Activation and Reaction Volumes and Their Correlations with the

Article pubs.acs.org/jced

Activation and Reaction Volumes and Their Correlations with the Entropy and Enthalpy Parameters Dmitry A. Kornilov and Vladimir D. Kiselev* Laboratory of High Pressure Chemistry, Butlerov Institute of Chemistry, Kazan Federal University, Kazan, 420008, Russian Federation ABSTRACT: Data for the enthalpies, entropies, and volumes of 271 liquid compounds at standard conditions as well as those for 103 isomerization and decomposition reactions have been collected and compared. It was observed that the values of liquid molar volumes are proportional to the standard molar entropies of these compounds (R = 0.9378, N = 271). For the reactions under consideration, the proportionality ΔVr‑n vs ΔSr‑n (R = 0.9019, N = 103) was also found. The correlation between the volume and enthalpy changes in these reactions, ΔVr‑n vs ΔHr‑n, was not established (R = 0.5719, N = 103). The angular coefficient values, namely, 3.8 (eq 7) and 3.8 (eq 11), are close to the value 4.4 (eq 3), observed for the dissociation of acids and bases. The proportionality between the changes of the volume and entropy of activation (ΔV⧧ vs ΔS⧧) at normal and elevated pressure has been also noted, whereas proportionality with the enthalpy of activation (ΔV⧧ vs ΔH⧧) under these conditions was not observed.

■

Table 1. Dissolving Enthalpy of Anhydrous Magnesium Perchlorate, Partial Molar Volume, and Volume Change in the Series of Solvents at 298.15 K

INTRODUCTION Favorable increase of the reaction rate or equilibrium constants in solution under high hydrostatic pressure has been described for a vast array of reactions.1−6 Such influence is caused by the free energy change on the value PΔV⧧ or PΔVr‑n, where P is the applied pressure and ΔV⧧ or ΔVr‑n correspond to the activation or reaction volumes, respectively (eqs 1 and 2). They are formed due to the difference in the volumes of the activated complex or reaction products regarding to the volume of the reagents. ∂ΔG⧧/∂P = −RT ∂ ln(k)/∂P = ΔV ⧧

(1)

∂ΔGr − n /∂P = −RT ∂ ln(K )/∂P = ΔVr − n

(2)

There are many examples of the changes in the reactions selectivity and the hard-to-reach products synthesis only under high pressure.1−3,7−9 For mechanistic consideration, it is important to know the ratio of the activation and reaction volumes, which allows us to consider the probability of a cyclic or linear type of the activated complex and the possible presence of electrostriction in the reaction. The values of reaction volumes determined from eq 2, and directly from the difference of partial molar volumes (PMVs) of products and reagents are in a good agreement.1−3,10 The activation volume can only be determined from relation 1.1−6 It is essential, that the absolute value of intrinsic or van der Waals volume changes in the reaction is several times smaller than that of the intermolecular voids due to the variations in the packing factor.2,11,12 These changes in the volume of intermolecular voids define the compressibility of liquids at the pressure up to several kbar.13 The pressure influence on permittivity is more complex, and the linear proportionality of density-permittivity observed for nonpolar liquids is often violated in polar medium.14 © XXXX American Chemical Society

−ΔHsol

V̅ a

−ΔVb

solvent

kJ·mol−1

cm3·mol−1

cm3·mol−1

water ethyl acetate acetone formamide dimethyl sulfoxide dimethylformamide propylene carbonate acetonitrile diethyl ether methanol ethanol

153 142 191 190 238 245 189 198

67.3 46.6 −2.4 82.3 62.3 42.3 56.7 20.3 24.3 −4.7 2.5

18.5 39.2 88.2 3.5 23.5 43.5 29.1 65.5 61.5 90.5 83.3

205 171

Volume of Mg(ClO4)2 in crystalline state is 85.8 cm3·mol−1. bVolume change, ΔV = V̅ − 85.8, cm3·mol−1.

a

Considering the relations ΔG⧧ = ΔH⧧ − TΔS⧧ and ΔGr‑n = ΔHr‑n − TΔSr‑n, it will be determined which parameter change, ΔH or ΔS, at an elevated pressure affects the volume value, ΔV, more. Enthalpy, entropy, and volume changes of dissociation processes in water for about 70 acids and bases have been compared.1,15 Clear proportionality (eq 3) between the volumes Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: June 19, 2015 Accepted: September 24, 2015

A

DOI: 10.1021/acs.jced.5b00514 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 2. Values of Standard Entropies and Volumes of Some Liquid Compoundsa S0

V N/N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

−1

cm ·mol 3

substance pentane hexane heptane octane nonane decane undecane dodecane tridecane 2-methylbutane 2-methylpentane 2-methylhexane 2-methylheptane 2-methylnonane 2-methyldecane 3-methylpentane 3-methylhexane 3-methylheptane 3-methylnonane 4-methylnonane 5-methylnonane 3-ethylpentane 2,4-dimethylpentane 2,3-dimethylpentane 2,3,4-trimethylpentane 2,2-dimethylpropane 2,2-dimethylbutane 2,2-dimethylpentane 3,3-dimethylpentane 2,2,3-trimethylbutane 2,2,4-trimethylpentane 3,3-diethylpentane 1-pentene 1-hexene 1-heptene 1-octene 1-nonene 1-decene cis-2-pentene trans-2-pentene cis-2-hexene 1,2-pentadiene 1,4-pentadiene 2,3-pentadiene 2-methyl-1-butene 2-methyl-2-butene 3-methyl-1-butene 2,3-dimethyl-2-butene 3,3-dimethyl-1-butene 2,4,4-trimethyl-1-pentene 2-methyl-1,3-butadiene 3-methyl-1,2-butadiene 2-butyne benzene toluene 1,3-dimethylbenzene 1,4-dimethylbenzene 1,2,3-trimethylbenzene 1,2,4-trimethylbenzene

116.1 131.6 147.5 163.5 179.7 195.9 212.3 228.6 244.9 117.5 132.9 148.6 163.7 196.9 213.2 130.6 146.7 163.0 195.0 195.4 195.2 144.4 150.0 145.0 159.8 123.3 133.7 150.4 145.5 146.2 166.1 171.1 110.4 125.5 141.8 157.8 174.0 190.3 107.8 109.1 124.7 99.1 103.9 98.7 108.8 106.8 112.8 119.6 128.9 154.8 100.8 100.0 78.9 89.4 106.9 123.5 123.8 134.9 137.8 B

J·mol−1·K−1 263.5 296.1 328.6 361.2 393.7 425.9 458.2 490.7 522.9 260.4 290.6 323.3 356.4 420.1 453.8 292.6 309.6 362.6 427.2 425.5 423.8 314.6 303.2 297.1 329.3 216.8 272.0 300.3 305.6 292.3 328.0 333.4 262.6 295.2 327.7 360.5 392.5 425.0 258.6 256.5 291.9 245.0 248.9 237.3 254.0 251.0 253.3 270.2 256.5 311.7 228.3 231.8 195.1 173.3 221.0 253.8 243.5 267.9 283.4 DOI: 10.1021/acs.jced.5b00514 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 2. continued S0

V N/N 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118

−1

cm ·mol 3

substance 1,3,5-trimethylbenzene 1,2,3,4-tetramethylbenzene 1,2,3,5-tetramethylbenzene ethylbenzene propylbenzene butylbenzene 1-methyl-4-isopropylbenzene isopropylbenzene tert-butylbenzene 1-methylnaphthalene cyclopentane cyclohexane cycloheptane cyclooctane cyclopentene cyclohexene 1,3,5,7-cyclooctatetraene spiropentane methylcyclopentane 1,1-dimethylcyclopentane cis-1,2-dimethylcyclopentane trans-1,2-dimethylcyclopentane trans-1,3-dimethylcyclopentane ethylcyclopentane propylcyclopentane methylcyclohexane 1,1-dimethylcyclohexane trans-1,2-dimethylcyclohexane trans-1,3-dimethylcyclohexane trans-1,4-dimethylcyclohexane ethylcyclohexane propylcyclohexane butylcyclohexane methanol ethanol propanol butanol pentanol hexanol heptanol 2-methyl-1-propanol 2-propanol 2-butanol 2-methyl-2-propanol 1,2,3-propanetriol 1,4-butanediol cyclohexanol cycloheptanol 3-methylphenol methyl propyl ether methyl isopropyl ether methyl tert-butyl ether dimethoxymethane 2-methyloxirane tetrahydrofuran ethanal propanal butanal pentanal

139.0 148.9 151.4 123.1 140.1 156.8 157.3 140.2 155.6 139.9 94.7 108.2 121.7 134.8 88.9 101.9 113.7 91.0 113.1 130.9 127.8 131.5 131.9 128.8 145.3 128.3 144.4 145.4 143.7 147.9 143.1 159.8 176.3 40.7 58.7 75.1 92.0 108.6 125.2 142.0 92.9 76.9 92.4 94.9 73.3 89.0 106.0 119.6 105.0 102.6 103.8 119.9 89.2 70.4 81.8 57.1 73.4 90.5 107.0 C



Article


V N/N 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177

−1

cm ·mol 3

substance propanone butanone 3-pentanone 5-nonanone cyclohexanone methanoic acid ethanoic acid propanoic acid butanoic acid pentanoic acid ethyl ethanoate methyl amine n-propyl amine 1,2-ethanediamine 2-aminopropane 2-amino-2-methylpropane aniline acetonitrile propionitrile propenenitrile benzonitrile hydrazine pyrrolidine pyridine quinoline 2-methylpyridine 3-methylpyridine nitromethane ethanethiol 1-propanethiol 1-butanethiol 1-pentanethiol 1-hexanethiol 1-heptanethiol 2-propanethiol 2-butanethiol 2-methyl-1-propanethiol 2-methyl-2-propanethiol 2-methyl-2-butanethiol cyclopentanethiol cyclohexanethiol benzenethiol dimethyl sulfide ethyl methyl sulfide diethyl sulfide isopropyl methyl sulfide methyl propyl sulfide butyl methyl sulfide ethyl propyl sulfide dibutyl sulfide dimethyl disulfide dipropyl disulfide dimethyl sulfoxide thiacyclobutane thiacyclopentane thiacyclohexane hexafluorobenzene fluorobenzene chloroethane

74.0 90.2 106.4 174.0 104.2 37.9 57.5 75.0 92.4 109.3 98.6 47.3 83.0 67.3 86.5 105.9 91.5 52.9 70.9 66.3 103.0 31.9 83.3 80.9 118.6 99.1 97.8 54.0 74.6 91.1 107.8 124.4 141.1 157.6 94.2 109.4 108.8 113.5 126.9 107.4 119.3 102.7 73.8 91.0 108.5 109.3 107.7 124.4 125.2 190.9 89.1 157.4 71.2 73.1 88.7 104.2 115.8 94.3 72.6 D



Article


V N/N

substance

178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236

1,2-dichloroethane 1,1-dichloroethane 1,1,1-trichloroethane 1,1-dichloroethylene chlorobenzene 1,2-dibromoethane bromobenzene iodobenzene 1,1,2-trichloro-1,2,2-trifluoroethane chloropentafluorobenzene 3,3-dimethyl-1-butene 2,4,4-trimethyl-1-pentene styrene methylenecyclobutane butylcyclopentane cis-decalin trans-decalin 1,2-ethanediol cyclopentanol diethyl ether di-n-propyl ether methyl butyl ether ethyl propyl ether diisopropyl ether dipropyl sulfide diisopropyl sulfide nitrobenzene methyl nitrate ethyl nitrate piperidine 1,1-dimethylhydrazine methylhydrazine cyclopentylamine 4-butanolactone 2-oxetanone 2,4-dimethyl-3-pentanone 3,3-dimethyl-2-butanone 3-hexanone 2-hexanone 2-pentanone nonanal octanal hexanal tert-butyl methyl sulfide diethyl disulfide 1,2-difluorobenzene 1,3-difluorobenzene 1,2,4,5-tetrafluorobenzene 1,2,3,5-tetrafluorobenzene pentafluorobenzene 1,1,1,3-tetrachloropropane hexachloroethane 1-chloro-1,1,3,3,3-pentafluoropropane 1,3-cyclohexadiene 1,4-cyclohexadiene 1,5-cyclooctadiene 1,3,5-cycloheptatriene tetrachloromethane trichloromethane

−1

cm ·mol 3

79.4 84.8 100.4 82.5 102.2 86.6 105.5 111.9 119.8 129.2 128.9 154.8 115.6 92.6 161.6 154.8 159.7 55.9 90.8 104.7 137.7 118.5 119.1 142.2 145.3 145.2 102.6 64.0 82.2 98.8 75.8 52.4 98.7 76.5 62.9 143.0 125.0 122.2 124.2 107.5 172.0 156.2 122.9 126.2 123.1 98.5 98.1 111.7 113.8 111.0 121.2 113.3 141.0 95.3 94.6 122.7 103.8 96.9 80.2 E



Article


V N/N 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 a

−1

J·mol−1·K−1

cm ·mol 3

substance dichloromethane trithiocarbonic acid iodomethane carbon disulfide dimethyl sulfone pyruvic acid isopropyl alcohol furan thiophene acetic anhydride 1,4-dioxane 2-furaldehyde glutaronitrile 2-methylfuran furfuryl alcohol 2-methylthiophene 3-methylthiophene cyclopentanol tert-pentyl alcohol 2-picoline 3-picoline 2,5-dimethylthiophene p-fluorotoluene benzyl alcohol n-methylaniline acetophenone n,n-dimethylaniline n-ethylaniline indene indane tetralin n,n-diethylaniline 1,2-dimethylhydrazine water mercury

64.1 74.3 62.3 60.1 64.9 70.5 76.5 72.7 80.1 94.4 85.3 82.8 94.5 88.6 87.0 96.8 96.6 90.8 109.5 98.8 97.3 113.9 110.1 103.6 108.2 116.9 126.8 125.8 116.5 123.1 135.9 160.5 72.6 18.1 14.8

178.7 223.1 162.8 151.1 145.5 179.5 180.6 176.7 181.2 268.7 195.3 218.0 239.5 213.9 215.5 218.5 218.4 205.9 229.3 217.9 216.4 244.8 237.2 216.8 224.3 249.5 256.1 239.4 214.2 234.4 251.5 265.8 199.2 70.0 75.8

The uncertainties for the values of S0 are ± 1 J·mol−1·K−1,19,20 and of V are ± 0.1 cm3·mol−1.21

(ΔV/cm3·mol−1) and the entropies (ΔS/(J·mol−1·K−1)) for dissociation is observed, whereas there is no such a proportionality for the relation ΔV vs ΔH.15 ΔS = 4.4ΔV − 29.2

(3)

This dependence (eq 3) can be attributed to the substantial electrostriction of water molecules in the generated ions solvation.15 It has been found that the change in PMVs of some salts in the series of solvents does not correlate with the difference in their dissolution enthalpy.16,17 Thus, the dissolving of magnesium perchlorate in polar solvents is always accompanied by a very strong exothermic effect,17 but there is no proportionality of the PMVs and dissolving enthalpies changes (Table 1). Unfortunately, data for these entropy changes are absent. Total volume of a dilute solution (V) can be represented by eq 4: V = VANA + VSNS + (V S* − VS)zNA

Figure 1. Relationship between the entropies and volumes of 271 liquids according to Table 2.

shell of the dissolved compound (A); NA and NS are the number of moles of the dissolved compound and free solvent in this solution. From eq 4 it follows that the experimental value of PMV (V̅ exp) in a dilute solution is given by eq 5:

(4)

Here, VA, VS and V*S are the molar volumes of the dissolved compound, pure solvent, and the solvent in the solvate shell, respectively; z is the number of solvent molecules in the solvate

∂V /∂NA = Vexp ̅ = VA + z(V S* − VS) F

(5)



Article

Table 3. Enthalpies, Entropies, and Volumes of Some Isomerization and Decomposition Reactionsa N/N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

reaction cyclopentane → cis-2-pentene cyclopentane → trans-2-pentene cyclohexane → cis-2-hexene cyclopentane → 2-methyl-1-butene cyclopentane → 3-methyl-1-butene cyclohexane → 3,3-dimethyl-1-butene cyclooctane → 2,4,4-trimethyl-1-pentene cyclopentene → 2-methyl-1,3-butadiene cyclopentene → 3-methyl-1,2-butadiene spiropentane → 2-methyl-1,3-butadiene spiropentane → 3-methyl-1,2-butadiene butanol → methyl propyl ether butanol → methyl isopropyl ether 2-methyloxirane → propanal tetrahydrofuran → butanal 2-methyloxirane → propanone tetrahydrofuran → butanone decane → 1-pentene + pentane undecane → 1-pentene + hexane tridecane → 1-heptene + hexane dodecane → cyclohexane + hexane decane → cyclopentane + pentane undecane → cyclopentane + hexane tridecane → cycloheptane + hexane 1,2,3-propanetriol → formic acid + ethanol pentanoic acid → propanal + ethanal cyclohexanol → cyclopentene + methanol cycloheptanol → cyclopentene + ethanol 1-hexanol → cyclopentane + methanol 1-heptanol → cyclohexane + methanol 1-heptanol → cyclopentane + ethanol butylcyclohexane → 2 cyclopentane butylcyclohexane → 2 pentene-1 5-nonanone → butanone + cyclopentane 5-nonanone → butanone + pentene-1 5-nonanone → propanone + hexene-1 5-nonanone → ethanal + heptene-1 1-hexanol → pentene-1 + methanol 1-heptanol → hexene-1 + methanol 1-heptanol → pentene-1 + ethanol octanal → propanone + pentene-1 octanal → propanone + cyclopentane octanal → ethanal + hexene-1 1,2-dichloroethane → 1,1-dichloroethane dimetyl sulfide → ethanethiol 1,2-dimethylhydrazine → 1,1-dimethylhydrazine propylene oxide → propanone 1-propanol → 2-propanol 1-propanethiol → ethyl methyl sulfide 1-propanethiol → 2-propanethiol ethyl methyl sulfide → 2-propanethiol 1,2-butadiene → 1,3-butadiene 1,2-butadiene → 2-butyne 2-butyne → 1,3-butadiene butanone → butanal 1,4-dioxane → butanoic acid 1,4-dioxane → ethyl ethanoate butanoic acid → ethyl ethanoate 1-butanol → 2-methyl-2-propanol G

ΔVr‑n

ΔSr‑n

ΔHr‑n

cm3·mol−1

J·mol−1·K−1

kJ·mol−1

13.2 14.4 16.0 12.1 18.1 20.2 20.0 11.9 11.1 9.8 9.0 10.6 11.9 3.0 8.8 3.6 8.4 30.6 29.7 28.4 11.2 14.9 14.0 8.4 23.3 21.2 23.6 28.0 10.2 6.9 11.4 13.1 44.4 10.8 26.5 25.5 24.9 25.9 24.3 27.1 28.2 12.6 26.4 4.1 0.6 3.3 3.5 1.8 0.0 3.0 3.0 4.1 0.1 4.0 0.2 6.8 12.6 5.8 2.4

54 52 88 47 49 52 50 27 31 35 38 28 28 17 39 4 35 100 100 101 10 42 42 16 85 70 125 119 44 6 38 63 180 42 100 94 44 102 96 97 98 39 47 3 11 1 4 −12 −4 −9 −6 −11 −15 4 8 31 64 33 −33

52 47 72 45 54 68 22 42 95 −109 −56 61 49 −93 −23 −126 −57 80 81 81 −3 21 22 22 −34 151 116 79 33 9 20 51 169 19 78 78 108 93 93 79 48 −11 79 4 −8 −1 −128 −14 8 −6 −14 −54 −19 −35 35 −180 −126 55 34 DOI: 10.1021/acs.jced.5b00514 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

Table 3. continued ΔVr‑n

ΔSr‑n

ΔHr‑n

N/N

reaction

cm3·mol−1

J·mol−1·K−1

kJ·mol−1

60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

2-methyl-2-propanol → diethyl ether 1-butanol → diethyl ether 1-butanethiol → diethyl sulfide 1-butanethiol → isopropyl methyl sulfide 1-butanethiol → methyl propyl sulfide diethyl sulfide → isopropyl methyl sulfide diethyl sulfide → methyl propyl sulfide methyl propyl sulfide → isopropyl methyl sulfide cyclopentene → 2-methyl-1,3-butadiene cyclopentene → 1,4-pentadiene cyclopentene → spiropentane 2-methyl-1,3-butadiene → 1,4-pentadiene spiropentane → 2-methyl-1,3-butadiene spiropentane → 1,4-pentadiene cyclopentane → 2-methyl-1-butene 2-methyl-1-butene → pentene-1 cyclopentane → pentene-1 1-pentanethiol → ethyl propyl sulfide aniline → 2-picoline cyclohexane → 2,3-dimethyl-2-butene 2,3-dimethyl-2-butene → 1-hexene cyclohexane → hexene-1 1-hexanol → diisopropyl ether cycloheptane → 1-heptene methylcyclohexane → 1-heptene cycloheptane → methylcyclohexane 1,3,5,7-cyclooctatetraene → styrene cyclooctane → 1-octene butylcyclohexane → 1-decene dodecane → hexane + 1-hexene pentanol → 1-pentene + water hexanol → 1-hexene + water heptanol → 1-heptene + water methyl butyl ether → 1-pentene + water ethyl propyl ether → 1-pentene + water pentanol → 2-methyl-2-butene + water methyl butyl ether → 2-methyl-2-butene + water methyl tert-butyl ether → 2-methyl-2-butene + water hexanol → 2,3-dimethyl-2-butene + water 1-decene → pentene-1 + cyclopentane 1-decene → pentene-1 + pentene-1 1-decene → pentane + cyclopentene 1-decene → pentane + spiropentane 1-decene → pentane + 1,4-pentadiene

9.8 12.3 0.2 1.5 0.2 1.3 0.0 1.3 11.9 14.9 2.0 3.0 9.9 12.9 13.8 1.7 15.4 1.0 7.5 10.6 6.3 16.9 14.7 19.6 13.2 6.4 1.8 22.6 13.8 28.0 19.7 18.3 17.8 9.9 9.2 16.1 6.3 4.9 12.4 14.7 30.4 14.7 16.8 29.7

60 27 −7 −13 −3 −6 3 −9 28 42 −8 14 36 50 50 8 58 −1 27 66 25 91 8 85 80 5 17 98 80 101 74 78 72 37 38 62 26 56 53 42 100 40 32 87

80 46 5 0 7 −5 1 −7 45 71 153 26 −108 −82 43 16 59 5 25 54 30 84 28 60 92 −32 −151 46 89 80 19 19 19 −42 −29 −2 −63 −40 −10.8 21 80 7 158 81

The uncertainties for the values are ΔHr‑n = ± 1.0 kJ·mol−1, entropies ΔSr‑n = ± 2 J·mol−1·K−1,18−20 and volumes of reactions, ΔVr‑n = ± 0.2 cm3·mol−1.21 In all cases (Table 3) the reactions are recorded in order, when the values of their volumes are positive. a

■

Hence, it follows that the observed value (V̅ exp) of solute molar volume (A) in the solution consists of its own volume, VA, and the solvent volume change, z(VS* − VS), when transfers from the bulk to the solvation shell of the solute occur. From Table 1 data it follows that the compressed volume of the solvent, z(VS* − VS), can exceed the salt volume, VA, which gives negative values of the observed PMV. However, even in the case of abundant heat effects, the PMV changes are not determined by the changes in enthalpy of dissolution.16,17 Taking into account eq 5 it has become clear that the observed activation and reaction volumes should be represented as ΔV⧧exp = ΔV⧧ + ΔV⧧solv and ΔVr‑n, exp = ΔVr‑n + ΔVr‑n, solv.

RESULTS AND DISCUSSION

Table 2 gives the standard molar entropies and volumes of 271 individual liquids at 298.15 K. The molar volumes and standard molar entropies of 271 liquids are compared in Figure 1. It should be noted that the clear proportionality S0i vs Vi of liquid compounds (Figure 1, eq 6) has been observed for the first time: 0 S liquid = (1.76 ± 0.04)Vliquid + (55.2 ± 4.7);

R = 0.9378, N = 271 H

(6) DOI: 10.1021/acs.jced.5b00514 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


Article

proportional to the change of the nonpolar and low-polar reactions volumes. At present, there are no reliable explanations of such correlations.1,22 It should be noted that one of the Maxwell relations22,23 can be considered in conjunction with eq 6:

The data above allow us to exclude the problems associated with the charge generation and solvent electrostriction. The collected data concerning the enthalpy formation (ΔHform),18−20 standard molar entropy (So),19,20 and molar volume (V)21 in a liquid phase make it possible to calculate the changes in the volumes (ΔVr‑n), enthalpies (ΔHr‑n), and entropies (ΔSr‑n) of 103 nonpolar and low-polar possible reactions of isomerization and decomposition in the liquid phase (Table 3). Figure 2 compares the changes in the volume and entropy of the processes collected in Table 3:

(∂S /∂V )T = (∂P /∂T )V Pintern = T (∂P /∂T )V = T (∂S /∂V )T

(10)

The internal pressure, Pintern, can be estimated for liquids using So as a function of V in eq 10 (Table 2). For mercury this value is 15 200 bar (lit.,22,23 13 200 bar) and that of water is 11 600 bar (lit.,1,22,23 data spread up to 20 000 bar) . The changes in the volume, enthalpy, and entropy of activation are known only for few reactions. The rate constants of cyclopentadiene dimerization have been measured at (273, 293, 303, and 313) K and at (0.001, 1, 2, 3, and 4) kbar.24 According to these data, the values of enthalpy, entropy, and volume of activation have been calculated (Table 4).

ΔSr ‐ n = (3.77 ± 0.18)ΔVr ‐ n − (4.5 ± 2.8); R = 0.9019, N = 103

(9)

(7)

Table 4. Pressure Influence on the Rate of Cyclopentadiene Dimerization, Enthalpy, Entropy, Gibbs Energy, as Well as the Volume of Activation at 293 K

Figure 2. Relationship between the entropies and volumes of 103 reactions according to Table 3.

Figure 3 compares the changes in the enthalpy and volume of these processes (Table 3):

a

kP

ΔH⧧

ΔS⧧

ΔG⧧

ΔV⧧a

kg·cm−2

k1

kJ·mol−1

J·mol−1·K−1

kJ·mol−1

cm3·mol−1

1 1000 2000 3000 4000

1 3.12 7.75 15.4 33.3

68.6 71.3 73.9 75.3 76.4

130 113 96.2 83.7 75.3

106.7 104.4 102.1 99.8 98.4

−30.2 −24.4 −20.4 −17.6 −15.4

Calculated in the present work. All other data are from ref 24.

From these data follow that the favorable change in entropy of activation accelerates the rate as pressure increases. In the investigated range of pressures there is simple proportionality ΔS⧧P vs ΔV⧧P :

ΔHr ‐ n = (4.07 ± 0.58)ΔVr ‐ n − (30.5 ± 9.1); R = 0.5719, N = 103

P

(8)

ΔSP⧧ = (3.76 ± 0.19)ΔV ⧧ − (18.5 ± 4.2); R = 0.9962, N = 5

(11)

Reaction rates Z/E isomerization of 4-(dimethylamino)-4′nitroazobenzene in the range of temperatures and pressures in some solvents have been also studied, and very small changes in the energy of activation were found (Table 5).25 Table 5. Pressure Influence on the Activation Enthalpy Z/E Isomerization of 4-(Dimethylamino)-4′-nitroazobenzene in the Pressure Range Figure 3. Plot of enthalpies and volumes of 103 reactions according to Table 3.

ΔH⧧/kJ·mol−1

It can be seen from the data that for low-polar reactions in the absence of the solvent notable changes in the reaction enthalpy (333 kJ·mol−1), from −180 kJ·mol−1 (entry 56, Table 3) to +153 kJ·mol−1 (entry 70, Table 3) do not define the changes in the volume of the reactions (Figure 3, eq 8). On the other hand, the maximum entropy change (212.6 J·mol−1·K−1), from −32.6 J·mol−1·K−1 (entry 59, Table 3) to +180 J·mol−1·K−1 (entry 33, Table 3), corresponds to the energy contribution, T·ΔΔSr‑n, equal only to 63 kJ·mol−1. It was noted that the processes accompanied by a decrease in volume usually produce a negative entropy change.1−3,22,23 From the data observed (Figure 2, eq 7), the entropy contribution is to a large extent

a

solvent

1 bar

2000 bar

4000 bar

6000 bar

methyl acetate glycerol triacetate ethanol

48.6 49.5 48.7

52.0 50.9 49.0a

50.4 50.8 48.8b

50.3 50.9

At 1500 bar. bAt 2400 bar.

On the other hand, the free activation energies in the range of 1 bar to 6000 bar are decreased by more than 6 kJ·mol−1 in these solvents. Consequently, in this Z/E isomerization the acceleration of the reaction rate under high pressure is also due to the favorable change in the entropy of activation.25 Similar dependences have been observed for the Menshutkin reaction of pyridine with ethyl iodide in acetone at pressures up I



Article

to 8.5 kbar26 and for decomposition of the Diels−Alder adduct resulting between 9-chloroanthracene and tetracyanoethylene in the range of temperatures and pressures.10,27

(13) Kiselev, V. D.; Bolotov, A. V.; Satonin, A. P.; Shakirova, I. I.; Kashaeva, E. A.; Konovalov, A. I. Compressibility of Liquids. Rule of Noncrossing V−P Curvatures. J. Phys. Chem. B 2008, 112, 6674−6682. (14) Kiselev, V. D.; Kornilov, D. A.; Konovalov, A. I. Changes in Permittivity and Density of Molecular Liquids under High Pressure. J. Phys. Chem. B 2014, 118, 3702−3709. (15) Hepler, L. G. J. Phys. Chem. 1965, 69, 965−967. (16) Kiselev, V. D.; Kashaeva, E. A.; Iskhakova, G. G.; Potapova, L. N.; Konovalov, A. I. Solvent effect on the heat of solution and partial molar volume of some non-electrolytes and lithium perchlorate. J. Phys. Org. Chem. 2006, 19, 179−186. (17) Kiselev, V. D.; Bolotov, A. V.; Satonin, A. P.; Shakirova, I. I.; Averyanova, A. D.; Kashaeva, H. A.; Konovalov, A. I. Solvent effect on the heat of solution and partial molar volume of magnesium perchlorate. J. Phys. Org. Chem. 2011, 24, 29−37. (18) Cox, J. D.; Pilcher, G. Thermochemistry of organic and organometallic compounds; Academic Press: London, NY, 1970. (19) Domalski, E. S.; Hearing, E. D. Estimation of the thermodynamic properties of C-H-N-O-S-Halogen compounds at 298.15 K. J. Phys. Chem. Ref. Data 1993, 22, 805−1159. (20) Stull, D. R.; Westrum, E. F.; Sinke, G. C. The Chemical Thermodynamics of Organic Compounds; John Wiley & Sons: New York, London, Sydney, Toronto, 1969. (21) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents; John Wiley & Sons: New York, Chichester, Brisbane, Toronto, Singapore, 1986. (22) Moore, W. J. Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1972. (23) Marcus, Y. Internal pressure of liquids and solutions. Chem. Rev. 2013, 113, 6536−6551. (24) Raistrick, B.; Sapiro, R. H.; Newitt, D. M. Liquid-phase reactions at high pressures. Part V. The polymerization of cyclopentadiene and αdicyclopentadiene. J. Chem. Soc. 1939, 1761−1769. (25) Cossticks, K.; Asano, T.; Ohno, N. Pressure effects on thermal isomerizations in highly viscous media. The first clear-cut example of viscosity-induced retardation of “slow” thermal reactions. High Pressure Res. 1992, 11, 37−54. (26) Stearn, A. E.; Eyring, H. Pressure and rate processes. Chem. Rev. 1941, 29, 509−523. (27) Kiselev, V. D.; Kashaeva, E. A.; Bolotov, A. V.; Shakirova, I. I.; Konovalov, A. I. Energy and volume activation parameters of the retroDiels-Alder reaction in different solvents. Russ. Chem. Bull. 2009, 58, 21−24.

■

CONCLUSIONS From the analysis performed it follows that the values of molar volumes of 271 liquids are reliably proportional to their standard entropies (R = 0.9378, Figure 1). For the isomerization and decomposition reactions (Table 3) the proportionality ΔVr‑n vs ΔSr‑n (R = 0.9019, N = 103, Figure 2) is also observed. The correlation between the volume and enthalpy changes for these reactions, ΔVr‑n vs ΔHr‑n, is rather weak: (R = 0.5719, N = 103, Figure 3). The values of angular coefficients: 3.8 (eq 7) and 3.8 (eq 11) for low-polar processes are close to the value 4.4 (eq 3) obtained1,15 for the dissociation of acids and bases. Therefore, the value of the activation or reaction volume can be estimated semiquantitatively via the activation or reaction entropy. For reactions with large and negative entropies, similar values for the volume changes should be expected.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +7 843-2927949. E-mail: [email protected]. Funding

Contract grant sponsor: Russian Government Program of Competitive Growth of Kazan Federal University. Contract grant sponsor: U.S. Civilian Research and Development Foundation and Ministry of Science and Education of the Russian Federation (Joint Program “Fundamental Research and High Education.” Contract Grant No. REC 007). Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Isaacs, N. S. Liquid Phase High Pressure Chemistry; WileyIntersience: Chichester, New York, Brisbane, Toronto, 1981. (2) Wurche, F.; van Eldik, R.; Klärner, F.-G. High Pressure Chemistry; Wiley−VCH: Weinheim, Germany, 2002. (3) Le Noble, W. J. Organic High Pressure Chemistry; Elsevier: Amsterdam, 1988. (4) Asano, T.; le Noble, W. J. Activation and reaction volumes in solution. Chem. Rev. 1978, 78, 408−489. (5) van Eldik, R.; Asano, T.; le Noble, W. J. Activation and reaction volumes in solution. Chem. Rev. 1989, 89, 549−688. (6) Drljaca, A.; Hubbard, C. D.; van Eldik, R.; Asano, T.; Basilevsky, M. A.; le Noble, W. J. Activation and reaction volumes in solution. Chem. Rev. 1998, 98, 2167−2289. (7) Kobayashi, S.; Jorgensen, K. A. Cycloaddition reaction in organic synthesis; Wiley: New York, 2001. (8) Klärner, F.-G.; Breitkopf, V. The effect of pressure on retro DielsAlder reactions. Eur. J. Org. Chem. 1999, 1999, 2757−2762. (9) Iskhakova, G. G.; Kiselev, V. D.; Kashaeva, E. A.; Potapova, L. N.; Berdnikov, E. A.; Krivolapov, D. B.; Litvinov, I. A. Diels-Alder reaction between naphthalene and N-phenylmaleimide under ambient and high pressure conditions. Arkivoc 2004, 12, 70−79. (10) Kiselev, V. D.; Kashaeva, E. A.; Konovalov, A. I. Pressure effect on the rate and equilibrium constants of the Diels-Alder reaction 9chloroanthracene with tetracyanoethylene. Tetrahedron 1999, 55, 1153−1162. (11) Le Noble, W. J.; Asano, T. Comment to “Phantom activation volumes. J. Phys. Chem. A 2001, 105, 3428−3429. (12) Kiselev, V. D.; Iskhakova, G. G.; Kashaeva, E. A.; Potapova, L. N.; Konovalov, A. I. Diels-Alder reaction volumes in the solid state and solution. Russ. Chem. Bull. 2004, 53, 2490−2495. J


Activation and Reaction Volumes and Their Correlations with the

Recommend Documents