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Original citation: Glasser, Leslie and Jenkins, H. Donald Brooke. (2016) Predictive thermodynamics for ionic solids and liquids. Physical Chemistry Chemical Physics, 18 (31). pp. 21226-21240. Permanent WRAP url: http://wrap.warwick.ac.uk/81104 Copyright and reuse: The Warwick Research Archive Portal (WRAP) makes this work of researchers of the University of Warwick available open access under the following conditions. This article is made available under the Attribution-NonCommercial 3.0 Unported (CC BY-NC 3.0) license and may be reused according to the conditions of the license. For more details see: http://creativecommons.org/licenses/by-nc/3.0/ A note on versions: The version presented in WRAP is the published version, or, version of record, and may be cited as it appears here. For more information, please contact the WRAP Team at: [email protected]
21226 | Phys. Chem. Chem. Phys., 2016, 18, 21226--21240 This journal is© the Owner Societies 2016
Cite this:Phys.Chem.Chem.Phys.,
2016, 18, 21226
Predictive thermodynamics for ionic solids andliquids†
Leslie Glasser*a and H. Donald Brooke Jenkins*b
The application of thermodynamics is simple, even if the theory may appear intimidating. We describe
tools, developed over recent years, which make it easy to estimate often elusive thermodynamic parameter
values, generally (but not exclusively) for ionic materials, both solid and liquid, as well as for their solid
hydrates and solvates. The tools are termed volume-based thermodynamics (VBT) and thermodynamic
difference rules (TDR), supplemented by the simple salt approximation (SSA) and single-ion values for
volume, Vm, heat capacity, C�p, entropy, S�298, formation enthalpy, DfH1, and Gibbs formation energy, DfG1.
These tools can be applied to provide values of thermodynamic and thermomechanical properties such as
standard enthalpy of formation, DfH1, standard entropy, S�298, heat capacity, Cp, Gibbs function of formation,
DfG1, lattice potential energy, UPOT, isothermal expansion coefficient, a, and isothermal compressibility, b,
and used to suggest the thermodynamic feasibility of reactions among condensed ionic phases. Because
many of these methods yield results largely independent of crystal structure, they have been successfully
extended to the important and developing class of ionic liquids as well as to new and hypothesised
materials. Finally, these predictive methods are illustrated by application to K2SnCl6, for which known
experimental results are available for comparison. A selection of applications of VBT and TDR is presented
which have enabled input, usually in the form of thermodynamics, to be brought to bear on a range of
topical problems. Perhaps the most significant advantage of VBT and TDR methods is their inherent
simplicity in that they do not require a high level of computational expertise nor expensive high-
performance computation tools – a spreadsheet will usually suffice – yet the techniques are extremely
powerful and accessible to non-experts. The connection between formula unit volume, Vm, and standard
thermodynamic parameters represents a major advance exploited by these techniques.
Introduction
Consider what obliges one to attempt to estimate the propertiesof a known inorganic material or predict the properties of anas-yet unprepared material. Examine the complexities! Thereare about 100 chemical elements, which combine to form about100 million already-known compounds, of which some 10%could be classified as inorganic/mineral.1 There remains analmost limitless range of possible combinations as yet unexplored.By contrast, the most comprehensive current crystallographicdatabases report data on only about one million of these organiccompounds and on only about one-quarter of a million inorganic
compounds.2 Ionic liquids are combinations of such a broadrange of cations and anions so that the in-principle possiblenumber of such liquids is of the order of 1018 (although therealistically possible number is orders of magnitude smaller) –already, some 1000 have been reported in the literature.3 On theother hand, thermodynamic data is available for only some30 000 compounds, of which about 60% (20 000) are inorganic(see ESI† for a list of thermodynamic data compendia). Thus, thechance of finding the property data one seeks is miniscule; add tothis, the need to obtain data on as-yet unprepared material, such asmight be required for a proposed synthesis. As a consequence, anumber of simple empirical rules have been developed for a varietyof thermodynamic properties (see Table 1).
The most basic data that needs to be obtained for thisessentially unlimited set of materials is thermodynamic becausesuch data informs us of the stability of the materials, our ability tosynthesise them, and to maintain their integrity. In the absence ofpublished data, the question then arises as to how one shouldproceed in order to obtain that data.
The most fundamental approach would be through quantummechanical (QM) calculation,10 where one considers in detail
a Nanochemistry Research Institute, Department of Chemistry, Curtin University,
Perth 6845, Western Australia, Australia. E-mail: [email protected];
Fax: +61 8 9266-4699; Tel: +61 8 9848-3334b Department of Chemistry, University of Warwick, Coventry, West Midlands CV4
7AL, UK. E-mail: [email protected]; Fax: +44 (0)2476-466-747,
+44 (0)2476-524-112; Tel: +44 (0)2476-466-747, +44 (0)2476-523-265
† Electronic supplementary information (ESI) available: Lists of predictive thermo-dynamic group estimation methods, and of thermodynamic databases. See DOI:10.1039/c6cp00235h
Received 13th January 2016,Accepted 24th May 2016
DOI: 10.1039/c6cp00235h
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how the fundamental particles of which a material consists, suchas atoms and electrons, interact with one another throughelectrostatic forces, charge transfer, van der Waals (dispersion)interactions, electron correlation, and so forth. While such anapproach has yielded important results, it is complex, usesexpensive computation facilities, and requires considerableexpertise in both application and interpretation. At a somewhatsimpler level, density functional theory (DFT)11 has reduced thecomplexity of QM methods and, hence, their cost by relating theenergetics to the more readily computable electron density ofthe material and using functions of the electron density function(that is, functionals) to derive experimentally observable results.DFT has found increasing favour in recent years in providinguseful results but difficulties remain in dealing with dispersionand electron correlation. Thus, in stark contrast to the VBTapproach, these QM approaches require considerable expertiseto execute and interpret reliably.
A rational response has been to collect data on relatedmaterials and use that data to extrapolate (or interpolate) inorder to estimate the properties of the material under investiga-tion. We illustrate this approach in some general terms first, andthen focus on an approach which we have termed volume-basedthermodynamics (VBT)12,13 together with the thermodynamicdifference rule (TDR),9,14–16 both of which we and colleagueshave developed and fostered over the last two decades. Theseempirical procedures have proven to have great generality andutility, and have been widely implemented for ionic solids andliquids,17 as also illustrated in a list of applications in the finalsection of this paper. One further very successful method isthe ‘‘Simple Sum Approximation’’ (SSA)18 where the thermo-dynamic properties of a complex ionic, such as MgSiO3, istreated as a sum of its components, being the oxides MgO andSiO2 in this case.
Prediction basically relies on the combination, through theGibbs relation, of enthalpy, H, and entropy, S, contributions:19
DG = DH � TDS (1)
VBT and TDR provide estimates of values of standard enthalpy,DfH1, standard entropy, S�298, and hence, via eqn (1) lead to theprediction of DfG1 for individual materials as well as DrG1 for areaction of interest. It is often of little concern that suchestimates may not be highly precise, since the purpose ofthermodynamic prediction may, in many instances, simply beone of assessing synthetic feasibility or otherwise, i.e., simplywhether DrG is negative (feasible) or positive (infeasible inprinciple, although a small positive value, say B20 kJ mol�1,does not preclude formation of useful proportions of productwhich can be extracted from the reaction system).20 Furthermore,experimentally-derived thermodynamic values themselves canhave considerable uncertainties.21–23 The actual mathematicsrequired is minimal yet quantitative interpretation results. Thisreview summarises VBT, TDR, SSA, and single-ion additivity, andhighlights many of their successes – indeed, the scope of theirapplication has proved to be quite remarkable – and directs thereader to numerous applications where these procedures haveplayed a significant role in yielding the thermodynamics.
In essence, VBT [together with its isomegethic (‘‘equal size’’)rule,24 which vastly extends its application to new and hypothesisedmaterials] relates the formula unit volumes, Vm, of materials,however measured or estimated, to their thermodynamic quantities,thereby leading to practical prediction. TDR uses the differencesbetween related materials to predict values for other similarmaterials, while the additive SSA and single-ion values (and alsoTDR, in a slightly more complex way) demonstrate that theproperties of complex materials may be estimated by summingthe corresponding properties of their component parts.
Group additivity methods
Group methods operate by assuming that a material (typically,but not exclusively, an organic molecule) contains independententities (such as single bonds, double bonds, alcohol, amine, etc.)whose thermodynamic property values can be summed toproduce a property value for the whole material, but supplemented
Leslie Glasser
Leslie Glasser is South African-born with a degree in Applied &Industrial Chemistry, withdistinction, from Cape TownUniversity followed by a PhDfrom London University and aDIC from Imperial College. Hereturned to South Africa first asLecturer in Physical Chemistry atthe University of the Witwater-srand (‘Wits’) and then asProfessor at Rhodes Universityand, from 1980, again at Wits.He is an IUPAC Fellow and Life
Fellow of the Royal Society of Chemistry. He retired in 2000 asProfessor Emeritus and moved to Western Australia, where he isnow Adjunct Research Professor at Curtin University.
H. Donald Brooke Jenkins
Harry Donald Brooke Jenkins isEmeritus Professor of Chemistry,University of Warwick, U.K. Inter-national lecturer and researcherwith ongoing projects in Spain,Perth and Switzerland, he was,with Glasser, founder of the VBTand TDR approaches. He is authorof ‘‘Chemical Thermodynamics – ata glance’’ (Blackwell, Oxford), con-tributor to ‘‘Handbook of Chemis-try and Physics’’ and to NuffieldBook of Data. His interests arebridge, foreign travel, playing the
organ and painting. He has acted as consultant to numerous compa-nies, large and small, and has held several Directorships. His love ofthe repertoire has led him to arrange international organ concerts.
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by other terms to allow for the interactions between and amonggroups. (An extensive list of group methods is presented in ourESI.†) The most developed of these are termed Benson groupmethods.25 In order to permit broad application of the methods,it has been necessary to develop hundreds of group terms, withthe further complication of the necessity for the user to identifysuitable groups within the material under consideration. Manycomputer programs incorporate these methods, often as pre-liminary steps to a more complex analysis. The NIST WebBook26
provides a free service which implements the Benson groupadditivity scheme for gas-phase organic molecules.
Group methods have also been developed for ionic systems,by identifying constituent cations and anions whose propertiesare summed to provide the overall property value sought. Theresults are most reliable when based on related materials. Ingeneral, these methods have not received wide acceptance.
Volume-based thermodynamics
Early thermodynamic property-size relations were generallybased upon ion radii since the alkali metal and halide monatomic
ions of the most important alkali halides are spherical and radius,which could be quite readily established from X-ray data, was themost obvious measure of relative ion size. An important equationin this context was the Kapustinskii relation27 for lattice potentialenergy, UPOT:
UPOT ¼A nzþz�j jhri 1� r
hri
� �(2)
where z+, z�/electron units are the integer charges on thecations and anions, respectively, n is the number of ions performula unit, r is a compressibility constant (usually chosen asr = 0.345 nm), hri is the sum of the cation and anion radii(which is often equated to the shortest cation–anion distancefound in the lattice), and A (=121.4 kJ mol�1 nm) is anelectrostatic constant. While the contact distance, hri, betweencation and anion is a straightforward sum for simple ions, itbecomes ill-defined when complex ions are present. In additionto this conceptual problem, the Kapustinskii equation cannotbe applied beyond binary materials because (i) there is no
Table 1 Some empirical thermodynamic and volume rules
Rule Thermodynamic property Value Ref.
Dulong and Petit and Neumann–Koppsummation: heat capacity
Cp, per mole for atoms in solids E3R E 25 J K�1 mol�1
where R is gas constant4
Trouton: vaporization DvapS1 for organic molecules andnon-polar liquidsDvapH1 for organic molecules andnon-polar liquidsFor hydrogen bonding in liquids
DvapS1/J K�1 mol�1 E 85DvapH1/kJ mol�1 E 85Tb/KTb = boiling pointDvapH1/kJ mol�1 4 85Tb/K
Walden: fusion DfusS1 for rigid non-spherical molecules E20–60 J K�1 mol�1
Richards: fusion DfusS1 for rigid spherical molecules E7–14 J K�1 mol�1 5
Glasser & Jenkins: Cp, for silicate anions Single ion heat capacity, Cp, for silicateanions
E13.8n where n is the number of atomscontained within the silicate anion
6
Glasser & Jenkins: Cp for general anions Single ion heat capacity, Cp for generalanions
E17n where n is the number of atomscontained within the anion
6
Westwell, Searle, Wales & Williams:sublimation enthalpy from melting point
DsublH1 for molecules that do not possessinternal rotors, such as long chainorganic molecules
DsublH1/kJ mol�1 = 0.188Tm/K + 0.522Tm = melting pointR2 = 0.90
7
Westwell, Searle, Wales & Williams:sublimation enthalpy from boiling point
DsublH1 for molecules that do not possessinternal rotors, such as long chainorganic molecules
DsublH1/kJ mol�1 = 0.119Tb/K + 1.38Tb = boiling pointR2 = 0.96
Westwell, Searle, Wales & Williams:vaporization enthalpy of solids
DvapH1 for molecules that do not possessinternal rotors, such as long chainorganic molecules
DvapH1/kJ mol�1 = 0.166Tm/K � 3.99Tm = melting pointR2 = 0.86
Westwell, Searle, Wales & Williams:vaporization enthalpy of liquids
DvapH1 for molecules that do not possessinternal rotors, such as long chainorganic molecules
DvapH1/kJ mol�1 = 0.108Tb/K � 5.08Tb = boiling pointR2 = 0.98
Westwell, Searle, Wales & Williams:Tb from Tm
Tb from Tm for molecules that do notpossess internal rotors, such as longchain organic molecules
Tb/K = 1.52Tm/K + 14.5Tb = boiling pointTm = melting pointR2 = 0.86
Westwell, Searle, Wales & Williams:vaporization and sublimation enthalpies
DvapH1 for molecules that do not possessinternal rotors, such as long chainorganic molecules
DvapH1/kJ mol�1 = 0.889DsublH1/kJ mol�1 � 4.75R2 = 0.98
Kempster & Lipson; Glasser & Jenkins:formula unit volume
Vm mainly for organic solids Vm E 0.018 nm3 per atom 8Vm for water Vm E 0.0245 nm3 (see Table 3)9
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provision for more than one type of cation–anion contact, nor(ii) can more than a pair of charge types be accommodated.
Mallouk, Bartlett and coworkers28–31 presented some relation-ships between formula unit volume, Vm and thermodynamicproperties (notably lattice energy, UPOT, as a function of Vm
�1/3)and standard entropy, S�298 (as a function of Vm) but only for ahandful of MX (1 : 1) simple salts. Jenkins, Roobottom, Passmoreand Glasser32 explored these relationships further, by (i) replacingthe distance sum with the equivalently-dimensioned cube-rootof the formula unit volume, Vm
1/3, and (ii) using a generalisationof the charge product33 into an ionic strength factor-type sum-mation, I:
nzþz�j j )Xi
nizi2 ¼ 2I (3)
where ni = number of ions of type i in the formula unit.Scheme 1 summarises the processes and equations which
use material volumes to produce thermodynamic values.
Lattice energies for a large database of simple ionic solidscould be reliably correlated using this linear VBT function:34
UPOT ¼ 2Ia
Vm1=3þ b
� �ð4; Scheme1Þ
where a and b are empirical constants which differ dependingon stoichiometry, and have been determined by fitting toextensive experimental data.32 It is noteworthy that the fittedconstant, a, is found always to be close in value to the electrostaticfactor, A, in eqn (2), above.
Equivalent equations may be couched in terms of density,rm, and formula mass, Mm:
UPOT/kJ mol�1 = g(rm/Mm)1/3 + d (4, Scheme 1)
UPOT/kJ mol�1 = B(I4rm/Mm)1/3 (5, Scheme 1)
where B is a combined constant.For lattice energies greater than 5000 kJ mol�1, which includes
most minerals, a limiting version35 of this equation exists whichcontains no empirical constants whatsoever and yet satisfactorilypredicts lattice energies up to 70 000 kJ mol�1 and probablybeyond:
UPOT = AI(2I/Vm)1/3 (5, Scheme 1)
Lattice energy is readily converted to lattice enthalpy36 (as itneeds to be if it is to be included in an enthalpy-based thermo-chemical cycle such as that in Fig. 1 below) using the equation:
DLH ¼ UPOT þXni¼1
sici
2� 2
� �RT (9)
Scheme 1 Volume-based thermodynamics (VBT) flowchart. Data sourcesof various kinds are used to generate a formula unit volume, Vm, from whichthermodynamic properties are estimated. P(MpXq) represents any thermo-dynamic property, P, of the material MpXq. a, b, g, d, A, B, k, c, c0, k0 and k00
represent various constants obtained by fitting to experimental data.Eqn (4)–(8) appear in this scheme.
Fig. 1 Born–Haber–Fajans cycle for solids and aqueous solutions of formulaMpXq. IP = ionisation potential; EA = electron affinity; lattice enthalpy (DLH)and enthalpies of formation (DfH), sublimation (DsublH), dissociation (DdissH),hydration (DhydrH), and solution (DsolnH) are involved. UPOT represents the latticepotential energy. In the formula for DLH, m depends on p and q and the natureof the ions Mq+ and Xq� (see eqn (9) in text).36
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where DLH is the lattice enthalpy, n is the number of ion types inthe formula unit, si is the number of ions of type i, and ci isdefined according to whether ion i is monatomic (ci = 3), linearpolyatomic (ci = 5), or nonlinear polyatomic (ci = 6).
Using these approaches, it becomes simple to evaluate thelattice energies, UPOT (and enthalpies of formation, DfH1, viathe Born–Haber–Fajans relation) of ionic solids.
Thermodynamic difference rule (TDR)
The thermodynamic difference rule, TDR, is a complementaryset of procedures which utilizes additive connections amongrelated materials.9,12–16 Scheme 2 shows the steps by whichTDR is usually applied. The technique is extremely powerful asa result of its ability to enable estimates to be made ofthermodynamic data not otherwise available.
P(MpXq�nL,s) � P(MpXq,s) = nyP(L, s–s) (11a)
P(MpXq�mL,s) � P(MpXq�nL,s) = (m � n)yP(L, s–s) (11b)
Thus, various thermodynamic state properties may be estimatedas, for example, the lattice energies of hydrates using the thermo-dynamic difference rule relation:
UPOT(MpXq�nH2O,c) � UPOT(MpXq,c) = nyU(H2O) (12)
with yU(H2O) = 54.3 kJ mol�1, as empirically determined.Table 2 lists values for the fitted constants for various groupsof materials, while Table 3 lists values pertaining to the hydrateTDR rules. TDR constants for other solvates may be found inTable 1 in the literature referenced.9 An important recent paperconsiders the thermodynamics of hydration in minerals.37
Room-temperature ionic liquids
Room-temperature ionic liquids (RTILs)38–41 can replace organicsolvents used for the dissolution of both polar and non-polarsolutes and for processing or extraction of materials, while alsohaving useful catalytic features.42 ILs are low-polluting, with lowcombustibility, good thermal stability and low vapour pressures.They have high viscosities, and their liquid range can often coverseveral hundred degrees. The range of their applications has beenextended by use of mixtures of IL’s43 and as supercritical fluids.44
As their name implies, they are usually liquid at ambienttemperatures and consist solely of ionic species. In order toreduce the lattice energy of their crystalline state and hencetheir melting point, one or sometimes both of their cations andanions need to be large and their cations also often have lowsymmetry. The cations are generally organic with long-chainfeatures and buried charges, such as the pyrollidinium, methyl-imidazolium and pyridinium cations (see Fig. 2) while theanions, such as BF4
�, PF6�, or NTf2
� [formula: (CF3SO2)2N�]have diffuse charges.
Since there are, as noted above, many possible combinationsof cation and anion, it becomes possible to consider designingionic liquids to purpose. Although early QSAR predictions45–47
were not always regarded as satisfactory,48 molecular volume49
has emerged as an important observable. Thus, Glasser38 hasestimated a VBT-based entropy for ionic liquids, derived fromcorrelations for both inorganic solids and organic liquids:
S (J K�1 mol�1) = 1246.5(Vm/nm3) + 29.5 (13)
Similarly, Gutowski, et al.,50–52 have developed a lattice energycorrelation for 1 : 1 ionic liquids, with amended constants (eqn (4),Scheme 1): I = 1, a = 8326 kJ nm mol�1 and b = 157 kJ mol�1.
VBT relations have now been used to establish other physicalthermodynamic properties, independent of crystal structure,such as liquid entropy,53 melting point,54–56 heat capacity57
and critical micelle concentration (c.m.c.).58 A recent review byBeichel59 cites relevant literature from the Krossing laboratory;in order to emphasize lack of reliance on any experimental inputat all, this group has introduced the term ‘‘augmented volume-based thermodynamics’’.
An explanation for the simple volume relations
The striking simple relations to volume involved in VBT, almostindependent of structure, upon which we have reported invitesome explanation. We suggest that the bulk thermodynamic
Scheme 2 Thermodynamic difference rule (TDR) flowchart. The volumeof addend or solvate, L, is subtracted to generate the volume of the parentmaterial:
V(MpXq�nL) � nV(L) = V(MpXq) (10)
from which the thermodynamic property, P, is calculated. Finally, thethermodynamic property value, yP(L, s–s), of the addend or solvent (whichmay be water) is added (where ‘‘s–s’’ represents that the difference, yP,between materials each in the same phase, often solid).
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properties derive from the interactions between the particlesinvolved (complex ions or even molecules) rather than withinthose particles.60 For ionic materials, the interactions are largelycoulombic (electrostatic or Madelung energies) with lesser contribu-tions from specific repulsion and van der Waals-type interactions sothat (to the approximation inherent in our correlations) the interac-tions are similar, independent of the specific species involved andalso independent of structure. At this level of approximation we have
found that the thermodynamic values that emerge prove adequate,in the majority of cases, for deciding questions of alternativesynthetic routes for the preparation of inorganic materials.
Table 2 Constants for a selection of volume-based thermodynamic relations
Material Ionic strength factor, I a/kJ mol�1 (nm3 formula unit�1)�1/3 b/kJ mol�1 Mean absolute error (%)
Lattice energy from volume data, UPOT/kJ mol�1 = 2I(a/Vm1/3 + b) (4)
MX (1 : 1) 1 117 52 4MX2 (2 : 1) 3 134 61M2X (1 : 2) 3 165 �30MX (2 : 2) 4 119 60MpXq
12(pq2 + qp2) 139 28
Material Ionic strength factor, I g/kJ mol�1 cm�1 d/kJ mol�1 Mean absolute error (%)
Lattice energy from density data, UPOT/kJ mol�1 = g(r/M)1/3 + d (5)MX (1 : 1) 1 1981.2 103.8 4MX2 (2 : 1) 3 8375.6 �178.8M2X (1 : 2) 3 6764.3 365.4MX (2 : 2) 4 6864.0 732.0MpXq
12(pq2 + qp2) 2347.6 � I 55.2 � I
k/J K�1 mol�1 (nm�3 formula unit) c/J K�1 mol�1 Mean absolute error (%)
Entropy, S/J K�1 mol�1 = kVm + c (6)Anhydrous ionic salts 1360 � 56 15 � 6 12Hydrated ionic salts 1579 � 30 6 � 6 7.4Organic liquids 1133 � 7 44 � 2 5.7Organic solids 774 � 21 57 � 6 10.4
k0/J K�1 mol�1 (nm�3 formula unit) c0/J K�1 mol�1 Mean absolute error (%)
Heat capacity, Cp/J K�1 mol�1 = k0Vm + c0 (7)Non-framework silicates 1465 11General ionic solidsa 1322 �0.8 24.5Ionic liquids 1037 45
k00/GPa�1 (nm�3 formula unit) Mean absolute error (%)
Isothermal compressibility, b/GPa�1 = k00Vm (8)General ionic solids (no alkali halides) 0.634 12Perovskites 0.472 7
a Cp values have been estimated for 799 materials, ranging from small ionics to large mineral structures. Poor outliers may be avoided by using thelesser of the calculated value from eqn (7) and the approximate limiting Dulong–Petit value of 25 � m J K�1 mol�1, where m = number of atoms inthe formula unit (cf. Table 1).
Table 3 Thermodynamic difference values, yP, for hydrates for propertyP: P(MpXq�nH2O) � P(MpXq) = nyP(H2O,s–s)a
Thermodynamic property, P yP9
Vm/nm3 (mol of H2O)�1 0.0245UPOT/kJ (mol of H2O)�1 54.3DfH/kJ (mol of H2O)�1 �298.6DfS/J K�1 (mol of H2O)�1 �192.4DfG/kJ (mol of H2O)�1 �242.4
S�298
.J K�1 mol of H2Oð Þ�1 40.9
Cp�298
.J K�1 mol of H2Oð Þ�1 42.816
a A more complete table, including values of yP for solvates other thanH2O, has been published.16
Fig. 2 Principal cations involved in important ionic liquids. (I) Imidazoliumcations, (II) pyridinium cations, (III) tetraalkylammonium cations, (IV) tetra-alkylphosphonium cations, and (V) pyrollidinium cations.
Perspective PCCP
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
016.
Dow
nloa
ded
on 1
8/08
/201
6 14
:17:
00.
Thi
s ar
ticle
is li
cens
ed u
nder
a C
reat
ive
Com
mon
s A
ttrib
utio
n-N
onC
omm
erci
al 3
.0 U
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Tab
le4
Sin
gle
-io
nad
dit
ive
volu
me
s,e
ntr
op
ies
and
he
atca
pac
itie
sfo
ra
ran
ge
of
ino
rgan
icca
tio
ns
and
anio
ns.
No
teth
atth
eva
lue
slis
ted
for
H2O
we
reu
sed
asre
fere
nce
valu
es
inth
eo
pti
miz
atio
ns
tog
en
era
teth
ese
sin
gle
-io
nva
lue
s
Cat
ion
Vol
um
e/n
m3
S� ion
� JK�1mol�
1C
p(2
98) io
n/
JK�
1m
ol�
1�D
fH(2
98)/
kJm
ol�
1�D
fG(2
98)/
kJm
ol�
1A
nio
nV
olu
me/
nm
3S� ion
� JK�1mol�
1C
p(2
98) io
n/
JK�
1m
ol�
1�D
fH(2
98)/
kJm
ol�
1�D
fG(2
98)/
kJm
ol�
1
NH
4+
0.03
5667
.0F�
0.01
420
.65
5.0
Li+
0.00
6719
.421
.130
8.7
259.
8C
l�0.
0298
36.1
23.5
110.
811
3.7
Na+
0.01
5837
.229
.727
8.3
232.
2B
r�0.
0363
48.6
26.6
66.3
70.6
K+
0.02
7750
.531
.431
625
8.7
I�0.
0488
56.8
28.3
�8.
20.
0R
b+0.
0341
63.1
31.3
311.
725
7.4
N3�
0.04
1654
.8C
s+0.
042
69.2
31.7
315.
426
0.4
O2�
0.01
347.
4A
g+29
.9O
H�
0.01
8420
.721
.222
8.6
247.
9M
g2+
0.00
4920
.526
.149
1.4
374
S2�
0.03
222
.1C
a2+
0.02
0132
.528
.957
9.8
468.
2C
lO3�
70.1
68.5
Sr2
+0.
0213
37.9
30.3
627.
255
8.7
BrO
3�
76.1
39.7
Ba2
+0.
027
55.1
30.2
655
570.
1C
O3
2�
0.04
2652
.657
.559
4.3
582.
7M
n2
+30
.426
2.9
161.
3N
O3�
0.04
9278
.5Fe
2+
0.00
6738
.631
.813
8.5
32.3
PO4
3�
0.05
771
.8Zn
2+
0.01
2537
.3SO
42�
0.06
1174
.371
.581
2.2
802.
3C
u2
+0.
0053
33.5
ClO
4�
0.06
1910
5.8
134.
9N
i2+
0.00
0429
.612
6.7
Mn
O4�
0.06
65C
o2+
0.00
1939
.532
.016
1.8
AsO
43�
0.06
58Fe
3+
0.00
6128
.220
8.2
60.0
VO
43�
0.06
63A
l3+
17.3
20.9
630.
146
2.5
Fe(C
N) 6
4�
219.
8La
3+
28.8
785.
959
5.3
Cr3
+31
.028
2.1
85.6
Fe3
+30
.7Si
O3
2�
57.5
810
56.9
1090
.1Sc
3+
0.00
35Si
O4
4�
68.9
311
98.5
1300
.8Lu
3+
0.01
02Si
O5
6�
82.1
813
44.4
1520
.9Y
b3
+0.
0111
Si2O
52�
101.
8619
62.7
1920
.0T
m3
+0.
011
Si2O
76�
127.
422
46.4
2361
.2E
r3+
0.01
26Si
2O
10
12�
162.
2Y
3+
0.01
31Si
3O
10
8�
182.
7733
15.1
3476
.7D
y3+
0.01
37Si
5O
18
16�
317.
2156
60.3
6050
.0T
b3
+0.
0148
Si4O
11
6�
213.
0940
98.6
4108
.7G
d3
+0.
0133
Eu
3+
0.01
46Sm
3+
0.01
64Si
4+
24.5
Ti4
+35
.2H
2O
0.02
4540
.941
.328
5.8
237.
1
PCCP Perspective
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
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00.
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ticle
is li
cens
ed u
nder
a C
reat
ive
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mon
s A
ttrib
utio
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erci
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As we have noted above, an important consequence of theindependence of structure is that these relations apply equallyto pure liquids as to solids, so that they can be applied to theincreasingly important class of ionic liquids.38
Madelung energies – for known structures
The coulombic (or Madelung) energy, EM, of a material ofknown structure is readily calculated by means of standardcomputer programs, such as GULP61 and EUGEN.62 This energycorresponds to separating the constituent ions into indepen-dent gas phase ions against coulombic forces only. We haveobserved63 that the resulting Madelung energy is closely relatedto the corresponding lattice energy, in the form
UPOT/kJ mol�1 = 0.8518EM + 293.9 (14)
Eqn (14) thus provides a further simple direct means forobtaining lattice energies, apart from VBT. However, the Madelungcalculation comes into its own when applied to an ionic systemwith structures containing covalently-bonded complexes, such asK2SnCl6. If the complex ion, SnCl6
2� in this case, is treated as a‘‘condensed ion’’, with all the ion charge placed on the centralatom (thus Sn2�) and the ligands given zero charge (Cl0), then weare effectively dealing with a system which decomposes to 2K+(g) +Sn2�(g) when the Madelung energy, now EM
0, is supplied. Forthis system
UPOT/kJ mol�1 = 0.963EM0 (15)
From these values, we can determine a formation energy forthe ‘‘condensed ion’’ complex (see example below).
Isomegethic rule
Our isomegethic (‘‘equal size’’) rule24 states that ‘‘ionic salts of thesame empirical chemical formula having identical charge states(i.e., lattice ionic strength factors, I) will have approximately equalformula unit volumes, Vm.’’ Since I, Vm and stoichiometry are thenapproximately identical, isomegethic compounds will have almostidentical lattice potential energies too.
As an illustration, consider the relation:
Vm(NO+ClO4�) E Vm(NO2
+ClO3�) E Vm(ClO2
+NO3�) (14a)
and hence:
UPOT(NO+ClO4�) E UPOT(NO2
+ClO3�) E UPOT(ClO2
+NO3�) (14b)
Good examples of the scope of the isomegethic rule in providingmultiple estimates for the volumes of ions are given in detail inref. 24 and 64. Relations of this kind provide enormous scopefor estimation of formula unit volumes and lattice energies,
which is especially useful for hypothesised materials. If theenthalpies of formation of the individual gaseous componentions are known65,66 then the enthalpy of formation of theisomegethic compound may usually be estimated, thus takingus into the full compass of the thermodynamics of the materialconcerned.
Single-ion values
Since it is seldom that all the desired thermodynamic values areavailable to generate the desired data, we have prepared sets ofinternally consistent single-ion values which may be used additivelyto generate otherwise absent data, collected in Table 4. An earlyexample of this procedure is provided by the work of Latimer67,68 indeveloping single ion entropy estimates.
An example set of predictive thermodynamic calculations:K2SnCl6
We here provide a set of results for the material dipotassiumhexachlorostannate, K2SnCl6, where we have deliberately selectedthe difficult case of a partially covalent material for whichexperimental thermodynamic values are available for comparison.This demonstrates some of the weaknesses of these predictivemethods against some of their strengths in that they may providea wide range of otherwise unavailable thermodynamic values.
Simple salt approximation (SSA). Table 5 demonstrates thefeatures of the ‘‘Simple Salt Approximation’’ in generatingresults by combining reaction components.
For the SSA to be accurate, it is necessary that the reaction to formproduct should yield zero (or small) thermodynamic differences.As may be seen from the final column in Table 5, the reaction2KCl + SnCl4 - K2SnCl6 produces non-zero differences, so thatthe SSA results (3rd last column) are not accurate, but may beuseful as a general guide when the thermodynamic values areunknown.
Volume-based thermodynamics (VBT). VBT is a specificallyionic-based set of empirical procedures, correlated againststrongly ionic materials such as simple halides and morecomplex oxides. We examine its application to K2SnCl6 withits covalent central ion, SnCl6
2�.The constants used in the following calculations are selected
from Table 2.(a) Formula unit volume,70 Vm/nm3 = Vcell/Z = 1.0057/4 = 0.2514(b) Ionic strength factor, I ¼ 1=2
Pi
nizi2 ¼ 3 (eqn (3))
(c) Lattice (potential) energy, UPOT/kJ mol�1 = 2I(a/Vm1/3 + b)
(eqn (4)) = 2� 3 (165/0.25141/3� 30) = 1389 (cf. Born–Haber–Fajanscycle value71 = 1390, Fig. 3)
Table 5 Additive thermodynamic values for K2SnCl6, following the ‘‘Simple Salt Approximation’’.18 Data (columns 2, 3, 4 and 7) from HSC Chemistry 869
KCl SnCl4 K2SnCl6 2KCl + SnCl4 % Diff 2KCl + SnCl4 - K2SnCl6
DfH1(25 1C,s)/kJ mol�1 �436.7 �517.0 �1482.0 �1390.4 �6.2 �91.6S1(25 1C,s)/J K�1 mol�1 82.7 265.0 371.0 430.4 16.0 �59.4DfG1(25 1C,s)/kJ mol�1 �461.3 �596.0 �1592.6 �1518.7 �4.6 �73.9Cp(25 1C,s)/J K�1 mol�1 51.4 157.2 221.1 260.1 17.6 �39.0
Perspective PCCP
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
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on 1
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is li
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nder
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ive
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(d) Standard entropy, S/J K�1 mol�1 = kVm + c (eqn (6)) = 1360�0.2514 + 15 = 356.9 (cf. 371.0, diff. 3.9%, Table 5)
(e) Heat capacity, Cp/J K�1 mol�1 = k0Vm + c0 (eqn (7)) = 1322�0.2514 � 0.8 = 331.6 (cf. 221.1, diff. �33%, Table 5) (Neumann–Kopp atom additive value6 for 9 atoms = 25� 9 = 225: diff. 1.7%)
Comment: the VBT value calculated for Cp considerablyexceeds the 9-atom limiting Neumann–Kopp value, which wepropose is a preferred value (see Table 2). This suggests that therigid covalent SnCl6
2� structure corresponds to too-large avolume compared with a close-packed strictly ionic system.Correspondingly, the predicted entropy is also too large. Bycontrast, in calculating the lattice energy, any volume error isminimised by the use of a cube-root volume.
(f) DfH(SnCl62�,g)/kJ mol�1 = UPOT(K2SnCl6,s)71 +
DfH(K2SnCl6,s)69 � 2DfH(K+,g)71 = (1390) + (�1482) � 2(514) =�1120 (cf.65 �1156, diff. 3.1%)
(g) Madelung energy72 for K2SnCl6(s), EM/kJ mol�1 = 9322converted to UM/kJ mol�1 = 0.8518 � 9322 + 293.9 = 8234
Comment: see Born–Haber–Fajans cycle, Fig. 3.(h) Madelung energy, assuming the ‘‘condensed ion’’72
SnCl62�, EM
0/kJ mol�1 = 1613.7 converted to UPOT/kJ mol�1 =0.963 � 1614 = 1554
Comment: this result may be compared with the value notedin (c) above of 1390 kJ mol�1 (+11%).
Comment: see Born–Haber–Fajans cycle, Fig. 3.(i) By difference, dissociation energy to independent ions,
DdissH(SnCl62�,g) = 5199 kJ mol�1
Comment: this is a ‘‘new’’ value, not previously reported.(j) Lattice energy/kJ mol�1 to form independent gaseous ions
2 � K+ (DfH = 2 � 541.0),69 6 � Cl� (DfH = 6 � �227.6),69 andSn4+ (DfH = 9320.7)65 = 7501, diff. 10% from (g).
Tab
le6
Ap
plic
atio
ns
of
volu
me
-bas
ed
the
rmo
dyn
amic
s,V
BT
,an
dth
eth
erm
od
ynam
icd
iffe
ren
ceru
le,
TD
R
Vol
um
eB
ased
Th
erm
odyn
amic
s(V
BT
)or
Diff
eren
ceR
ule
(TD
R)
spec
ific
appl
icat
ion
Top
ictr
eate
dR
ef.
Th
erm
odyn
amic
sof
new
hom
opol
yato
mic
cati
onsa
lts
ofsu
lfu
ran
dse
len
ium
.A
stu
dy
des
ign
edto
inve
stig
ate
hit
her
tou
nkn
own
hom
opol
yato
mic
cati
onsp
ecie
sof
sulf
ur
and
sele
niu
m(e
.g.,
S 82
+an
dSe
82
+).
Th
ecr
ysta
llin
esa
lt,S
8(A
sF6) 2
and
its
sele
niu
man
alog
ue
wer
epr
edic
ted
,pri
orto
synt
hesi
s,to
bela
ttic
e-st
abil
ised
inth
eso
lid
stat
ere
lati
veto
the
corr
espo
nd
ing
AsF
6�
salt
sof
thei
rst
oich
iom
etri
call
ypo
ssib
led
isso
ciat
ion
.
73
Th
efl
uor
ide
ion
affin
ity
ofA
sF5
and
stan
dar
den
thal
pyof
form
atio
n,D
fH(A
sF6�
,g).
Tw
od
iffer
ent
valu
esfo
rD
fH1(A
sF6�
,g)
had
been
publ
ish
edin
the
lite
ratu
reat
the
tim
eof
our
inve
stig
atio
n.
Th
efi
rst
esti
mat
ew
asm
ade
byB
artl
ett,
etal
.Je
nki
ns,
Kro
ssin
g,Pa
ssm
ore
and
co-w
orke
rses
tim
ated
DfH
(AsF
6�
,g)
usi
ng
the
ther
moc
hem
ical
dat
afo
rth
esa
lts
[NF 4
+][
BF 4�
],[N
F 4+][
SbF 6�
],an
d[N
F 4+][
AsF
6�
],ob
tain
ing
ava
lue
wh
ich
was
low
erth
anB
artl
ett
etal
.’sva
lue.
Th
islo
wer
stan
dar
den
thal
pyof
form
atio
nim
plie
da
low
erfl
uor
ide
ion
affin
ity
ofA
sF5.I
nor
der
tod
ecid
ew
hic
hva
lue
(433
or46
7kJ
mol�
1)i
sli
kely
tobe
the
mor
eac
cura
te,w
em
odel
led
the
flu
orid
eio
naffi
nit
yu
sin
gab
init
iom
eth
ods
and
con
clu
ded
am
ost
like
lyva
lue
tobe
:430
.5�
5.5
kJm
ol�
1.I
na
furt
her
,lat
er,s
tud
yfu
rth
erFI
Ava
lues
wer
eas
sign
ed.
74–7
6
Th
erm
odyn
amic
sof
stab
ilis
atio
nof
S2+,
Se2
+an
dT
e2+
ion
sin
the
soli
dst
ate.
Ina
stu
dy
onth
eso
lvat
edsa
ltS 4
(AsF
6) 2�A
sF3
we
fou
nd
,u
sin
gth
eT
DR
,th
atth
eso
lvat
edsa
lt:
S 4(A
sF6) 2�A
sF3
was
mor
est
able
than
the
un
solv
ated
salt
,S 4
(AsF
6) 2
orm
ore
stab
leth
anth
ed
ecom
posi
tion
prod
ucts
ofS 4
(AsF
6) 2�A
sF3
(wh
ich
are
2S2A
sF6
(c)a
nd
AsF
3(l
)).S
uch
syst
ems
cou
ldn
oth
ave
been
exam
ined
ther
mod
ynam
ical
lyin
this
way
oth
erth
anby
usi
ng
VB
Tan
dT
DR
beca
use
ofth
eco
mpl
exit
yof
the
latt
ices
invo
lved
.
77
Stu
dy
offl
uor
ide
ion
don
orab
ilit
y.H
ere
was
stu
die
dth
eab
ilit
yof
flu
orid
eio
nd
onor
s,C
+F�
(s),
tod
onat
ea
flu
orid
eio
nto
anac
cept
or,
A(g
).T
he
tren
dam
ong
expe
rim
enta
list
sat
tem
ptin
gto
syn
thes
ise
incr
easi
ngl
ym
ore
effec
tive
flu
orid
eio
nd
onor
s:C
+F�
(s)
+A
(g)-
C+A
F�(g
)h
adbe
ento
incr
ease
the
cati
onsi
zefu
rth
eran
dfu
rth
erbu
tth
isst
ud
y,gu
ided
byV
BT
,sh
owed
that
ther
ew
asve
ryli
ttle
gain
edby
size
incr
ease
sbe
yon
da
crit
ical
leve
l.H
ere
VB
Tpl
ayed
ad
efin
ing
role
inth
atit
led
toan
abor
tion
ofce
rtai
nsy
nth
etic
wor
kw
hic
hw
asta
kin
ga
part
icu
lar
(un
frui
tfu
l)av
enu
eof
dev
elop
men
t.
78an
d79
Fig. 3 Born–Haber–Fajans cycle for K2SnCl6.
PCCP Perspective
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
016.
Dow
nloa
ded
on 1
8/08
/201
6 14
:17:
00.
Thi
s ar
ticle
is li
cens
ed u
nder
a C
reat
ive
Com
mon
s A
ttrib
utio
n-N
onC
omm
erci
al 3
.0 U
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ence
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This journal is© the Owner Societies 2016 Phys. Chem. Chem. Phys., 2016, 18, 21226--21240 | 21235
Tab
le6
(co
nti
nu
ed)
Vol
um
eB
ased
Th
erm
odyn
amic
s(V
BT
)or
Diff
eren
ceR
ule
(TD
R)
spec
ific
appl
icat
ion
Top
ictr
eate
dR
ef.
App
lica
tion
ofV
BT
and
TD
Rto
asse
ssm
ent
ofth
ere
lati
vest
abil
itie
sof
bisu
lfit
e(H
SO3�
)an
dm
eta-
bisu
lfit
e(S
2O
52�
)sa
lts.
Alt
hou
ghth
ebi
sulf
ites
,MH
SO3
(M=
Li,N
a,an
dK
),ar
ew
idel
ybe
liev
edto
best
able
com
pou
nd
s,th
eyh
ave
nev
erbe
enob
tain
edas
soli
ds.
VB
Tsu
gges
tsth
atth
eca
tion
volu
mes
,V m
(M+)
are
insu
ffici
entl
yla
rge
tost
abil
ize
the
HSO
3�
ion
rela
tive
toth
em
etab
isu
lfit
e,S 2
O5
2�
ion
.C
ryst
alli
ne
com
pou
nd
s,or
igin
ally
thou
ght
tobe
NaH
SO3
and
KH
SO3,
wer
eev
entu
ally
iden
tifi
edto
bem
etab
isu
lfit
es,N
a 2S 2
O5
and
K2S 2
O5.T
he
fact
that
RbH
SO3
and
CsH
SO3
can
beis
olat
ed,w
hil
stat
tem
pts
tocr
ysta
lliz
eM
HSO
3(M
=Li
,N
a,K
)le
adto
the
form
atio
nof
M2S 2
O5:
2MH
SO3(s
)-
M2S 2
O5(s
)+
H2O
(l)
has
been
expl
ain
edu
sin
gvo
lum
e-ba
sed
ther
mod
ynam
ics,
VB
T.
80
Use
ofV
BT
toid
enti
fyth
erm
odyn
amic
sof
com
plex
reac
tion
san
dto
assi
stin
dis
cern
ing
the
prob
able
syn
thet
icro
ute
offo
rmat
ion
ofpr
odu
cts.
Th
isap
plic
atio
nil
lust
rate
sth
ele
velo
fso
phis
tica
tion
ofth
eth
erm
och
emis
try
that
can
bed
ealt
wit
hu
sin
gV
BT
.Her
eth
esy
nth
esis
ofth
esa
lts
NO
[Al(
OR
) 4],
R=
C(C
F 3) 2
Phan
dC
(CF 3
) 3by
met
ath
esis
reac
tion
ofN
O[S
bF6]a
nd
the
corr
espo
nd
ing
Li[A
l(O
R) 4
]sa
lts
inli
quid
sulf
ur
dio
xid
eso
luti
onw
ere
stu
die
dan
dth
eco
mpl
ete
ther
mod
ynam
ics
invo
lved
inth
ere
acti
on(i
nth
eli
quid
sulf
ur
dio
xid
em
ediu
m):
3NO
(g)
+N
O2(g
)+
Li[A
l(O
R) 4
](s)
-N
O[A
l(O
R) 4
](s)
+Li
NO
3(s
)+
N2O
(g)
was
anal
ysed
usi
ng
VB
T,
wh
ereu
pon
itw
asse
enth
atan
un
favo
ura
ble
dis
prop
orti
onat
ion
reac
tion
:2N
O2(g
)-
NO
+(g
)+
NO
3�
(g)
ism
ore
than
com
pen
sate
dfo
rby
the
dis
prop
orti
onat
ion
enth
alpy
ofth
ere
acti
on:
3NO
(g)-
N2O
(g)
+N
O2(g
)an
dth
ela
ttic
een
ergy
ofLi
NO
3(s
).E
vid
ence
ispr
esen
ted
that
the
reac
tion
proc
eed
svi
aa
com
plex
ofLi
+w
ith
NO
,NO
2(o
rth
eir
dim
ers)
and
N2O
.
81
Ass
essm
ent
ofth
est
abil
ity
ofN
5+
salt
s.T
he
nit
roge
n-r
ich
ener
geti
csa
lts,
N5
+N
3�
and
N5
+N
5�
wer
ein
itia
lly
seen
ash
avin
gen
orm
ous
pote
nti
alas
envi
r-on
men
tall
ycl
ean
(fri
end
ly)
rock
etpr
opel
lan
tsan
dai
rcra
ftfu
els
offer
ing
the
poss
ibil
ity
ofch
eap
trav
el.
Th
eir
pote
nti
alca
ptu
red
the
exci
tem
ent
ofth
em
edia
.H
owev
er,
ina
theo
reti
cal
stu
dy,
VB
Tco
upl
edw
ith
abin
itio
calc
ula
tion
sfo
rth
esp
ecie
sN
3,N
3�
,N5
+an
dN
5�
show
edth
atn
eith
erN
5+N
3�
orN
5+N
5�
cou
ldbe
stab
ilis
edth
erm
odyn
amic
ally
and
that
they
wou
ldd
ecom
pose
inst
anta
neo
usl
yin
toN
3ra
dic
als
and
nit
roge
nga
s.
82an
d83
VB
Tan
dPr
uss
ian
blu
e–
aco
ntr
ibu
tion
toev
olvi
ng
tech
nol
ogy.
Th
isst
ud
yex
amin
edth
eso
lid
-sta
teth
erm
odyn
amic
sof
the
cati
onex
chan
ges
that
occu
rin
elec
troc
hro
mic
reac
tion
sof
Pru
ssia
nB
lue.
Th
ese
elec
troc
hem
ical
lyin
du
ced
chan
ges
ofva
len
ceth
atre
sult
inst
riki
ng
colo
rch
ange
sco
nst
itu
teth
epr
oces
sof
elec
troc
hro
mis
m,a
mod
ern
evol
vin
gte
chn
olog
yin
wh
ich
fin
al‘‘b
est
form
ula
tion
s’’a
reye
tbe
ing
sou
ght.
Ou
rst
ud
ypr
ovid
edan
inci
sive
ther
mod
ynam
iccl
arif
icat
ion
ofan
ill-u
nd
erst
ood
ion
exch
ange
that
acco
mpa
nie
sth
eea
rly
elec
troc
hro
mic
cycl
es.
Th
ere
sult
ssh
owed
byh
owm
uch
the
exch
ange
ofin
ters
titi
alFe
3+
ion
sby
alka
lim
etal
ion
s,as
exem
plif
ied
byK
+,
isth
erm
odyn
amic
ally
favo
ure
d.
84
Use
ofV
BT
toin
vest
igat
eth
eth
erm
odyn
amic
sof
an
ewbi
nar
yfl
uor
om
etal
dia
nio
n[T
i 4F 1
9]2�
pre-
pare
dby
auto
ion
isat
ion
ofT
iF4
byca
tion
com
plex
atio
nw
ith
crow
net
her
s.
Th
isap
plic
atio
nof
VB
Tsh
ows
how
the
met
hod
olog
yca
nbe
appl
ied
toin
vest
igat
en
ewan
dco
mpl
expr
oble
ms
inth
erm
odyn
amic
s.Fo
llow
ing
the
succ
essf
ul
prep
arat
ion
ofth
en
ewT
i 4F 1
92�
anio
n,
this
appl
icat
ion
was
use
dto
guid
esy
nth
etic
end
eavo
ur
byst
ud
yin
gw
het
her
the
Ti 4
F 19
2�
anio
nis
mor
eab
leto
form
salt
sw
ith
mon
oor
dic
atio
ns.
To
inve
stig
ate
this
we
con
sid
ered
two
reac
tion
s:2M
Ti 2
F 9(s
)-
M2T
i 4F 1
8(s
)(t
he
targ
etre
acti
on,
for
wh
ich
we
nee
ded
toes
tim
ateD
HE
DG
)an
dth
ega
sph
ase
dim
eris
atio
nre
acti
on:
2Ti 2
F 9�
(g)-
Ti 4
F 18
2�
(g).
85
Hyp
oth
etic
alco
mpo
un
ds
–n
itry
lch
lora
tean
dit
spo
ssib
lepr
epar
atio
n.
Vol
um
e-ba
sed
ther
mod
ynam
ics
(VB
T)
has
exam
ined
the
atte
mpt
edpr
epar
atio
nof
the
salt
,nit
ryl
chlo
rate
:[N
O2][
ClO
3].
Nit
rosy
lpe
rch
lora
te,
[NO
][C
lO4],
isa
know
nan
dst
able
salt
wh
ich
prov
oked
atte
mpt
sto
syn
thes
ize
the
isom
eric
nit
ryl
chlo
rate
,[N
O2][
ClO
3].
Ou
ris
omeg
eth
icru
leas
sign
sth
ese
two
mat
eria
lsto
hav
esi
mil
arla
ttic
epo
ten
tial
ener
gies
.Sil
ver
chlo
rate
,A
g[C
lO3],
was
reac
ted
wit
hn
itry
lh
exaf
luor
oan
tim
onat
e,[N
O2][
SbF 6
](i
nn
itro
met
han
e)at
room
tem
pera
ture
.Si
lver
hex
aflu
oroa
nti
mon
ate,
Ag[
SbF 6
]w
asid
enti
fied
ason
eof
the
reac
tion
prod
uct
sbu
tn
o[N
O2][
ClO
3]
was
det
ecte
d.
Nit
ric
acid
,H
NO
3,
was
fou
nd
asa
sid
epr
odu
ctan
dit
was
con
clu
ded
that
this
was
poss
ibly
cau
sed
byth
epr
esen
ceof
trac
esof
wat
erw
ith
inth
en
itro
met
han
eso
lven
tem
ploy
ed.A
fter
thre
eat
tem
pts,
we
fail
edto
prep
are
the
targ
etm
ater
ial,
[NO
2][
ClO
3].
How
ever
VB
Tca
lcu
lati
ons
ten
dto
con
firm
that
[NO
2][
ClO
3]i
sfo
rmed
butt
hen
dec
ompo
ses
inn
eatA
g[C
lO3]
and
[NO
2][
SbF 6
].
86
Nov
el,
stat
e-of
-th
e-ar
t,se
len
ium
chem
istr
yT
his
stu
dy
repr
esen
tsst
ate
ofth
ear
tch
emis
try
and
anex
trem
ely
com
plex
prob
lem
.Her
e7
7Se
NM
Rsp
ectr
osco
py,D
FTan
dM
Oco
mpu
tati
ons,
cou
pled
wit
hV
BT
and
TD
Res
tim
atio
ns,
wer
eu
tili
sed
toin
vest
igat
eth
ere
vers
ible
dis
soci
atio
nof
soli
dSe
6I 2
(AsF
6) 2�2
SO2
inli
quid
SO2
into
solu
tion
sco
nta
inin
g1,
4-Se
6I 2
2+
ineq
uil
ibri
um
wit
hSe
42
+,S
e 82
+an
dSe
10
2+
and
seve
nbi
nar
yse
len
ium
–iod
ine
cati
ons.
Th
est
ud
yal
sopr
ovid
edpr
elim
inar
yev
iden
cefo
rth
eex
iste
nce
and
stab
ilit
yof
the
1,1,
4,4-
Se4B
r 42
+an
dcy
clo-
Se7B
r+ca
tion
s.
87
Perspective PCCP
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
016.
Dow
nloa
ded
on 1
8/08
/201
6 14
:17:
00.
Thi
s ar
ticle
is li
cens
ed u
nder
a C
reat
ive
Com
mon
s A
ttrib
utio
n-N
onC
omm
erci
al 3
.0 U
npor
ted
Lic
ence
.View Article Online
21236 | Phys. Chem. Chem. Phys., 2016, 18, 21226--21240 This journal is© the Owner Societies 2016
Tab
le6
(co
nti
nu
ed)
Vol
um
eB
ased
Th
erm
odyn
amic
s(V
BT
)or
Diff
eren
ceR
ule
(TD
R)
spec
ific
appl
icat
ion
Top
ictr
eate
dR
ef.
Pred
icte
dst
abil
itie
sfo
rn
oble
-gas
flu
oroc
atio
nsa
lts
usi
ng
VB
T.
Inth
efe
wsi
tuat
ion
sin
nob
lega
s(N
g)ch
emis
try
wh
ere
ther
moc
hem
ical
fact
sar
ekn
own
,V
BT
can
beu
sed
tova
lid
ate
and
con
firm
thes
e.T
his
prov
ides
furt
her
evid
ence
that
,in
pred
icti
vem
ode,
resu
lts
from
VB
Tca
npr
ovid
ea
reli
able
guid
eto
ther
mod
ynam
icpo
ssib
ilit
ies.
Th
ela
ttic
een
ergi
es,
stan
dar
den
thal
pies
,an
dG
ibbs
ener
gies
offo
rmat
ion
for
salt
sco
nta
inin
gth
eN
gF+,
Ng 2
F 3+,
XeF
3+,
XeF
5+,
Xe 2
F 11
+,
and
XeO
F 3+
(Ng
=A
r,K
r,X
e)ca
tion
sw
ere
esti
mat
edu
sin
gcr
ysta
l-lo
grap
hic
and
esti
mat
edio
nvo
lum
es.
VB
Tw
asab
le,
inth
isw
ay,
topr
ovid
ees
tim
ates
and
pred
ict
stab
ilit
ies
–al
beit
som
etim
esw
ith
quit
ela
rge
un
cert
ain
ties
inth
ees
tim
ated
dat
a.W
hil
e,fo
rex
ampl
e,th
est
abil
itie
sof
[XeF
n][
Sb2F 1
1](
n=
2,3)
and
[XeF
][A
sF6]w
ere
con
firm
edw
ith
resp
ect
tod
isso
ciat
ion
toth
exe
non
flu
orid
ean
dth
epn
icto
gen
pen
tafl
uor
ide,
the
stab
ilit
ies
of[X
eF3][
AsF
6]
and
[XeF
3][
As 2
F 11]
wer
esh
own
tobe
mar
gin
alu
nd
erst
and
ard
con
dit
ion
s.
88
Th
eth
erm
odyn
amic
hyd
rate
diff
eren
ceru
le(H
DR
)ap
plie
dto
mat
eria
lsat
the
inor
gan
ic–o
rgan
icin
terf
ace.
Th
eth
erm
odyn
amic
hyd
rate
diff
eren
ceru
le(H
DR
)is
show
nh
ere
also
toap
ply
equ
ally
wel
lto
form
ate,
carb
onat
e,ac
etat
e,gl
ycol
ate
and
oxal
ate
salt
san
dth
eir
hyd
rate
s.89
Th
eth
erm
odyn
amic
diff
eren
ceru
lean
dth
eth
erm
odyn
amic
sof
hyd
rati
on(a
nd
solv
atio
n)
ofin
orga
nic
soli
ds
and
the
exis
ten
ce/a
bsen
ceof
cert
ain
hyd
rate
s.
Th
eth
erm
odyn
amic
sof
the
form
atio
nof
soli
dan
dli
quid
inor
gan
ich
ydra
tes
and
amm
onia
tes
was
exam
ined
inth
isap
plic
atio
n,
sugg
esti
ng
that
hyd
rati
onis
alw
ays
mar
gin
ally
ther
mod
ynam
ical
lyfa
vou
rabl
e.M
ore
det
aile
dco
nsi
der
atio
nfu
rth
erd
emon
stra
ted
that
the
mea
nva
lue
ofD
rGpe
rm
ole
ofw
ater
add
itio
n,
from
anh
y-d
rou
spa
ren
tto
hyd
rate
wit
hin
ase
quen
ce,i
ncr
ease
sco
nsi
sten
tly
tow
ard
zero
,bec
omin
gpr
ogre
ssiv
ely
less
favo
rabl
eas
the
deg
ree
ofh
ydra
tion
,n,
incr
ease
s,an
dis
also
broa
dly
ind
epen
den
tof
any
stru
ctu
ral
feat
ure
sof
the
mat
eria
ls.
90
VB
Td
eter
min
atio
nof
ion
icit
yor
cova
len
cyw
ith
inst
ruct
ure
s.T
he
ques
tion
asto
wh
y[P
(C6H
5) 4
]+N
3�
and
[As(
C6H
5) 4
]+N
3�
exis
tas
ion
icsa
lts
wh
ilst
[Sb(
C6H
5) 4
]+N
3�
and
[Bi(
C6H
5) 4
]+N
3�
are
cova
len
tso
lid
sw
asex
amin
ed.
Th
ees
tim
atio
ns
prov
ided
anu
nex
pect
edan
swer
!91
Inte
rpol
atio
nof
ther
mod
ynam
icd
ata
for
sulf
ur
com
pou
nd
san
du
seof
VB
Tto
exam
ine
poss
ible
syn
thet
icro
ute
san
dsu
bseq
uen
tst
abil
ity.
Usi
ng
VB
Tth
eva
lues
ofD
fGle
du
sto
ate
nta
tive
prop
osal
for
the
syn
thes
isof
Na 2
SO2.T
he
stab
ilit
yof
Na 2
SO2
how
ever
rais
esd
oubt
san
dN
a 2Se
O2
emer
ges
asa
mor
eat
trac
tive
targ
etm
ater
ial
for
syn
thes
is.
We
pred
ict
its
syn
thes
isw
ill
beea
sier
and
that
itis
stab
leto
dis
prop
orti
onat
ion
into
Na 2
Sean
dN
a 2Se
O4.(
Subs
equ
entl
yto
the
publ
icat
ion
ofth
ispa
per
itw
aspr
elim
inar
ily
repo
rted
toV
egas
verb
ally
that
Na 2
SO2
has
ind
eed
been
poss
ibly
iden
tifi
edin
aqu
eou
sso
luti
on).
92
Tet
raan
ion
icn
itro
gen
-ric
hte
traz
ole-
base
dsa
lts
Stu
dy
ofen
erge
tics
usi
ng
VB
T93
(TD
AE
)(O
2SS
SSO
2)(
s)ex
amin
edu
sin
gV
BT
and
con
tain
ing
the
very
firs
tpo
lyth
ion
ite
anio
n,
OSS
SSO
22�
.
Syn
thes
isof
(TD
AE
)(O
2SS
SSO
2).
94
Exa
min
atio
nof
VB
Tin
resp
ect
ofes
tim
atio
nof
latt
ice
ener
gies
ofsa
lts
con
tain
ing
the
5,50
-(te
traz
ole-
1N-o
xid
e)2�
anio
n.
Inve
stig
atio
nof
ener
geti
csof
def
ence
mat
eria
ls.
95
Use
ofT
DR
toex
amin
eth
erm
och
emic
ald
ata
for
arse
nic
and
phos
phor
us
com
pou
nd
s.A
rsen
icox
ides
/hyd
rate
sco
nfo
rmex
actl
yto
the
TD
Rw
hil
stan
alog
ous
phos
phor
us
oxid
es/h
ydra
tes
do
not
.Com
men
tson
enth
alpi
esof
form
atio
nof
phos
phat
es.
96an
d97
PCCP Perspective
Ope
n A
cces
s A
rtic
le. P
ublis
hed
on 2
6 M
ay 2
016.
Dow
nloa
ded
on 1
8/08
/201
6 14
:17:
00.
Thi
s ar
ticle
is li
cens
ed u
nder
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Conclusion
Neither volume-based thermodynamics (VBT) nor the thermo-dynamic difference rule (TDR), together with their supportingquantities, require a high level of computational expertise norexpensive high-performance computation tools – a spreadsheet willusually suffice – yet the techniques are extremely powerful andaccessible to non-experts. Table 2 summarises correlation equationsbetween formula unit volume, Vm, and various thermodynamicproperties, together with measures of anticipated errors. Thesecorrelation equations provide ready access to otherwise unavailablethermodynamic data, as also rapid checks of published data.The results should always be treated with appropriate cautionby checking against known values for related materials.
Applications of volume-based thermodynamics, VBT, and thethermodynamic difference rule, TDR
In rough chronological order, we present a selection of applica-tions of VBT and TDR which have enabled input, usually in theform of thermodynamics, to be brought to bear on a range oftopical problems, often ‘‘state of the art’’. These present adiverse range of applications for our techniques. The messagefor the reader is that:� VBT and TDR can be applied in numerous situations;� Their application can lead to surprising new results as well
as confirmatory ones;� The basic application is usually very straightforward
(Table 6).
Acknowledgements
LG and HDBJ thank their respective institutions for providingfacilities for the execution of this work. Witali Beichel (Freiburg)is thanked for helpful discussion on ILs. The Curtin UniversityLibrary is thanked for providing the means by which this articleis available in Open Access.
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2+ and of solid E8(AsF6)2(E = S, Se), Inorg. Chem., 2000, 39(25), 5614–5631.
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�, g) (m = 1, 2, 3), DHf1(AsF6�, g), and
DHf1(NF4+, g), Inorg. Chem., 2003, 42(9), 2886–2893.
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77 T. S. Cameron, I. Dionne, H. D. B. Jenkins, S. Parsons,J. Passmore and H. K. Roobottom, Preparation, X-ray CrystalStructure Determination, Lattice Potential Energy, andEnergetics of Formation of the Salt S4(AsF6)2�AsF3 Contain-ing the Lattice-Stabilized Tetrasulfur [2+] Cation. Implica-tions for the Understanding of the Stability of M4
2+ and M2+
(M = S, Se, and Te) Crystalline Salts, Inorg. Chem., 2000,39(10), 2042–2052.
78 K. O. Christe and H. D. B. Jenkins, Quantitative measure forthe ‘‘nakedness’’ of fluoride ion sources, J. Am. Chem. Soc.,2003, 125(31), 9457–9461.
79 K. O. Christe and H. D. B. Jenkins, Quantitative measure forthe ‘‘nakedness’’ of fluoride ion sources, J. Am. Chem. Soc.,2003, 125, 14210.
80 H. D. B. Jenkins and D. Tudela, New methods to estimatelattice energies – Application to the relative stabilities ofbisulfite (HSO3
�) and metabisulfite (S2O52�) salts, J. Chem.
Educ., 2003, 80(12), 1482–1487.81 A. Decken, H. D. B. Jenkins, G. B. Nikiforov and J. Passmore,
The reaction of LiAl(OR)4 R = OC(CF3)2Ph, OC(CF3)3 withNO/NO2 giving NO�Al(OR)4, LiNO3 and N2O. The synthesisof NO�Al(OR)4 from LiAl(OR) and NO.SbF6 in sulfur dioxidesolution, Dalton Trans., 2004, (16), 2496–2504.
82 D. A. Dixon, D. Feller, K. O. Christe, W. W. Wilson, A. Vij, V. Vij,H. D. B. Jenkins, R. M. Olson and M. S. Gordon, Enthalpies ofFormation of Gas-Phase N3, N3
�, N5+, and N5
� from Ab InitioMolecular Orbital Theory, Stability Predictions for N5
+N3� and
N5+N5�, and Experimental Evidence for the Instability of
N5+N3�, J. Am. Chem. Soc., 2004, 126(3), 834–843.
83 K. O. Christe, A. Vij, W. W. Wilson, V. Vij, D. A. Dixon,D. Feller and H. D. B. Jenkins, N5
+N5� allotrope is California
dreaming, Chem. Br., 2003, 39(9), 17.84 D. R. Rosseinsky, L. Glasser and H. D. B. Jenkins, Thermo-
dynamic clarification of the curious ferric/potassium ionexchange accompanying the electrochromic redox reactionsof Prussian blue, iron(III) hexacyanoferrate(II), J. Am. Chem.Soc., 2004, 126(33), 10472–10477.
85 A. Decken, H. D. B. Jenkins, C. Knapp, G. B. Nikiforov,J. Passmore and J. M. Rautiainen, The autoionization of [TiF4]by cation complexation with [15]crown-5 to give [TiF2([15]-crown-5)][Ti4F18] containing the tetrahedral [Ti4F18]2� ion,Angew. Chem., Int. Ed., 2005, 44, 7958–7961.
86 K. K. Bhasin, M. J. Crawford, H. D. B. Jenkins andT. M. Klapotke, The volume-based thermodynamics (VBT)and attempted preparation of an isomeric salt, nitryl chlo-rate: NO2�ClO3, Z. Anorg. Allg. Chem., 2006, 632(5), 897–900.
87 S. Brownridge, L. Calhoun, H. D. B. Jenkins, R. S. Laitinen,M. P. Murchie, J. Passmore, J. Pietikainen, J. M. Rautiainen,J. C. P. Sanders, G. J. Schrobilgen, R. J. Suontamo,H. M. Tuononen, J. U. Valkonen and C. M. Wong, 77SeNMR Spectroscopic, DFT MO, and VBT Investigations of theReversible Dissociation of Solid (Se6I2)[AsF6]2�2SO2 inLiquid SO2 to Solutions Containing 1,4-Se6I2
2+ in Equili-brium with Sen
2+ (n = 4, 8, 10) and Seven Binary SeleniumIodine Cations: Preliminary Evidence for 1,1,4,4-Se4Br4
2+
and cyclo-Se7Br+, Inorg. Chem., 2009, 48(5), 1938–1959.
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88 H. S. Elliott, J. F. Lehmann, H. P. A. Mercier, H. D. B. Jenkinsand G. J. Schrobilgen, X-ray Crystal Structures of XeF.MF6
(M = As, Sb, Bi), XeF�M2F11 (M = Sb, Bi) and EstimatedThermochemical Data and Predicted Stabilities for Noble-Gas Fluorocation Salts using Volume-Based Thermo-dynamics, Inorg. Chem., 2010, 49(18), 8504–8523.
89 H. D. B. Jenkins, L. Glasser and J. F. Liebman, The Thermo-dynamic Hydrate Difference Rule (HDR) Applied to Salts ofCarbon-Containing Oxyacid Salts and Their Hydrates: Mate-rials at the Inorganic–Organic Interface, J. Chem. Eng. Data,2010, 55(10), 4369–4371.
90 L. Glasser and F. Jones, Systematic Thermodynamics ofHydration (and of Solvation) of Inorganic Solids, Inorg.Chem., 2009, 48(4), 1661–1665.
91 K. O. Christe, R. Haiges, J. A. Boatz, H. D. B. Jenkins, E. B.Garner and D. A. Dixon, Why Are [P(C6H5)4]+N3
� and[As(C6H5)4]+N3
� Ionic Salts and Sb(C6H5)4N3 and Bi(C6H5)4N3
Covalent Solids? A Theoretical Study Provides an UnexpectedAnswer, Inorg. Chem., 2011, 50, 3752–3756.
92 A. Vegas, J. F. Liebman and H. D. B. Jenkins, Uniquethermodynamic relationships for DfH1 and DfG1 for crystal-line inorganic salts. I. Predicting the possible existence and
synthesis of Na2SO2 and Na2SeO2, Acta Crystallogr., Sect. B:Struct. Sci., 2012, 68, 511–527.
93 D. Srinivas, V. Ghule, K. Muralidharan and H. D. B. Jenkins,Tetraanionic Nitrogen-Rich Tetrazole-Based salts, Chem. –Asian J., 2013, 8, 1023–1028.
94 P. Bruna, A. Decken, S. Greer, F. Grein, H. D. B. Jenkins,B. Mueller, J. Passmore, T. A. P. Paulose, J. M. Rautiainenand S. Richardson, Synthesis of (TDAE)(O2SSSSO2) andDiscovery of (TDAE)(O2SSSSO2)(s) containing the first poly-thionite anion, Inorg. Chem., 2013, 52, 13651–13662.
95 L. Glasser, H. D. B. Jenkins and T. M. Klapotke, Is the VBTApproach valid for estimation of the lattice enthalpy of saltscontaining the 5,50-(Tetrazole-1N-oxide)2�?, Z. Anorg. Allg.Chem., 2014, 640, 1297–1299.
96 H. D. B. Jenkins, D. Holland and A. Vegas, Thermodynamicdata for crystalline arsenic and phosphorus compounds,M2O5�nH2O reexamined using the Thermodynamic Differ-ence Rules, Thermochim. Acta, 2016, 633, 24–30.
97 H. D. B. Jenkins, D. Holland and A. Vegas, An assessment ofthe TDR for mixed inorganic oxides and comments on theenthalpies of formation of phosphates, Thermochim. Acta,2015, 601, 63–67.
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