Physical properties and thermochemistry for reactor technology

GBH Enterprises, Ltd.

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.

Refinery Process Stream Purification Refinery Process Catalysts Troubleshooting Refinery Process Catalyst Start-Up / Shutdown
Activation Reduction In-situ Ex-situ Sulfiding Specializing in Refinery Process Catalyst Performance Evaluation Heat & Mass
Balance Analysis Catalyst Remaining Life Determination Catalyst Deactivation Assessment Catalyst Performance
Characterization Refining & Gas Processing & Petrochemical Industries Catalysts / Process Technology - Hydrogen Catalysts /
Process Technology – Ammonia Catalyst Process Technology - Methanol Catalysts / process Technology – Petrochemicals
Specializing in the Development & Commercialization of New Technology in the Refining & Petrochemical Industries
Web Site: www.GBHEnterprises.com

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
4.2
4.3
4.4
4.5

Form of Equations
The Physical Property System: “The VAULT”
Physical Property Programs
Physical Property Estimation
Sources of Expertise

3
4
5
5
5

5

INTERFACING COMPUTER PROGRAMS TO THE
GBHE VAULT PHYSICAL PROPERTIES
PACKAGE

7

Preparation of the Physical Property Data

6

5.1


6

THERMOCHEMISTRY

6

6.1
6.2
6.3
6.4

Hess's Law
Standard States
Heats of Formation
Determination of Heats of Reaction

8
8
8
9

7

CALCULATION OF HEATS OF REACTION

9

7.1
7.2
7.3
7.4
7.5

Analogous Reactions
Heat of Formation Data Compilations
Estimation of Standard Heats of Formation
Heats of Neutralization
Temperature Effect on Heat of Reaction

9
10
10
13
14

8

HEATS OF SOLUTION, DILUTION AND MIXING

14

8.1

Calculation of Heats of Solution / Dilution from
Literature Data
Estimation of Heats of Solution and Mixing
Integral and Differential Heats

15
16
18

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

8.2
8.3

9

10

11

COMPUTER CALCULATION OF ENTHALPY OR
TEMPERATURE

BIBLIOGRAPHY

20

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 precomputer 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

EF
ER
ΔH

–
–
–

REACTION POTENTIAL ENERGY DIAGRAM

Activation energy of forward reaction;
Activation energy of reverse reaction;
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

6.2

ΔH

= ΔH1 + ΔH2 + ΔH3

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)

(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)

(b)

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

Must be used where data cannot be satisfactorily estimated.

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)

(4)

Avoids use of toxic/hazardous substances,

(5)

Does not allow for unknown side-reactions,

(6)

7

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

May require use of other parameters that are unknown or introduce
greater uncertainty.

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
D
ER
ES

=
=
=
=

Average bond energy term for each bond;
Heat of dissociation (atomization) of each element;
Resonance energy of compound in gas phase;
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

T1
T2
HT

=
=
=

r indicates reactant mixture
p indicates product mixture

reactant temperature
product temperature
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 preestimated, 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
[1]

J D Cox and G Pilcher, "Thermochemistry of Organic and
Organometallic Compounds" Academic Press (1970).

[2]

D R Stull, E F Westrum, and G C Sinke, "The Chemical
Thermodynamics of Organic Compounds" Wiley (1969).

[3]

J B Pedley, and J Rylance, "Sussex-NPL Computer-Analysed
Thermochemical Data," Univ of Sussex (1977).

[4]

J B Pedley, R D Naylor and S P Kirby, "Thermochemical Data of
Organic Compounds," Chapman and Hall (1986).

[5]

US National Bureau of Standards, Technical Notes 270-3 to 270-8,
"Selected Values of Chemical Thermodynamic Properties" (19681981).

[6]

Landolt-Bornstein, 6th ed. vol 2, "Kalorische Zustandgrossen"
Springer-Verlag (1961).

[7]

Perry and Green, "Perry's Chemical Engineers' Handbook", 6th ed.
McGraw-Hill (1984).

[8]

D R Lide (ed), "Handbook of Chemistry and Physics", 71st ed.,
Chemical Rubber Co. (1990).

[9]

JANAF Thermochemical Tables, 2nd ed. NSRDS-NBS37, US
National Bureau of Standards (1971).

[10]

S W Benson et al, Chem Revs 69 (1969), 279.

[11]

R C Reid, J M Prausnitz, and T K Sherwood, "The Properties of
Gases and Liquids", 3rd ed., McGraw-Hill (1977).

[12]

R C Reid, J M Prausnitz, and B E Poling, "The Properties of Gases
and Liquids," 4th ed., McGraw-Hill (1986).

[13]

J L Franklin, Ind. Eng. Chem. 41, 1070 (1949).

[14]

K R Verma and L R Doraiswamy, Ind. Eng. Chem. Fundamentals,
4, 389 (1965).


[15]

G E Coates and L E Sutton, J Chem. Soc. 1948, 1187.

[16]

L Pauling, "The Nature of the Chemical Bond," 3rd ed. Oxford Univ.
Press (1960).

[17]

J Timmermans, "The Physiochemical Constants of Binary Systems
in Concentrated Solutions" Vols 1-4, Interscience (1959).

[18]

J L Christenson, R W Hanks and R M Izatt, "Handbook of Heats of
Mixing," Wiley (1982).

[19]

J Bickerton, MSc Thesis, Univ. of Manchester (1981).

[20]

J A Dean (ed), "Lange's Handbook of Chemistry", 13th ed.,
McGraw-Hill, (1985).

[21]

R W Gallant, "Physical Properties of Hydrocarbons" Vols 1-2, Gulf
Publ. Co. (1968).

[22]

Hockley R (1991) TABLES User Manual, IC 01273/2.

[23]

Binns D T (1974) CL-R/HT/74/52.A. A Review of Physical Property
Correlations.

[24]

Hockley et al (1987) Physical Properties Package Interfacing
Manual, IC 06687.

[25]

Smithers J (1981) CL-R/81/1696/A Equations of State and their
Application to Phase Equilibrium.

[26]

Lyman W J Reehl W F and Rosenblatt D H (1982) Handbook of
Chemical Property Estimation Methods. Environmental Behaviour
of Organic Compounds (McGraw-Hill).

[27]

International Critical Tables (McGraw-Hill).

[28]

Binns D T (1983) Petrochemicals and Plastics Division R&T Paper
83/8. Facilitation of Reactor Heat Balances using the Company
Data Bank System.


Physical properties and thermochemistry for reactor technology

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Viewers also liked

Viewers also liked (18)

Similar to Physical properties and thermochemistry for reactor technology

Similar to Physical properties and thermochemistry for reactor technology (20)

More from Gerard B. Hawkins

More from Gerard B. Hawkins (20)

Recently uploaded

Recently uploaded (20)

Physical properties and thermochemistry for reactor technology