituent groups such that the sum of the values equals the heat of formation of the compound. It must be emphasized that the fragment values must not be regarded as a heat of formation of the fragment as an organic radical. The main drawback to use of all these methods is the lack of a value for a required fragment. The principal estimation methods are outlined below. It is important to be aware that all the prediction methods in common use and described in this manual give only gas phase values. To obtain the condensed phase data required for many processes, the estimated value must be appropriately adjusted by the heat of vaporization/sublimation. 7.3.1 Benson Group Contribution Method (Refs. [10], [11] and [12]) This is the most widely used method, applicable to many organic compounds. It is based on each atom or functional group (e.g. >CO) having attributed to it a different value according to its nearest neighbors; a distinction is made between atoms that are single, double or triple bonded, e.g.:

Aromatic carbons are symbolized as Cb It should be noted that in some tabulations of values the statement of the group and its environment is abbreviated by omission of implicit groups, e.g. Cd or Ct must automatically be bonded to one similar atom and an aromatic carbon is bonded to two other aromatic carbons. Thus, an alkyl substituted aromatic carbon may be symbolized as Cb – (C). The sum of values for all the atoms/groups in a molecule is an estimate of the gas phase standard heat of formation.



Example : p–Ethylphenol.

The widespread use of this method is reflected by the continued expansion of the table of group values and its use in programs such as CHEMCAD for chemical hazard evaluation and thermophysical property estimation respectively. The most up-to-date tables of values are those published by Reid, Prausnitz et al (Refs. [11] and [12]). The tables contain ring strain corrections for hydrocarbon and several O– and N–heterocyclics. Aromatic resonance energy is automatically included in Cb terms. No account is however taken of polysubstitution effects and it has been claimed recently that estimates for polysubstituted aromatic molecules may be significantly in error. Results for heterocyclic compounds may be unreliable as there are fewer compounds with known heats of formation from which group values may be reliably derived and it is common for complex molecules to have 'unknown' groups. In these instances it may be possible to 'assign' a value for a similar group but great care is required in this; otherwise, a serious error may be introduced. Familiarity with the method is advised for the handling of other than simple molecules. Because the group contributions are an arbitrary allocation of fractions of a heat of formation to molecular fragments, a group value is significantly determined by its neighbors. Additionally, potential for variation within a (notionally) constant group value is illustrated by the aromatic nitro group.



No value is listed but calculation from several compounds gives a spread of 11 kcal/mole for the Cb – (NO2) group. This must reflect more distant interactions and illustrates the need for caution in assigning values. 7.3.2 Franklin Method (see Ref. [13]) This method was originally devised for calculation of gas phase heats of formation as a function of temperature and values are listed up to 1500K. While this offers a notional advantage for calculation of ΔH298 at elevated temperatures, the problem may be overcome by combining ΔH with heat capacity data (see 7.5) and some confusion is risked if the heat of formation is calculated at different temperatures for different purposes. Values for HF(g) at 298K for this method are listed by Reid, Prausnitz et al (Refs. [11] and [12]). Many fewer group values have been published than for the Benson method but as some groups are less specifically defined there are occasions when the Franklin method may be used when Benson may not. 7.3.3 Verma & Doraiswamy Method (Ref. [14]) Like Franklin, this method was intended for calculation of gas phase heats of formation as a function of temperature and is more refined than the former. It is applicable to hydrocarbons, including aromatics and alicyclics, with ring strain corrections, and to several O and N groups. The method is recommended should the heat of formation be explicitly required as a function of temperature; it is generally more useful, however, to use it as an alternative should the Benson method fail. Values for HF(g) at 298K are listed by Reid, Prausnitz et al (Refs. [11] and [12]). 7.3.4 Bond Energy Methods Bond energy methods are based on the notional assignment of energy values to values to specific bonds. These values are derived from the heat of atomization, Ha, the enthalpy required to convert a molecule in gas phase to atoms at the same temperature, after correction for resonance (stabilization) and destabilization energies. There are many problems in the definition and measurement of bond energies but it is not the role of this Guide to discuss them.



The calculation of gas phase heats of formation is based on the cycle:

where : B = Average bond energy term for each bond; D = Heat of dissociation (atomization) of each element; ER = Resonance energy of compound in gas phase; ES = Strain energy of compound in gas phase. Calculation of HF(g) by this equation requires values for B and D. Bond energy values (B) were given by Coates and Sutton (Ref. [15]) and by Pauling (Ref. [16]). The dissociation energy D is the heat of formation of gas phase atoms, expressed per g-atom. Values for common atoms in organic molecules calculated from NBS data are listed below.



Resonance and strain energies are more complex to assess except for a simple aromatic ring not conjugated with any other π-electron system. It is recommended that a chemist is consulted. Although simple in concept this bond energy approach is unreliable except for simple compounds and it is recommended to be used for estimation only as a last resort or for a very approximate figure. Bond energy methods developed by Allen and by Laidler are described by Cox and Pilcher (Ref.[1]), but they are exactly equivalent to the Benson group contribution scheme. There is no advantage in detailing this alternative approach. 7.4 Heats of Neutralization Neutralization reactions occur in many processes and it is not uncommon for them to be a major source of exotherm. The neutralization may involve organic or inorganic acids and bases. 7.4.1 Inorganic Acids and Bases Neutralization of inorganic acids and bases is treated as a normal heat of reaction calculation, data being obtained from the references in Clause 7. It is essential that the initial states of the acid and base and final state of the salt are taken into account; the assumption of 13 kcal/mole is fallacious except in highly dilute aqueous solution. The extent of possible variation is exemplified by the neutralization of hydrochloric acid and sodium hydroxide in different states:



7.4.2 Organic Acids and Bases There are published heat of formation and solution data for a number of carboxylic acids and their salts (Ref. [5]) from which heats of neutralization may be calculated. As the heats of solution of both the acids and their salts are generally small the heats of neutralization of different acids are taken to be similar. An approximate value may therefore be obtained using a simpler carboxylic acid. There are very few published data for sulfonic acids but it has been shown that phenylsulfonic acids behave as strong acids. Their heats of solution in water, and those of their sodium salts are approximately thermoneutral or endothermic (Ref. [19]). Neutralization of organic bases has not been studied systematically but there are data for neutralization of amines by hydrochloric and a few other acids. Some published data are understood to be unreliable and therefore such reactions need to be treated carefully. They are, however, generally less exothermic than inorganic/inorganic neutralizations in the same states. Limited data on phenols show that neutralization with aqueous alkali is also less exothermic than the corresponding neutralization of strong acids. In general, obtaining accurate values for the heat of neutralization of weak acids or bases requires careful appraisal of specialist literature or an experimental measurement. 7.5 Temperature Effect on Heat of Reaction As stated in Clause 6, literature data refer to standard states at 25°C and thus ΔH also relates to that temperature. By Hess's Law, it is evident the heat of reaction at temperature t, ΔHt, is given by the expression:



where Cp is the specific heat capacity. In many reactions the change in total heat capacity from reactants to products is small and not greatly influenced by temperature. At high temperatures, say >200°C, however, it is desirable the effect should be considered. It should be noted that the heat capacity of most substances increases moderately with temperature. A detailed discussion of heat capacity is outside the scope of this section but it may be noted that a few publications list specific heat capacity data at several temperatures (e.g. Refs. [2], [20] and [21]), while several other well-known data compilations give values at 25°C or various temperature ranges. In some high temperature processes it may also be necessary to take account of latent heats as the states of reactants or products may not be those in the standard reaction at 25°C. It should be noted that heat of vaporization is strongly temperature dependent, but detailed discussion of this is also beyond the scope of this manual. The use of computer methods interfaced to ChemCAD for the calculation of total enthalpies of systems, and thus also temperatures and heat balances, is described in Clause 10. 8 HEATS OF SOLUTION, DILUTION AND MIXING The terms solution and dilution are specific examples of mixing but the treatment of the calculation and the form of literature data vary with the type of process. Solution includes the dissolution of solids or liquids, usually, but not exclusively, in an excess of solvent. Dilution implies the initial existence of a solution, whereas mixing implies any two or more liquids (or suspensions). These are important parameters as in some processes they are major sources of exotherms. It should be noted there is no formal means of estimation analogous to the heat of formation methods and literature data or experimental measurements are therefore the most reliable sources.



8.1 Calculation of Heats of Solution / Dilution from Literature Data In any mixing process there are, by definition, two or more substances present and it is therefore possible, in principle, to express quantities in terms of any component. It is usual in thermochemistry to work in molar rather than mass quantities and it is usual also to express concentration as 1 mole solute in n moles solvent. This is consistent with the solute being either a main reactant or product or stoichiometrically related to it, whereas solvent quantities are less directly connected. The most extensive and reliable data sources are the NBS series of publications (Ref. [5]); these include aqueous solutions for most inorganics and many organic compounds (up to C2) and also a limited number of organic compounds in organic solvents. Inorganic data are frequently also given in handbooks (Refs. [7] and [8]). The data are presented as the standard heat of formation of compound X in the state of solution in n moles solvent. The heat of formation of the solvent does not enter into the value. It follows that the enthalpy change accompanying one mole of a compound, solid or liquid, dissolving in n moles of solvent, is the difference between the enthalpies of formation in its standard state and in solution. Enthalpies of dilution are obtained as the difference between enthalpies of formation of the compound in the corresponding concentrations, provided the number of moles of solute remain constant. Calculation of these heats is exemplified by the solution of crystalline cupric chloride.

ΔH dil of a solution containing 1 mole CuCl2 per 20 mole water diluted to 1 mole CuCl2 per 100 mole water is –10.9 kJ/mole CuCl2.



Where the quantity of solute changes, for example by mixing of two streams of different concentrations, the advised procedure is to notionally separate solute and solvent in each stream and then combine them. The overall heat of dilution is then the sum of the heats calculated for each notional step. Where heats of formation are tabulated for several concentrations it is common for the value at infinite dilution to be given. This is stated as "X in ȸH2O" and refers to the infinitely dilute real solution. It is also common to list the heat of formation of the standard state for a substance in solution, this being the hypothetical ideal solution of unit molality, designated as 'X, standard state, m=1'. It is important to recognize that this value corresponds to that of the real solution at infinite dilution; it must not be confused with the value for a real solution of either unit molality or unit molarity. Extensive heat of mixing data have been collected and published by Christensen et al in the Handbook of Heats of Mixing (Ref. [18]). Excess enthalpy data are tabulated versus composition as a single value or smoothed points from a regression equation. This is the most comprehensive source of organic mixing data. An assorted range of heat of solution data and other thermal properties are included in tables by Timmermans (Ref. [17]). These are frequently old data and the format is variable. 8.2 Estimation of Heats of Solution and Mixing 8.2.1 Chemically similar solutes in same solvent There is no formal method for estimation of heats of solution or dilution from molecular structure. Because they are related to physical interactions and parameters; e.g. polarity, which depend upon molecular structure, however, heats of solution of a given solute in chemically similar solvents are usually also similar and it is thus possible to use data for chemically similar solvents where available to obtain an approximate value for a heat of solution/dilution. Thus, a heat of solution in alcohols is likely to diminish slowly with increasing alcohol chain length if solvation results from interaction with the hydroxy group. This approach cannot be employed where the solvent is water as it is chemically too dissimilar to organic solvents.



8.2.2 From solubility - temperature data A measure of the heat of solution can be obtained from the variation of solubility with temperature. The equation (3),

where N is mole fraction of solute, relates the differential heat of solution in the saturated solution to the rate of change of solubility with temperature. In principle it is therefore possible to estimate the heat of solution from measurements of the solubility at two temperatures. 8.2.3 Mixing of organic liquids The dissolution of an organic solute in an organic-liquid presents a special case. Where the solute is a liquid, the process is conventionally regarded as mixing. A number of situations are considered. Where data exist, as described under heats of solution, these should be used. Where no data exist and the liquids have low polarity, the mixing may be regarded as mixing of two ideal liquids, the heat of which is zero. Thus, it may be assumed that ΔHmix = 0, plus an allowance for some uncertainty, ±5–10 kJ/mole is usually sufficient. (a) Dissolution of non-polar solutes

It follows from the above that dissolution of a low polarity organic solid in an organic solvent may be treated as a two-stage process:



Thus, the heat of solution equals the heat of fusion with the allowance for uncertainty in stage 2.

(b) Dissolution of ionizable / highly polar solutes

The assumption of ideal behavior is precluded for highly polar or ionizable compounds and use of the best analogous data provides the best estimate.

(c) Solvates and hydrates

Hydrates and, more generally, solvates are formed where a distinct new crystalline substance is formed containing a stoichiometric ratio of solvent to solute molecules and where some form of bonding occurs between them, e.g. CuSO4.5H2O. These are treated as separate compounds and the heat of formation includes the contribution of the solvent molecules. The difference between the sum of the separate heats of formation and that of the solvate is therefore a measure of binding energy of the solvate.

Correspondingly, the calculation of the heat of solution of a crystalline solvate in an excess of the same solvent must take account of the transfer of solvent molecules from their state in the solvate to their state in 'solution' in itself. Consider solution of Na2CO3.10H2O in water to a concentration of 1 mole/100 H2O.



A non-crystalline example of this is ammonia, the name often being applied loosely to both gas (NH3) and aqueous solution (NH4OH). The heat of formation of NH4OH includes the contribution from the H20. If ammonia is written in a reaction scheme as NH4OH and the corresponding value taken, it is essential that the water derived from it 8.3 Integral and Differential Heats Heats of solution/dilution at a given temperature vary with the concentration of the solution and the distinction between integral and differential heats can cause many problems. 8.3.1 Integral heat of solution The integral heat of solution is the total heat change per mole solute when it is dissolved in a given quantity of solvent. The heat usually increases to a constant value as the solution becomes more dilute. It may be exo- or endothermic. In Figure 2 the heat at a point X is the integral heat for solution up to a given concentration.



FIGURE 2 INTEGRAL AND DIFFERENTIAL HEATS OF SOLUTION

8.3.2 Differential heat of solution The differential heat of solution is the heat change per mole solute when it is dissolved in a large excess of solution at a particular concentration. It is thus the heat per mole of solute at any point during the course of the solution process, and equals the tangent to the integral curve in Figure 2. Heat of solution data are normally tabulated: (a) As heats of formation of pure solute and at several dilutions, from which

the integral heat of solution is derived, or; (b) As integral heats of solution to a specified dilution. For the purpose of calculating process heat changes it is strongly recommended that the overall concentration change is identified and the corresponding total heat is calculated from the above data. It should be noted the differential heat of solution carries no implication of heat flow rate, i.e. differential with respect to time.



The experimental determination of heats of solution is similar to reaction heats and is referred to in Clause 9. The nature of the experiment determines whether the integral or differential heat is measured directly. It follows there must be a clear understanding of the nature of the data required and the significance of the experimentally determined data; the onus is on the user and supplier of the data to ensure this is understood. 9 EXPERIMENTAL DETERMINATION OF THERMOCHEMICAL

PARAMETERS It is not the purpose of this Guide to detail experimental calorimetric techniques for the determination of thermochemical parameters. It is pertinent, however, for the process engineer to be aware of the different techniques and the information obtained from them. For process engineering applications, experimental calorimetry is generally concerned with accurate direct measurement of parameters for plant design or safety. Those considered in this section are heats of reaction, solution/ dilution and mixing, the principles being essentially the same for all these processes. 9.1 Isoperibol Calorimetry for Heats of Reaction and Solution The principle of this method is that by holding the calorimeter in a constant temperature environment an accurate correction can be applied to the experimentally determined heat for the heat transfer to or from the calorimeter during the experiment. It is based on the calorimeter and thermostat bath being in thermal equilibrium before and after a reaction, and determination of the temperature rise (or fall) associated with a known extent of reaction. The technique is limited to small temperature rises but use of high precision temperature measurement and thermostatic control and accurate determination of reactant quantities can enable high calorimetric precision to be attained. For many purposes this method offers the greatest accuracy and precision.



In normal operation, small quantities of reactant A are added to an excess of reactant B, which must be liquid/solution. By successive increments the total heat of reaction is determined. The separate heats for each increment represent the differential heat for that extent of reaction; it is common to find a change over the course of the reaction. Similarly, addition of successive quantities of a solute gives the differential heat of solution; integration of the resulting curve thus gives the integral over the chosen concentration limits. The technique is most conveniently applicable to reactions going to completion within 20 minutes and at temperatures in the range 0–100°C. It has been operated at Blackley, however, between –50 and 250°C (the latter at high pressure) and could in principle be operated at higher temperatures. 9.2 Heat Flow Calorimetry Heat flow calorimeters are based on the measurement of the heat flow requirement to maintain a system at constant temperature. In the single reaction cell types, this is achieved by measuring a variable cooling demand or by applying a constant cooling effect and measuring the variable power required to maintain the temperature during a reaction. This type of calorimeter has the advantage of permitting continuous charging of the second reactant. The observed heat flow rate (with respect to time) is dependent on the feed rate but integration gives the total heat for a given addition. The differential process heat (see 8.3) can also be derived. An advantage of this type of calorimeter is its convenience for carrying out a complete stoichiometric charge and simulating pump-fed batch processes. It is limited by the need to balance the cooling capacity (assuming an exothermic reaction) and the reaction heat flow, the maximum charging rate being determined by this balance. Problems may also be caused by changes in heat transfer behavior. There are various forms of heat flow calorimeter for different applications but it is most common for liquid or gas to be charged to a liquid/solution. An alternative type from above is the twin-cell microcalorimeter, so termed because the absolute heat flows are very small. These commercial instruments have very high sensitivity and may be used for measurement of slow reactions, e.g. with a duration of several days, and vaporization/sublimation. Most versions are not amenable to a wide variety of reactions.



9.3 Adiabatic Calorimeter The adiabatic calorimeter is based on the elimination of heat transfer between the calorimeter and its surroundings. This requires maintaining a very small temperature difference by adjusting the jacket temperature to follow that of the calorimeter. For accurate work this method is best suited to slow reactions, the limit being determined by the maximum rate at which the jacket can follow the calorimeter. It offers the advantage, however, of allowing a complete batch charge in one step but the evaluation of the result may be complicated by other processes (e.g. vaporization) if a large temperature rise ensues. The relationship between temperature rise and process heat is determined by electrical calibration. 9.4 Differential Scanning Calorimetry Differential scanning calorimetry (DSC) is a widely used technique for measurement of many thermal properties. Strictly, it is a type of heat flow calorimetry but that term is reserved for the isothermal instruments described in 9.3 above. DSC is one of a range of techniques collectively known as 'thermal analysis'. DSC functions by measuring the heat flow to/from a sample, relative to a reference, as its temperature is programmed upwards or held isothermal. The direct signal is thus heat flow and total heat is obtained by integration. Modern DSCs are sophisticated instruments and offer many options for data processing and application. DSC is the most widely used and rapid calorimetric technique for most purposes but it cannot approach the precision of other instruments. Nevertheless, for many purposes it is capable of ±5–10% which is adequate for many engineering purposes. It has the disadvantage that materials cannot be agitated or mixed at a given temperature, or added continuously, and accurate quantitative measurements at elevated temperatures require more attention to calibration than is normally suggested. The major applications are measurements of heats of fusion and heats of reaction. While it is relatively difficult to simulate some plant conditions, the instrument is ideal for determination of specific properties and its ease of control allows the ingenious thermal analyst to devise procedures to measure the required property and relate it to the chemical or physical process. Many DSCs have crucibles suitable for operation at high pressures.



10 COMPUTER CALCULATION OF ENTHALPY OR TEMPERATURE The GBHE VAULT and CHEMCAD are major parts of the process engineers tool-kit and can display physical data for mixtures over a range of temperatures and pressures, and can also perform thermodynamic calculations. Other programs can be interfaced to CHEMCAD, the calculation routines used by “The VAULT”. This system has a number of different methods for calculating enthalpy, ranging from simple polynomial correlations in temperature to sophisticated correlations involving both temperature and pressure. For physical operations (i.e. operations where there is no chemical change), the datum points of these correlations (i.e. the temperature and pressure at which the correlations calculate zero) are irrelevant, except perhaps for reasons associated with the numerical methods used by the computer, or the machine's precision. This assumes, however, that the correlations used for a component in different phases have a common datum. “The VAULT” uses the Ideal Gas Enthalpy = 0 at 25°C as the standard. The principle is that the specific enthalpy of any phase is the sum of the specific enthalpies of the components in that phase, weighted by the concentrations of those components, i.e.

Binns (1983) has reviewed the calculation of heats of reaction and the variation with temperature. He has also proposed a method for using the “The VAULT” and Physical Properties System to calculate enthalpies which incorporate heats of reaction. This means that the existing computer programs could be used for calculating heat balances across both physical and chemical operations. The principle of the method requires the definition of the specific enthalpy of a phase to be :



where: HAi(T)= Absolute specific enthalpy of the ith component at temperature T. This is defined as: HAi(T) = HFi(To) + Hi(T) – Hi(To) where: HFi(To) = Heat of formation of the ith component at defined state,

temperature And pressure; Hi(To) = Specific enthalpy of the ith component at defined state, temperature

and pressure, as calculated by the enthalpy correlation being used. Note: (To) need not be the same for all components. It is again emphasized that if different equations are used to calculate the H(T) and H(To) for a given component they must have a common datum. There is an option in “The VAULT” whereby the constant terms:

HFi(To) – Hi(To) can be added to the constant temperature/pressure independent term of the Hi correlation(s). This only available for temperature correlation methods and is invoked by setting the BASE parameter to 4 (see User Manual, Section 6.3). The facility can be used off-line by adding:

to the phase specific enthalpy as calculated by the “The VAULT”. This would allow the calculation of an enthalpy balance given initial and final mixture composition, temperature and pressure. Temperature from enthalpy can be calculated using the following approach:



where:

subscript r indicates reactant mixture p indicates product mixture

T1 = reactant temperature T2 = product temperature HT = heat transferred out of the system.

The first term on the left hand side is the enthalpy of the reactant mixture as calculated by The VAULT. The second and third terms would have been pre-estimated, using The VAULT” for the Hi(To) and Hj(To). The sum of the left hand side would be the enthalpy to be input to The VAULT” to calculate the temperature of the product mixture. It is possible to interface reactor model programs to the CHEMCAD such that these operations, described above in terms of The VAULT, can be performed by the model program, see Clause 5.



11 BIBLIOGRAPHY

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