New aspects of relationship between the enthalpies of fusion of aromatic compounds at the melting temperature and the enthalpies of solution in benzene at 298.15 K. Part II

Accepted Manuscript New aspects of relationship between the enthalpies of fusion of aromatic compounds at the melting temperature and the enthalpies of solution in benzene at 298.15 K. Part II Mikhail I. Yagofarov, Ruslan N. Nagrimanov, Marat A. Ziganshin, Boris N. Solomonov PII: DOI: Reference:

S0021-9614(17)30458-5 https://doi.org/10.1016/j.jct.2017.12.022 YJCHT 5292

To appear in:

J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

10 July 2017 27 December 2017 31 December 2017

Please cite this article as: M.I. Yagofarov, R.N. Nagrimanov, M.A. Ziganshin, B.N. Solomonov, New aspects of relationship between the enthalpies of fusion of aromatic compounds at the melting temperature and the enthalpies of solution in benzene at 298.15 K. Part II, J. Chem. Thermodynamics (2017), doi: https://doi.org/10.1016/j.jct. 2017.12.022

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New aspects of relationship between the enthalpies of fusion of aromatic compounds at the melting temperature and the enthalpies of solution in benzene at 298.15 K. Part II Mikhail I. Yagofarov, Ruslan N. Nagrimanov, Marat A. Ziganshin, Boris N. Solomonov1 Department of Physical Chemistry, Kazan Federal University, Kremlevskaya str. 18, 420008 Kazan, Russia Abstract In the present work we demonstrate how the relationship between fusion enthalpies at the melting temperature of aromatic compounds and solution enthalpy values in benzene at 298.15 K values is affected by the fusion enthalpy temperature dependence and the solution enthalpy of hypothetical liquid in benzene. The fusion enthalpies at 298.15 K were independently calculated from the solution enthalpies in benzene and the fusion enthalpies at the melting temperatures according to Kirchhoff’s law. Kirchhoff’s law was applied for fusion enthalpy adjustment calculation, assuming that the heat capacities of the aromatic compounds studied in the molten state can be extrapolated down to 298.15 K. The fusion enthalpies at 298.15 K derived from the solution calorimetry and from the fusion enthalpies at the melting temperatures are in good agreement, including the compounds with significant fusion enthalpy adjustments, demonstrating the validity of the assumptions made. The solution enthalpies of six aromatic compounds in benzene and the fusion enthalpy of dimethyl terephthalate were measured. Keywords: fusion enthalpy; solution enthalpy; aromatic compounds; heat capacity

11

To whom correspondence should be addressed, E-mail: [email protected] (B.N. Solomonov)

1

1.

Introduction

Fusion enthalpies of individual organic compounds are the source of information about solid-liquid equilibria in complex systems. Drug solubility [1] and phase diagram shape [2] may be predicted from the fusion enthalpies. However, accurate application of the fusion enthalpy measured at the melting temperature requires knowledge of the fusion enthalpy temperature dependence for prediction of solid-liquid equilibrium parameters. Neglecting fusion enthalpy temperature dependence of drugs leads to a significant error in estimation of their solubility at the ambient conditions [1,3]. On the other hand, fusion enthalpies at 298.15 K ( ∆ lcr H Ai (298.15 K)) together with vaporization enthalpies at 298.15 K found from correlation gas chromatography [4] or melt vaporization studies [5] are used for calculation of sublimation enthalpy. Fusion enthalpy adjustments to 298.15 K can make a large contribution to resulting sublimation enthalpy values. The enthalpy of solution of a solid compound may be represented as a sum of the enthalpy of its melting and solution of formed melt at the same conditions. In Ref. [6,7] it was shown that the solution enthalpies of solid aromatic compounds not capable of self-association due to intermolecular hydrogen bonding in benzene at 298.15 K ( ∆ soln H A i /C 6 H 6 (cr, 298.15 K)) are close to the fusion enthalpies at the melting temperatures ( ∆ lcr H A i (Tm ) ). This finding led to the development a new approach for estimating sublimation enthalpies of aromatic compounds based on fusion enthalpies at the melting temperatures and solvation enthalpies in benzene calculated according to a group-additivity scheme [6-8]. Since the solution enthalpies in benzene of liquid aromatic compounds not capable of self-association due to intermolecular hydrogen bonding are close to zero (for example, solution enthalpy of liquid 1-phenylnapthalene in benzene at 298.15 K is 0.65 kJ mol-1 [9]), ∆ soln H Ai /C6 H 6 (cr, 298.15 K) should be close to ∆ lcr H Ai (298.15 K). Approximate equality between ∆ soln H A i /C 6 H 6 (cr, 298.15 K) and ∆ lcr H Ai (Tm ) led to conclusion that the fusion enthalpies of the studied compounds weakly depend on temperature [6]. Nevertheless, we also observed the compounds the solution enthalpies of which are notably lower than the fusion enthalpies at the melting temperature. In the case of anthracene, recommended value for ∆ lcr H Ai (Tm ) (29.4 kJ mol-1 [10]) exceeds the ∆ soln H A i /C 6 H 6 (cr, 298.15 K) (24.7 kJ mol-1 [11]) by 4.7 kJ mol-1. A quantitative approach to the analysis of a connection between fusion enthalpy at the melting temperature and solution enthalpy at 298.15 K of solid aromatic compounds in benzene was developed in Ref. [12]. The comparison was carried out between the fusion enthalpies at 2

298.15 K calculated in several ways. On the one hand, we derived the ∆ lcr H Ai (298.15 K) values from ∆ lcr H Ai (Tm ) using Kirchhoff’s law. On the other, we calculated the ∆ lcr H Ai (298.15 K) values with the help of solution calorimetry. In Ref. [12] we studied compounds for which the fusion enthalpy adjustments from Tm to 298.15 K are small and the ∆ lcr H Ai (Tm ) values are approximately equal to ∆ soln H A i /C 6 H 6 (cr, 298.15 K). In this work we carry out an analogous analysis for compounds with larger temperature adjustments, based on the heat capacity measurements over the wide temperature ranges reported in Ref. [13-25].

2. Experimental part

2.1 Materials Phenazine,

triphenylmethane,

diphenylmethane,

triphenylene,

perylene,

dibenzothiophene, dimethyl terephthalate and benzene were of commercial origin with mass fraction purities better than 0.98. Benzene was purified before use according to Ref. [26]. Purity of benzene was analyzed using an Agilent 7890 B gas chromatograph (GC) equipped with a flame ionization detector. Water content was checked using Karl Fischer titration. Dimethyl terephthalate was recrystallized from ethanol. Phenazine, triphenylmethane, perylene, triphenylene, diphenylmethane and dibenzothiophene were used without further purification (see Table S1).

2.2 Solution calorimetry Solution enthalpies of solid compounds in benzene were measured at T = 298.15 K in a concentration range from 0.42 to 9.39 mmol kg-1 using a TAM III precision solution calorimeter. Solid compounds were dissolved by breaking a glass ampule filled with 0.01 – 0.1 g of the studied sample in a glass cell containing 90 ml of pure solvent. Liquid diphenylmethane was injected in 25 µL portions using an electronically operated syringe equipped with a long gold cannula immersed in the solvent. The details of the solution calorimetry experimental procedure have been fully described elsewhere [27]. Average experimental solution enthalpies of aromatic compounds in benzene measured in this work are listed in Table 1.

Table 1

2.3 Differential scanning calorimetry 3

The enthalpy and temperature of fusion of dimethyl terephthalate were measured using the differential scanning calorimeter DSC 204 F1 Phoenix (Netzsch, Germany) as described previously [28]. Samples of 14.55 and 15.98 mg were placed in a 40 µL aluminum crucible and closed with a lid having a hole of 0.5 mm diameter. Experiments were performed in an argon dynamic atmosphere (150 mL·min−1) with the heating/cooling rate of 10 K·min−1. The measurements on two samples were performed. Three cycles of “heating-cooling” runs from room temperature up to temperature 40 K higher than the melting point and back were carried out. DSC was calibrated according to the manufacturer's recommendation using six substances (Hg, In, Sn, Bi, Zn and CsCl). Each value (onset temperature and area of the peak) was determined three times. Using the average values obtained, calibration curves were built. Uncertainties in onset temperature and enthalpy determination by this procedure were of 0.1 K and 3%, respectively. Experimental results from DSC measurements are presented in the Supporting Information (see Table S4).

3. Methodology The molar enthalpy of solution ( ∆ soln H A i /S (298.15 K) ) is the enthalpy of transfer of 1 mole of a solute Ai to an infinitely diluted solution in a solvent S at 298.15 K. The enthalpy of solution of Ai(cr) in a solvent S ( ∆ soln H Ai /S (cr, 298.15 K)) may be represented as a sum of the fusion enthalpy of Ai at 298.15 K ( ∆ lcr H Ai (298.15 K)) and the solution enthalpy of Ai in a virtual liquid state at 298.15 K in S ( ∆ soln H Ai /S (l, 298.15 K)): ∆ soln H Ai /S (cr, 298.15 K) = ∆ lcr H Ai (298.15 K) + ∆ soln H Ai /S (l, 298.15 K)

(1)

∆ lcr H Ai (298.15 K) is bound with the fusion enthalpy of Ai at the melting temperature Tm

( ∆ lcr H A i (Tm ) ) as follows:

∆ H (298.15 K) = ∆ H (Tm ) + ∑ ∆trns H (Ttrns ) − l cr

Ai

l cr

Ai

Ai

Tm

∫

[CpAi (l, T ) − CpAi (cr, T )]dT (2)

298.15

Here

∑∆

trns

H A i (Ttrns ) is a sum of all solid-solid phase transitions enthalpies occurring Tm

from 298.15 K to Tm;

∫

[CpAi (l, T ) − CpAi (cr, T )]dT is the adjustment term related to the

298.15

temperature dependence of the fusion enthalpy. The adjustment of fusion enthalpy from Tm to 298.15 K according to Eq. (2) presents a challenge. While C pA (cr, T ) below the melting temperature can be measured, C pA (l, T ) between i

i

4

298.15 K and Tm is usually unknown and not measurable [29]. At the same time CpA (l, T ) i

measurement of molten organic compounds is obstructed, especially when the melting temperature is high [30]. In some studies the temperature dependence of the fusion enthalpy is neglected [31,32]. It is also supposed that the C pA (l, Tm ) − C pA (cr, Tm ) value does not depend on i

i

temperature [33,34]. Various methods of estimation C pA (l, T ) − C pA (cr, T ) have been proposed i

i

[35-37]. Nevertheless, calculation of the temperature dependence of fusion enthalpy remains an estimate. Solution calorimetry can be also used for estimation of the fusion enthalpy temperature dependence. Combining Eqs. (1) and (2), we obtain the relationship between the enthalpy of fusion at the melting temperature and the enthalpy of solution at 298.15 K:

∆ soln H Ai /S (cr, 298.15 K) − ∆soln H Ai /S (l, 298.15 K) = Tm

= ∆ H (Tm ) + ∑ ∆ trns H (Ttrns ) − l cr

Ai

∫

Ai

(3)

[CpAi (l, T ) −CpAi (cr, T )]dT

298.15

In recent paper [12], based on Eq. (3) and known to us data on C pA (l, T ) and C pA (cr, T ) , i

i

we analyzed the relationship between ∆ soln H A /C H (cr, 298.15K) and ∆ lcr H A (Tm ) of the i

6

6

i

compounds which do not exhibit solid-solid phase transitions between 298.15 K and Tm and have Tm

the

∫

[CpAi (l, T ) −CpAi (cr, T )]dT values less than 3 kJ mol-1. The ∆ soln H Ai /C6H 6 (cr, 298.15K)

298.15

values were used for calculation of ∆ lcr H Ai (298.15 K) and compared to the ∆ lcr H Ai (298.15 K) values determined from Kirchhoff’s law (Eq. 2), considering temperature dependence of the liquid and solid phase heat capacities. Good agreement between ∆ lcr H A (298.15 K) derived from i

solution calorimetry and Kirchhoff’s law was shown. Tm

Mutual cancellation of small

∫

[CpAi (l, T ) −CpAi (cr, T )]dT and ∆soln H Ai /C6H6 (l, 298.15 K)

298.15

leads to approximate equality of ∆ soln H A /C H (cr, 298.15K) and ∆ lcr H A (Tm ) . In the present i

6

6

i

study we investigate the compounds for which large fusion enthalpies adjustments lead to the significant differences between ∆ soln H Ai /C6H6 (cr, 298.15 K) and ∆ lcr H Ai (Tm ) . The ∆ soln H A /C H (cr, 298.15K) , ∆ lcr H A (Tm ) and i

6

6

i

from the literature or measured in this work.

5

∑∆

trns

H A i (Ttrns ) values were taken

Tm

The

∫

[CpAi (l, T ) −CpAi (cr, T )]dT values were calculated from the reference data on

298.15

liquid and solid heat capacities. We do not distinguish between heat capacity at saturated vapor pressure CsatAi and isobaric heat capacity at 1 bar CpA , as well as melting temperature Tm and triple i

point temperature Ttp, because the difference between these quantities affects the Tm

∫

[CpAi (l, T ) −CpAi (cr, T )]dT value within the limits of 0.1%.

298.15

C pA i (cr, T ) were represented as linear functions of temperature using numeric data

points. In the cases of dibenzothiophene [16] and dimethyl terephthalate [23] C pA (cr, T ) i

functions derived by the authors were used. CpA (l, T ) in the range [298.15 K; Tm] were also i

represented as linear functions of temperature (except for dimethyl terephthalate), assuming that the temperature dependence of heat capacity below Tm is an extension of the temperature dependence above Tm. Linear temperature dependence of 14 molten polyaromatic hydrocarbons heat capacities demonstrated in [14] confirms the appropriateness of linear representation of CpA i (l, T ) functions for the studied aromatic compounds. Tm

∫

The compilation of the C (cr, T ) , C (l, T ) and Ai p

Ai p

[CpAi (l, T ) −CpAi (cr, T )]dT values

298.15

is provided in Table 2 together with the references used for calculations. Tm or Ttp derived in corresponding work are pointed out in the second column.

Table 2

The ∆soln H Ai /S (l, 298.15 K) value is necessary for calculation of ∆ lcr H Ai (298.15 K). It cannot be measured directly for the compounds that are solid at 298.15 K. However, for aromatic compound Ai not capable of self-association due to intermolecular hydrogen bonding and without long-chain alkyl substituents, in most cases ∆soln H A /C H (l, 298.15 K) does not exceed 2 kJ i

6

6

mol-1. Previously we showed [12] that ∆soln H Ai /C6H6 (l, 298.15 K) of aromatic compound Ai that is solid at 298.15 K may be estimated from the solution enthalpy of a structurally similar liquid compound. For example, isomeric liquid o-, m-, and p-xylenes have the solution enthalpies in benzene of 0.9, 1.1 and 0.8 kJ mol-1, respectively [12]. We assume that

of dimethyl terephthalate is equal to

∆soln H Ai /C6H6 (l, 298.15 K)

-1 ∆soln H Ai /C6H6 (l, 298.15 K) of dimethyl phthalate (1.9 kJ mol [12]); ∆soln H Ai /C6H6 (l, 298.15 K) of

6

triphenylmethane is equal to ∆soln H Ai /C6H6 (l, 298.15 K) of diphenylmethane (0.12 kJ mol-1). Solution enthalpies of diphenylmethane were taken as the average value between 0.03 kJ mol-1, [38] and the value obtained in the present work equal to 0.2 kJ mol-1 (see Table S2). The ∆soln H Ai /C6H6 (l, 298.15 K)

values

of

thianthrene

and

dibenzothiophene

are

equal

to

-1 ∆soln H Ai /C6H6 (l, 298.15 K) of thiophene (0.1 kJ mol [8]). For phenanthridine and phenazine we

accept

that

their

∆soln H Ai /C6H6 (l, 298.15 K)

values

are

equal

to

the

mean

of

the

-1 -1 ∆soln H Ai /C6H6 (l, 298.15 K) values of quinoline (0.7 kJ mol [8]) and isoquinoline (0.53 kJ mol

[39]), 0.6 kJ mol-1. For the remaining compounds (anthracene, p-terphenyl, perylene, triphenylene) we accept the value of 0 kJ mol-1 as the lower limit of ∆soln H Ai /C6H6 (l, 298.15 K) .

4. Results and discussion

Heat capacity of molten organic compounds, especially if they have a high melting temperature, is measured rarely. Nevertheless, for several compounds studied in the present paper more than one result on CpA (l, T ) measurements is available (see Table 2). In the case of i

anthracene, dibenzothiophene, triphenylmethane the disagreement between the C pA (l, Tm ) values i

obtained in different reports is less than 3%. In the case of perylene it is equal to 4% and for pterphenyl it reaches 8%. However, the CpA (l, T ) functions derived based on these measurements i

Tm

are considerably more distinct. It leads to notable differences in

∫

[CpAi (l, T ) −CpAi (cr, T )]dT

298.15

calculation for anthracene, p-terphenyl and, the most, for perylene. We used smoothed CpA (l, T ) and C pA (cr, T ) reference values for linear fit if available. i

Tm

The

∫

i

[CpAi (l, T ) −CpAi (cr, T )]dT values derived from the raw experimental and smoothed data

298.15

from one reference differ by less than 0.1 kJ mol-1, except for perylene and triphenylene. In the case of triphenylene [25] and perylene [24], linear fitting of unsmoothed data leads to significant standard errors in the linear fit coefficient determination. For perylene linear fit of 4 unsmoothed -1

-1

C pA i (l, T ) values between 554 K and 573 K [24] gives C pA i (l, T ) /(J K mol ) = (313.5±72.6) +

(0.368±0.128) · (T/K). In the case of triphenylene analogous fitting of unsmoothed data between 481 K and 510 K [25] leads to a function CpA (l, T ) /(J K-1 mol-1) = (172.0±22.0) + (0.568±0.044) i

7

Tm

· (T/K). Accurate determination of the

∫

[CpAi (l, T ) − CpAi (cr, T )]dT value from CpA (l, T ) i

298.15

which is available in a restricted temperature range is strongly affected by errors in C pA (l, T ) i

measurement. However, even in an inert atmosphere, thermal decomposition [40], polymerization [41] or vaporization may prevent accurate studies of the thermal properties of melt. The comparison between the ∆ lcr H A (298.15 K) values calculated from the solution i

enthalpies in benzene and obtained from ∆ lcr H Ai (Tm ) according to Kirchhoff’s law with the use of experimental data on the heat capacities (Eq. 2) is shown in Table 3. The ∆ lcr H A (Tm ) values are listed in column 2. For anthracene, p-terphenyl, i

triphenylmethane, perylene, triphenylene we used the recommended fusion enthalpies values from Ref. [10]. For phenanthridine, phenazine and thianthrene we used the ∆ lcr H A (Tm ) values i

obtained by adiabatic calorimetry. For dimethyl terephthalate literature data are slightly scattered (see Table S3). We measured ∆ lcr H A (Tm ) of dimethyl terephthalate by DSC (see Table S3). The i

obtained value (35.5±0.2 kJ·mol-1) is slightly larger than the literature values. The reasons for the disagreements are not clear and the average ∆ lcr H A (Tm ) value was used. Compilation of the i

experimental data on the fusion enthalpies is provided in Table S4 of Supporting Information. Uncertainties of the average ∆ lcr H Ai (Tm ) values correspond to standard deviations of experimental values. ∆ lcr H A i (298.15 K) calculated from the solution enthalpies are listed in column 3.

Compilation of ∆ soln H Ai /C6H6 (cr, 298.15 K) and ∆soln H Ai /C6H6 (l, 298.15 K) is provided in Table S5. Uncertainty of ∆ lcr H Ai (298.15 K) calculated in this way is a combined uncertainty of the ∆ soln H A i /C6 H 6 (cr, 298.15 K) and ∆soln H Ai /C6H6 (l, 298.15 K) .

∆soln H Ai /C6H6 (l, 298.15 K) estimation

uncertainty cannot be strictly calculated. It has approximately the same magnitude as the variance of the mean of ∆ soln H Ai /C6 H 6 (l, 298.15 K) of the liquid compounds used in the present work and in Ref. [12] (0.9±0.7 kJ mol-1). ∆ lcr H A i (298.15 K) obtained from ∆ lcr H A i (Tm ) according to Eq. (2) are listed in column 4. Tm

Previously [12] we estimated limit of uncertainty of the

∫

[CpAi (l, T ) − CpAi (cr, T )]dT value as

298.15 Tm

-1

0.2 kJ mol

based on deviations between

∫

[CpAi (l, T ) − CpAi (cr, T )]dT calculated from

298.15

8

different reference data for the same compound. In the present paper significant deviations Tm

between the

∫

[CpAi (l, T ) − CpAi (cr, T )]dT values for perylene, anthracene, p-terphenyl prevent

298.15

using 0.2 kJ mol-1 as a higher estimate for the integral uncertainty. For these compounds we provide several ∆ lcr H Ai (298.15 K) values together with the references based on which the adjustments were carried out. For p-terphenyl [15], dibenzothiophene, triphenylmethane, thianthrene, phenazine, phenanthridine, dimethyl terephthalate liquid phase heat capacities were Tm

measured in a fairly wide range and

∫

[CpAi (l, T ) − CpAi (cr, T )]dT calculation uncertainties

298.15

associated with a scatter from the linear fit are negligible compared with ∆ lcr H A (Tm ) standard i

uncertainties. In Ref. [14] only linear fit coefficients are provided without standard errors and initial numeric data for fitting, so we do not provide the uncertainties for the ∆ lcr H Ai (298.15 K) values calculated using data from Ref. [14]. The fifth column contains the ∆ lcr H A (298.15 K) values obtained from ∆ lcr H A (Tm ) i

i

according to the empirical scheme of Chickos et. al. scheme [42]. The scheme [42] is often used by researchers in phase transitions thermochemistry for adjustment of fusion, vaporization and sublimation enthalpies to 298.15 K [43-45]. According to the scheme, ∆ lcr H Ai (298.15 K) = ∆ lcr H A i (Tm ) – ∆ lcr C pAi · (Tm – 298.15 K), where ∆ lcr C pAi is calculated as follows [10]: -1 -1 ∆ lcr CpAi /(J K mol ) = 9.83 + 0.26 · CpAi (l, 298.15 K) – 0.15 · CpAi (cr, 298.15 K)

(4)

The values of CpA (l, 298.15 K) and CpA (cr, 298.15 K) can be taken from the literature or i

i

calculated according to an additive scheme [45]. In the present work we used the CpA (l, 298.15 i

K) and CpA (cr, 298.15 K) values derived from temperature dependencies that are provided in i

Table 1. For each ∆ lcr H Ai (298.15 K) value adjusted according to Eq. (4) we also provide literature references to the corresponding CpA (l, 298.15 K) and CpA (cr, 298.15 K) values. The i

i

values of adjustments to 298.15 K calculated from Chickos et. al. scheme [42], CpA (l, 298.15 K) i

and CpA (cr, 298.15 K) are listed in Table S6. Uncertainties of the ∆ lcr H Ai (298.15 K) values i

calculated according to Eq. (4) correspond to propagated errors of the sums of ∆ lcr H A (Tm ) and i

Chickos et. al. scheme (one-third of thermal adjustment [10]) uncertainties.

Table 3

9

It can be seen from Table 3 that for the most of compounds studied in this work agreement between columns 3 and 4 is within the limits of 1-2 kJ mol-1. In the case of phenazine ∆ lcr H A i (298.15 K) values calculated from the solution enthalpies and Kirchhoff’s law differ by

2.6 kJ mol-1. Slight differences may be explained by the uncertainty of ∆soln H A /C H (l, 298.15 K) i

6

6

estimation, as well as by experimental errors of ∆ lcr H Ai (Tm ) , ∆ soln H Ai /S (cr, 298.15 K), C pA i (cr, T ) and CpA i (l, T ) determinations.

Among two ∆ lcr H A (298.15 K) of perylene calculated according to Eq. (2), the value i

derived based on the data from Ref. [14] fits better with the quantity calculated from the solution enthalpy in benzene. It should be taken into account that in [14] CpA (l, T ) is measured in a wider i

temperature range than in [24]. For perylene [24], the uncertainty in the linear fit of C pA (l, T ) of triphenylene [25] may i

be a reason for the discrepancy observed between the ∆ lcr H A (298.15 K) values calculated by i

Eqs. (1, 2). In the case of anthracene, the value 24.7 kJ mol-1 derived by Eq. 1 fits with both values 23.1 kJ mol-1 and 24.8 kJ mol-1 calculated according to Eq. 2 within the limits of ∆soln H Ai /C6H6 (l, 298.15 K) estimation accuracy.

In the case of p-terphenyl, the value 27.5 kJ mol-1 calculated by Eq. 1 fits better with -1 ∆ lcr H Ai (298.15 K) = 27.7 kJ mol derived basing on the data on CpA (l, T ) from [15]. i

The comparison of the values in columns 3 and 4 with the fusion enthalpies adjusted to 298.15 K according to Chickos et. al. scheme [42] shows that the scheme has good performance in the case of dibenzothiophene, triphenylmethane, thianthrene, phenazine, phenanthridine, dimethyl terephthalate. In the case of anthracene it predicts a greater temperature adjustment for ∆ lcr H Ai (298.15 K) than it is obtained from Eqs. (1) and (2). For perylene the slight

overestimation of the adjustment by the scheme [42] is also present. In the case of perylene and triphenylene the uncertainty of heat capacities derived in [24,25] inevitably leads to analogous discrepancies with ∆ lcr H Ai (298.15 K) calculated by Eq. (1). ∆ lcr H Ai (298.15 K) = 17.8 kJ mol-1 of perylene derived using the scheme [42] is also smaller than it is predicted by Kirchhoff’s law. Combining the observations of relations between the ∆ lcr H A (298.15 K) values derived i

from ∆ lcr H A (Tm ) based on [42] on the one hand and calculated according to Eqs. (1, 2) on the i

other carried out in this work and [12], we may conclude that frequently scheme [42] performs well. However, it overestimates temperature dependence of the fusion enthalpies of naphthalene, fluorene, acenaphthene, pyrene, anthracene, perylene. Table 4 contains the comparison between 10

∆ lcr CpAi calculated according to Eq. (4) and as the mean C pA i (l, T ) − C pA i (cr, T ) value in the Tm

temperature range between 298.15 K and Tm

∫

[CpAi (l, T ) −CpAi (cr, T )]dT / (Tm − 298.15 K) for

298.15

the compounds with close CpA (l, 298.15 K) and CpA (cr, 298.15 K) values. The heat capacities of i

i

liquids at 298.15 K that are used in Eq. (4) are calculated by linear extrapolation of the literature heat capacities of the melt.

Table 4

It can be seen that for the compounds with similar CpA (l, 298.15 K) and CpA (cr, 298.15 i

i

K) the mean ∆ lcr C pA values between 298.15 K and Tm are notably distinct, while ∆ lcr C pA i

i

calculated according to Eq. (4) remain similar. The distinctions are connected with the different slopes of CpA (l, T ) and C pA (cr, T ) temperature dependencies and melting temperatures. i

i

5. Conclusions

Summing up, the following conclusions about the relationships between ∆ soln H A /S (cr, i

298.15 K) and ∆ lcr H Ai (Tm ) may be made based on the results obtained in the present study and in the previous work [12]. ∆ soln H A i /C6 H 6 (cr, 298.15 K) of aromatic compound not capable of self-association due to

intermolecular hydrogen bonding in benzene reflects the value of its ∆ lcr H Ai (298.15 K) within the limits of ∆soln H Ai /C6H6 (l, 298.15 K) estimation (2 kJ mol-1). Therefore, for compounds with small difference between ∆ lcr H A (298.15 K) and ∆ lcr H A (Tm ) approximate equality between i

i

∆ soln H A i /C6 H 6 (cr, 298.15K) and ∆ lcr H A i (Tm ) is observed. The notable ∆ lcr H A i (Tm ) – ∆ lcr H A i

(298.15 K) differences can be detected with the help of solution calorimetry. Thus, solution calorimetry can be used as a complementary tool for adjustment of the fusion enthalpy to 298.15 K, especially in the case of high-melting organic compounds. The assumption about the possibility of extending the C pA (l, T ) temperature dependence i

below the melting temperature is validated for a set of hypothetical aromatic liquids by comparison of ∆ lcr H Ai (298.15 K) derived by Kirchhoff’s law and solution enthalpies in benzene,

11

within the limits of the fusion and solution enthalpies measurements and ∆ soln H A i /C 6 H 6 (l, 298.15 K) estimation uncertainty. Solution calorimetry may be used not only for fusion enthalpy adjustment, but also for validation of the experimentally measured and empirically calculated heat capacities of organic compounds in the liquid state. In the last decades several schemes for estimation of liquids heat capacities at 298.15 K [49] or as a function of temperature [50,51] have been developed. The analysis Tm

∫

of

the

connection

between

∆ lcr H Ai (Tm ) ,

∆ soln H Ai /C6H 6 (cr, 298.15K) ,

[CpAi (l, T ) −CpAi (cr, T )]dT may be useful for indirect confirmation of the robustness of such

298.15

schemes.

Acknowledgements

This work has been performed according to Grant No. 14.Y26.31.0019 from Ministry of Education and Science of Russian Federation.

References

[1]

S. Gracin, T. Brinck, Å.C. Rasmuson, Ind. Eng. Chem. Res. 41 (2002) 5114-5124.

[2]

J. Sangster, J. Phys. Chem. Ref. Data 28 (1999) 889-930.

[3]

S.H. Neau, S.V. Bhandarkar, E.W. Hellmuth, Pharm. res. 14 (1997) 601-605.

[4]

J.S. Chickos, P. Webb, G. Nichols, T. Kiyobayashi, P.-C. Cheng, L. Scott, J. Chem.

Thermodyn. 34 (2002) 1195-1206. [5]

S. Vecchio, M. Tomassetti, Fluid Phase Equilib. 279 (2009) 64-72.

[6]

B.N. Solomonov, M.A. Varfolomeev, R.N. Nagrimanov, T.A. Mukhametzyanov, V.B.

Novikov, Thermochim. Acta 622 (2015) 107–112. [7]

B.N. Solomonov, R.N. Nagrimanov, M.A. Varfolomeev, A.V. Buzyurov, T.A.

Mukhametzyanov, Thermochim. Acta 627–629 (2016) 77-82. [8]

B.N. Solomonov, R.N. Nagrimanov, T.A. Mukhametzyanov, Thermochim. Acta 633

(2016) 37-47. [9]

B.N. Solomonov, M.A. Varfolomeev, R.N. Nagrimanov, V.B. Novikov, D.H. Zaitsau,

S.P. Verevkin, Thermochim. Acta 589 (2014) 164-173. [10]

M.V. Roux, M. Temprado, J.S. Chickos, Y. Nagano, J. Phys. Chem. Ref. Data 37 (2008)

1855-1996. [11]

B.N. Solomonov, A.I. Konovalov, V.B. Novikov, A.N. Vedernikov, M.D. Borisover,

V.V. Gorbachuk, I.S. Antipin, J.Gen.Chem.USSR (Engl.Transl.) 54 (1984) 1444-1453. 12

[12]

M.I. Yagofarov, R.N. Nagrimanov, M.A. Ziganshin, B.N. Solomonov, J. Chem.

Thermodyn. 116 (2018) 152-158. [13]

P. Goursot, H.L. Girdhar, E.F. Westrum, J. Phys. Chem. 74 (1970) 2538-2541.

[14]

N. Durupt, A. Aoulmi, M. Bouroukba, M. Rogalski, Thermochim. Acta 260 (1995) 87-

94. [15]

S.S. Chang, J. Chem. Phys. 79 (1983) 6229-6236.

[16]

D. O’Rourke, S. Mraw, J. Chem. Thermodyn. 15 (1983) 489-502.

[17]

R. Chirico, S. Knipmeyer, A. Nguyen, W. Steele, J. Chem. Thermodyn. 23 (1991) 431-

450. [18]

M. Spaght, S.B. Thomas, G. Parks, J. Phys. Chem. 36 (1932) 882-888.

[19]

V.Y. Kurbatov, Zhur. Obshch. Khim. 20 (1950) 1139-1144.

[20]

W. Steele, R. Chirico, S. Knipmeyer, A. Nguyen, J. Chem. Thermodyn. 25 (1993) 965-

992. [21]

R.D. Chirico, A.F. Kazakov, W.V. Steele, J. Chem. Thermodyn. 42 (2010) 571-580.

[22]

W.V. Steele, R.D. Chirico, I.A. Hossenlopp, A. Nguyen, N.K. Smith, B.E. Gammon, J.

Chem. Thermodyn. 21 (1989) 81-107. [23]

J.H. Elliott, M.D. Chris, J. Chem. Eng. Data 13 (1968) 475-479.

[24]

W.-K. Wong, E.F. Westrum, Mol. Cryst. Liq. Cryst. 61 (1980) 207-228.

[25]

W.-K. Wong, E.F. Westrum, J. Chem. Thermodyn. 3 (1971) 105-124.

[26]

D. Perrin, W. Armarego, Purification of Laboratory Chemicals, Pergamon Press: Oxford,

1980. [27]

B.N. Solomonov, M.A. Varfolomeev, R.N. Nagrimanov, V.B. Novikov, A.V. Buzyurov,

Y.V. Fedorova, T.A. Mukhametzyanov, Thermochim. Acta 622 (2015) 88-96. [28]

M.A. Ziganshin, A.A. Bikmukhametova, A.V. Gerasimov, V.V. Gorbatchuk, S.A.

Ziganshina, A.A. Bukharaev, Prot. Met. Phys. Chem. 50 (2014) 49-54. [29]

W.J. Lyman, W.F. Reehl, D.H. Rosenblatt, Handbook of chemical property estimation

methods, American Chemical Society: Washington, DC, 1990. [30]

D.S. Mishra, S.H. Yalkowsky, Pharm. Res. 9 (1992) 958-959.

[31]

T. Reschke, K.V. Zherikova, S.P. Verevkin, C. Held, J. Pharm. Sci. 105 (2016) 1050-

1058. [32]

C. Held, L.F. Cameretti, G. Sadowski, Ind. Eng. Chem. Res. 50 (2010) 131-141.

[33]

Z. Lisicki, M.E. Jamróz, J. Chem. Thermodyn. 32 (2000) 1335-1353.

[34]

M.E. Jamróz, J.C. Dobrowolski, J. Polaczek, A.M. Szafrański, J.K. Kazimirski, Z.

Lisicki, J. Chem. Thermodyn. 33 (2001) 565-579. 13

[35]

G.D. Pappa, E.C. Voutsas, K. Magoulas, D.P. Tassios, Ind. Eng. Chem. Res. 44 (2005)

3799-3806. [36]

J.S. Chickos, Thermochim. Acta 313 (1998) 19-26.

[37]

M. Wu, S. Yalkowsky, Ind. Eng. Chem. Res. 48 (2008) 1063-1066.

[38]

I. Uruska, H. Inerowicz, J. Sol. Chem. 9 (1980) 97-108.

[39]

M. Lal, , F.L. Swinton, J. Chem. Soc. Faraday Trans. 63 (1967) 1596-1602.

[40]M. Fulem, V.c. Laštovka, M. Straka, K. Ruzicka, J.M. Shaw, J. Chem. End. Data 53 (2008) 2175-2181. [41]

T. Mahnel, V. Štejfa, M. Fulem, K. Růžička, Fluid Phase Equilib. 434 (2017) 74-86.

[42]

J.S. Chickos, S. Hosseini, D.G. Hesse, J.F. Liebman, Struct. Chem. 4 (1993) 271-278.

[43]

W.E. Acree, J.S. Chickos, J. Phys. Chem. Ref. Data 39 (2010) 043101-043101.

[44]

S.P. Verevkin, S.A. Kozlova, Thermochim. Acta 471 (2008) 33-42.

[45]

A.R.R.P. Almeida, M.J.S. Monte, J. Chem. Thermodyn. 65 (2013) 150-158.

[46]

H. Finke, J. Messerly, S. Lee, A. Osborn, D. Douslin, J. Chem. Thermodyn. 9 (1977)

937-956. [47] R. Chirico, S. Knipmeyer, A. Nguyen, W. Steele, J. Chem. Thermodyn. 21 (1989) 13071331. [48] R. Chirico, S. Knipmeyer, A. Nguyen, W. Steele, J. Chem. Thermodyn. 25 (1993) 14611494. [49] J.S. Chickos, D.G. Hesse, J.F. Liebman, Struct. Chem. 4 (1993) 261-269. [50]

M. Luria, S.W. Benson, J. Chem. End. Data 22 (1977) 90-100.

[51]

Z. Kolska, J. Kukal, M. Zabransky, V. Ruzicka, Ind. Eng. Chem. Res. 47 (2008) 2075-

2085.

14

• The general scheme for the analysis of the relationship between solution and fusion enthalpies was developed. •

The solution enthalpies of six aromatic compounds in benzene were determined.

•

The fusion enthalpies of dimethyl terephthalate were measured.

15

Table 1

Average experimental solution enthalpies of aromatic compounds in benzene measured in this work at 298.15 K and 0.1MPaa. ∆soln H Ai /C6H6 Compound kJ mol-1 dibenzothiophene (cr) 20.29±0.07 phenazine (cr) 20.61±0.19 perylene (cr) 25.27±0.55 triphenylmethane (cr) 17.10±0.18 triphenylene (cr) 22.34±0.23 diphenylmethane (l) 0.21±0.05 a The detailed compilation of the experimental solution enthalpies measured at different solute concentrations for each compound is listed in Table S2. Uncertainties correspond to expanded uncertainties of the mean U (0.95 level of confidence. Student’s t distribution 2.0).

16

Table 2 Ai p

Tm

Ai p

The compilation of C (cr, T ) , C (l, T ) and

∫

[CpAi (l, T ) −CpAi (cr, T )]dT values with the references which were used for CpAi (T ) functions fitting.

298.15

Crystal Compound

Tm, K

Ai p

C

-1

-1

(cr, T) , J K mol a

Liquid

acr + bcr·(T/K) +ccr·(T/K)2

T b, K

Ai p

C

-1

∫

-1

(l, T) , J K mol a

Tm

al + bl·(T/K) +cl·(T/K)2

∆Cpl-cr dT c,

298.15

Tb, K

Ref.

kJ mol-1

488.9

– 21.9 + 0.779 · T

298.2 – 488.9

133.2 + 0.469 · T

488.9 – 500.0

6.3

[13]

-

-

-

113.2 + 0.497 · T

492 – 592

4.6

d

[14]

487.0

– 6.0 + 0.956 · T

298.2 – 487.0

94.2 + 0.804 · T

487.0 – 580.0

7.7

[15]

-

-

-

149.4 + 0.614 · T

492 – 592

4.0

d

[14]

371.0

– 5.4 + 0.671 · T

220.0 – 371.0

123.8 + 0.422 · T

371.0 – 560.0

3.3

[16]

371.8

– 2.6 + 0.674 · T

298.2 – 371.8

118.4 + 0.443 · T

298.2 – 371.8

3.3

[17]

365.3

– 105.1 + 1.364 · T

303 – 353

184.9 + 0.716 · T

373 – 393

5.0

[18]

365.2

-

-

150.5 + 0.813 · T

373 – 615

4.9

d

[19]

thianthrene

429.6

27.9 + 0.647 · T

298.2 – 429.6

154.7 + 0.431 · T

298.2 – 429.6 f

6.3

[20]

phenazine

447.9

4.4 + 0.664 · T

298.2 – 447.9

153.6 + 0.399 · T

447.9 – 520.0

7.5

[21]

phenanthridine

379.7

– 8.2 + 0.705 · T

298.2 – 354.0

– 82.3 + 0.922 · T

354.0 – 379.7

127.2 + 0.468 · T

379.7 – 450.0

4.4

[22]

dimethyl

413.8

159.2 + 0.154 · T +

303.2 – 413.8

499.1 – 0.944 · T +

413.8 – 473.2

7.3

[23]

anthracene

p-terphenyl dibenzothiophene triphenylmethane

e

17

e

f

+ 6.34 · 10-4 · T 2 d

terephthalate perylene triphenylene

+ 1.53 · 10-3 · T 2 d

551.0

26.9 + 0.848 · T

298.2 – 551.0

355.08 + 0.295 · T

551.0 – 575.0

23.6

[24]

-

-

-

150.5 + 0.630 · T

552 – 652

7.9

d

[14]

471.0

11.8 + 0.838 · T

298.2 – 471.0

217.7 + 0.474 · T

471.0 – 500.00

11.4

[25]

a

Temperature dependence of the molar isobaric heat capacity of the compound at solid and liquid states.

b

Temperature range in which fit of the heat capacity as a function of temperature was made.

c

The integral with respect to temperature of the difference between the molar isobaric heat capacities of compound in solid and hypothetical liquid

states in the range [298.15 K, Ttp]. Tm d

The

∫

∆Cpl-cr dT value is calculated from CpA (l, T) in this line and CpA (cr, T) in the line above. i

i

298.15 e

The temperature dependencies of heat capacity reported by the authors.

f

Authors point out that the values of heat capacities at these temperatures were calculated with graphical extrapolation.

g

Average heat capacity in the temperature range 303 – 363 K.

18

Table 3 Comparison between fusion enthalpies at the melting temperature and at 298.15 K adjusted to 298.15 K according to Eq. (2) (column 4) and to Chickos et. al. scheme [42] (column 5) and calculated from solution enthalpies in benzene at 298.15 K (column 3).

∆lcr H Ai (298.15

∆lcr H Ai (298.15

2

K) (Eq. 1) , kJ mol-1 3

anthracene

29.4±0.1 (488.9±0.1)

24.7

p-terphenyl

35.4±0.1 (478.0±0.1)

27.5

dibenzothiophene triphenylmethane thianthrene phenazine phenanthridine dimethyl terephthalate

21.8±0.4 (371.8±0.6) 20.7±0.4 (367.2±0.1) 27.6±0.1 (429.6±0.1) 24.9±0.1 (447.9±0.1) 22.8±0.1 (379.7±0.1)

20.2 17.0 22.4 20.0 19.4

K) (Eq. 2) , kJ mol-1 4 23.1 [13] 24.8 [13,14] 27.7±0.1 [15] 31.4 [14,15] 18.5±0.4 15.7±0.4 21.3±0.1 17.4±0.1 18.4±0.1

5 20.0±3.1 [13] 20.6±2.9 [13,14] 25.1±3.4 [15] 25.1±3.4 [14,15] 18.5±1.2 16.1±1.6 21.0±2.2 17.4±2.5 18.8±1.3

33.7±1.8 (413.9±1.1)

27.5

26.4±1.8

27.5±2.8

Compound

∆ lcr H Ai (Tm ) a, kJ mol-1

1

b

c

∆lcr H Ai (298.15 K) d, kJ mol-1

24.0 [14,24] 17.8±4.7 [14,24] 8.3 [24] 10.9±7.0 [24] triphenylene 24.7±0.1 (471.0±0.1) 22.4 11.0 11.3±4.5 a The fusion enthalpies at the melting temperatures. Primary data are collected in Table S3. . Uncertainties of average fusion enthalpies and melting temperatures values correspond to the standard deviations of experimental data points. The uncertainties which are less than 0.1 kJ mol1 and 0.1 K were rounded to 0.1 kJ mol-1 and 0.1 K. b The fusion enthalpy values at 298.15 K calculated from Eq. (1). The primary data for calculation are collected in Table S5. c The fusion enthalpy values at 298.15 K calculated according to Eq. (2) from the fusion perylene

31.9±0.1 (551.0±0.1)

25.3

Tm

enthalpies listed in the second column and

∫

[CpAi (l, T ) −CpAi (cr, T )]dT listed in Table 1.

298.15 l cr

Ai

Uncertainties are equal to ∆ H (Tm ) standard uncertainties. The fusion enthalpy values at 298.15 K calculated according to Chickos et. al. scheme [42]. The procedure is described in details in Supplementary material. Uncertainties correspond to propagated errors of the sums of ∆ lcr H Ai (Tm ) and Chickos et. al. scheme (one-third of thermal d

adjustment [10]) uncertainties.

19

Table 4 Comparison between the Tm

∫

∆ lcr CpAi

values calculated according to Eq. (4) and as

[CpAi (l, T ) −CpAi (cr, T )]dT / (Tm − 298.15 K) for the compounds with the close CpAi (l, 298.15

298.15

K) and CpAi (cr, 298.15 K). Compound fluorene biphenyl 2,6-dimethylnaphthalene 2,7-dimethylnaphthalene dibenzothiophene Tm

a

Calculated as

∫

CpAi (l, 298.15 K)

CpAi (cr, 298.15 K)

∆ lcr CpAi (Eq. 4)

J K-1 mol-1

J K-1 mol-1

J K-1 mol-1

250.7 [46] 250.9 [47] 247.7 [46] 251.9 [48] 250.0 [17]

203.1 [46] 198.4 [47] 203.6 [46] 204.4 [46] 198.3 [17]

44.5 45.3 43.7 44.7 45.0

[CpAi (l, T ) −CpAi (cr, T )]dT / (Tm − 298.15 K)

298.15

20

∆ lcr CpAi (mean)a J K-1 mol-1 26.1 45.2 36.0 39.2 45.8