**2.1 Experimental and mathematical processing**

Fig. 1 presents a schematic view of a setup designed for determinations of the temperature dependence of saturation vapor pressure by comparative ebulliometry (Varouchtchenko & Droujinina, 1995).

Fig. 1. The setup for determination of the *pT* parameters: DE, differential ebulliometer; MS, manometer system; (1) mercury-contact manometer; (2) electromagnetic valve; (3) roughing pump; (4) ballast reservoir; (5) traps

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 599

The setup consists of a differential ebulliometer used for measuring the boiling and condensation temperatures and manometer system operating in the manostat mode. The main part of MS system is a mercury-contact (tungsten) manometer that serves for automatic control and determination of the pressure inside the ebulliometer. Argon was introduced into the system to maintain the constant pressure equal to that of the saturation vapors of the substance under study. The temperature of the (liquid + vapor) equilibrium

A schematic view of modified Swietoslawski –type ebulliometer is given in Fig. 2. The differential ebulliometer was used for determination of the temperature dependence of the vapor pressure by measuring the boiling, *Tboil* , or (rarely) condensation, *Tcond* , temperatures and for estimation of an ebulliometric degree of purity for the samples by the difference (*T T boil cond* ). The latter is below 0.005 K for the pure substances. The boiling and condensation sections and other parts of differential ebulliometer were made of "Pyrex" glass and were sealed together. The modification of the ebulliometer was directed for solving three basic problems: 1) increasing the thermometric sensitivity of a system used for temperature measurements of the (liquid – vapor) equilibrium; 2) decreasing a heat exchange of the temperature sensors with the surrounding, and 3) reducing the superheating of the boiling liquid, that leads to increasing the accuracy of the temperature

For increasing the sensitivity of the thermometers, their protecting tubes were soldered in the boiling and condensation sections of the ebulliometer. Sensing elements of vibration – resistant thermometers ( *R* 100 ) consisted of a few platinum spirals wound around glass

Connecting wires (current and potential) of the thermometer were vacuum – tight sealed through the glass-molybdenum part of a passage (12, Fig. 2) of the protecting tube. The thermometers were graduated in Mendeleev's Institute of Metrology (S. Petersburg) at the triple – point temperature of water (273.16 K) and melting temperatures of tin (505.118 K) and gallium (302.920 K). The summary error of graduation is <sup>3</sup> 3 10 *<sup>K</sup>* . A special system of heat insulation of the thermometers was employed. It consisted of: glass screens washed by boiling liquid or by condensate (21 or 21'), respectively (Fig. 2); silver radiation screens; vacuum jackets ( <sup>3</sup> *<sup>p</sup>* 1.3 10 *Pa* ); heat – insulating layers (asbestos), and electrically heated screens (25 and 25') for upper parts of thermometers overhanging from ebulliometer. Application of such heat – insulating system made it possible to conduct precision temperature measurements without heating the main part of the ebulliometer. The error of temperature measurements caused by heat exchange of the thermometers with the surroundings, were estimated on the basis of heat – exchange laws to be <sup>3</sup> 1 10 *<sup>K</sup>* . The superheating of the liquid was reduced by using several internal and two external boiler heaters which promoted to smooth boiling of the liquid. Performed modification of the ebulliometer allowed cutting down substantially the amount of liquid which was spent for

Thus, the necessary volume of liquid was reduced several times: down to <sup>3</sup> <sup>5</sup>*cm* when measuring only the boiling temperature and to <sup>3</sup> <sup>8</sup>*cm* when both boiling and condensation temperatures were measured. The use of the comparison method makes it possible to

capillaries. The latter had coefficients of linear expiation close to that of platinum.

heating the inner surfaces of instrument up to working temperature.

was measured at 20 fixed pressures controlled by manometer system.

measurements.

Fig. 2. The differential ebulliometer: I, boiling section; II, rectification column; III, condensation section; IV, system of coolers for returning and collecting a condensate; (1, 1') platinum resistance thermometers; (21, 21') glass screens of thermometers; (22, 22') silver radiation screens; (23, 23') vacuum shells; (24, 24') heat-insulating layer (asbestos); (25, 25') shells for heating the thermometer parts extending from the ebulliometer; (3) boiler; (3') Ushaped liquid valve; (4) Cottrell pump; (5) spherical reservoir; (6 (13), 6') differential Chromel-Alumel thermocouples; (7, 7') droplet counters; (8, 8') branches for outlet and inlet of liquid; (9) sensing element of platinum resistance thermometer; (10) platinum wires; (11) protective glass tube; (12) Pyrex-tungsten glass-molybdenum glass transition.

Fig. 2. The differential ebulliometer: I, boiling section; II, rectification column; III,

protective glass tube; (12) Pyrex-tungsten glass-molybdenum glass transition.

condensation section; IV, system of coolers for returning and collecting a condensate; (1, 1') platinum resistance thermometers; (21, 21') glass screens of thermometers; (22, 22') silver radiation screens; (23, 23') vacuum shells; (24, 24') heat-insulating layer (asbestos); (25, 25') shells for heating the thermometer parts extending from the ebulliometer; (3) boiler; (3') Ushaped liquid valve; (4) Cottrell pump; (5) spherical reservoir; (6 (13), 6') differential

Chromel-Alumel thermocouples; (7, 7') droplet counters; (8, 8') branches for outlet and inlet of liquid; (9) sensing element of platinum resistance thermometer; (10) platinum wires; (11)

The setup consists of a differential ebulliometer used for measuring the boiling and condensation temperatures and manometer system operating in the manostat mode. The main part of MS system is a mercury-contact (tungsten) manometer that serves for automatic control and determination of the pressure inside the ebulliometer. Argon was introduced into the system to maintain the constant pressure equal to that of the saturation vapors of the substance under study. The temperature of the (liquid + vapor) equilibrium was measured at 20 fixed pressures controlled by manometer system.

A schematic view of modified Swietoslawski –type ebulliometer is given in Fig. 2. The differential ebulliometer was used for determination of the temperature dependence of the vapor pressure by measuring the boiling, *Tboil* , or (rarely) condensation, *Tcond* , temperatures and for estimation of an ebulliometric degree of purity for the samples by the difference (*T T boil cond* ). The latter is below 0.005 K for the pure substances. The boiling and condensation sections and other parts of differential ebulliometer were made of "Pyrex" glass and were sealed together. The modification of the ebulliometer was directed for solving three basic problems: 1) increasing the thermometric sensitivity of a system used for temperature measurements of the (liquid – vapor) equilibrium; 2) decreasing a heat exchange of the temperature sensors with the surrounding, and 3) reducing the superheating of the boiling liquid, that leads to increasing the accuracy of the temperature measurements.

For increasing the sensitivity of the thermometers, their protecting tubes were soldered in the boiling and condensation sections of the ebulliometer. Sensing elements of vibration – resistant thermometers ( *R* 100 ) consisted of a few platinum spirals wound around glass capillaries. The latter had coefficients of linear expiation close to that of platinum.

Connecting wires (current and potential) of the thermometer were vacuum – tight sealed through the glass-molybdenum part of a passage (12, Fig. 2) of the protecting tube. The thermometers were graduated in Mendeleev's Institute of Metrology (S. Petersburg) at the triple – point temperature of water (273.16 K) and melting temperatures of tin (505.118 K) and gallium (302.920 K). The summary error of graduation is <sup>3</sup> 3 10 *<sup>K</sup>* . A special system of heat insulation of the thermometers was employed. It consisted of: glass screens washed by boiling liquid or by condensate (21 or 21'), respectively (Fig. 2); silver radiation screens; vacuum jackets ( <sup>3</sup> *<sup>p</sup>* 1.3 10 *Pa* ); heat – insulating layers (asbestos), and electrically heated screens (25 and 25') for upper parts of thermometers overhanging from ebulliometer. Application of such heat – insulating system made it possible to conduct precision temperature measurements without heating the main part of the ebulliometer. The error of temperature measurements caused by heat exchange of the thermometers with the surroundings, were estimated on the basis of heat – exchange laws to be <sup>3</sup> 1 10 *<sup>K</sup>* . The superheating of the liquid was reduced by using several internal and two external boiler heaters which promoted to smooth boiling of the liquid. Performed modification of the ebulliometer allowed cutting down substantially the amount of liquid which was spent for heating the inner surfaces of instrument up to working temperature.

Thus, the necessary volume of liquid was reduced several times: down to <sup>3</sup> <sup>5</sup>*cm* when measuring only the boiling temperature and to <sup>3</sup> <sup>8</sup>*cm* when both boiling and condensation temperatures were measured. The use of the comparison method makes it possible to

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 601

ln <sup>Δ</sup> ln / 1 2

*RT p H T α T α TTT TT*

where *Z* denotes the difference of compression factors of gas and liquid. Equation (3) in turn was developed by integration of the approximation for

*<sup>o</sup> C C g C liq pm pm pm T T* , as a linear function of the temperature. The treatment of the *pT* parameters was carried out by the least-squares method [LSM] using orthogonal functions (Kornilov & Vidavski, 1969). Mathematical processing of the saturation vapor pressures is given in Appendix. A system of normal equations of LSM is a diagonal matrix relative to the orthogonal functions. The latter are mutually independent that allows to evaluate their uncertainties and those ones for the ln{ ( ) *p T* /Pa} and *H T*( ) *vap m* functions and, as a result, to choice of an adequate number of terms of relations (1) and (3) by curtailing or expanding terms to suit the accuracy of the parameters of these relations without a new treatment of *pT* data. Final equations for these functions are set out

' 2 / ( ) ( ) ( ) (1 /2) ( ) , 2 3 *vap m m m H Z HT H T T T T T* (3)

<sup>2</sup> <sup>2</sup> 1/2 ln / <sup>3</sup>

*α T T TT T T*

*m*

where *T* denotes the mean temperature and ( ), ,

 2 3

with the approximation for *vap mH Z* / :

,, , () ( ) ( )

for compactness, as:

orthogonal functions (Appendix).

the error of the smallest parameter

Equation (1) was derived by integration of the Clapeyron equation:

 1 2 *H T m* , and

<sup>2</sup> *d p dT H Z R T* ln( ) / /( ) *vap m* (2)

ln( / ) / ln( / ) *p Pa A B T C T K D T* (4)

<sup>3</sup> of the equation (1) (accordingly, D of equations (4)

2 2 / ( ) (1, ), 3 3 0.05 *F s Ff* (6)

<sup>2</sup> *H R B CT DT Z s H T H Z* ( ) [ { ( )} ( )] *vap m m vap m* (5)

where *A*, *B*, *C,* and *D* are constants related to the parameters of equation (1) by linear correlations; *sH T* { ( )} *m* is the uncertainty of *vap mH* value resulting from errors of ( *p*,*T* ) parameters; and ( ) *Z* is the error of the *Z* difference estimation. The *sH T* { ( )} *m* values are evaluated by the law of random errors accumulation on the basis of dispersions of the

Because the coefficients of equations (4) and (5) are correlated, the numbers of digits in *A*, *B*, *C*, and *D* coefficients were selected so that the calculated *p* values would not exceed the experimental errors of the vapor pressure determination. (Appendix). Statistical analysis of

> 

and (5)) was evaluated by the Fisher criterion, *F* . If the inequality:

 (1)

<sup>3</sup> are parameters.

 

reduce the *pT* parameters determination to the precision temperature measurements. The temperature was automatically measured by potentiometer method and the results were displayed on a personal computer [PC] screen with the aid of the AK-6.25 computermeasurement system designed at All-Russia Research Institute of Physico-technical and Radio-technical Measurements [VNIIFTRI].

An automatic maintenance of the constant pressure was attained by a mercury-contact manometer which was controlled by vacuum pump via an electromagnetic valve (Fig. 1). The pressure of argon fluctuated in the limits from ( 20 to 40 ) Pa. The boiling temperature was measured at the highest pressure in the cycle at the moment of mercury-to-tungsten contact. The manometer was thermostated at the temperature (300.00±0.02) K. The measurements of the boiling and condensation temperatures were conducted after attaining thermodynamic equilibrium in the ebulliometer. To be assured that the liquid under study had not decomposed, the boiling temperature at one of initial points of the *pT* curve was measured several times during the ebulliometric experiments.

Errors of temperature *ST* and vapor pressure *Sp* measurements were calculated as:

$$\begin{aligned} \left| \mathbf{S}\_T \right| &= \left\langle \left( \mathbf{t} \cdot \mathbf{S}\_{T1} \right)^2 + \left( \mathbf{S}\_{T2} \right)^2 \right\rangle^{1/2} \\\\ \left| \mathbf{S}\_p \right| &= \left\langle \left( \mathbf{d}p \right/\mathbf{d}T \right)\_1^2 \cdot \left( \mathbf{t} \cdot \mathbf{S}\_{T1} \right)^2 + \left( \mathbf{d}p \right/\mathbf{d}T \right)\_3^2 \cdot \left( \mathbf{t} \cdot \mathbf{S}\_{T3} \right)^2 \right\rangle^{1/2} \end{aligned}$$

where <sup>1</sup> *t ST* and <sup>3</sup> *t ST* denote the instrumental errors of the temperature measurements ( <sup>3</sup> 5 10 *<sup>K</sup>* ) at the substance research and at graduation of the mercury-contact manometer; *t* is Student's criterion; <sup>3</sup> 3 10 <sup>2</sup> *S K <sup>T</sup>* denotes the error of graduation of the thermometer; and ( / )1 *dp dT* and ( / )3 *dp dT* are temperature coefficients of the pressure for standard and studied substances, respectively. The total uncertainty of temperature measurement was <sup>3</sup> *S K* 6 10 *<sup>T</sup>* . The error of graduation of the mercury-contact manometer by means of water and *n*-decane and the error of determination of the vapor pressure of the substance under study were equal to *S* ( .) *grad p* = (13 to 20) Pa and *Sp* = (20

to 26) Pa, respectively.

The accuracy of ebulliometric measurements was checked by determinations of the saturation vapor pressures of substances having significantly different boiling temperatures, namely benzene and undecane. The normal boiling temperatures of the standard substances obtained in this work agree within errors limits 0.01 K with precise values of reference (Boublik et al., 1984).

Comparative ebulliometry was employed for determination a series of saturation vapor pressures in dependence on temperature for some freons; halogen - ethanes and –propanes; alkyladamantanes; *cis-* and *trans-* hydrindanes, *cis-* and *trans-* decalines, and their fluoridated counterparts.

The mathematical processing of the observed boiling temperatures and vapor pressures were conducted by the semi -empirical equation:

$$\begin{aligned} -R \cdot T \cdot \ln\left(p\right) &= \Delta H\_{\text{III}}\left(\left\{T\right\}\right) - a\_1 \cdot T + a\_2 \cdot \left\{T - \left\{T\right\} - T \cdot \ln\left(T \nmid \left\{T\right\}\right)\right\} \\ -a\_3 \cdot \left\{\left(1 \land 2\right)\left(T^2 - \left\{T\right\}^2\right) - T \cdot \left\{T\right\} \cdot \ln\left(T \nmid \left\{T\right\}\right)\right\} \end{aligned} \tag{1}$$

where *T* denotes the mean temperature and ( ), , 1 2 *H T m* , and <sup>3</sup> are parameters. Equation (1) was derived by integration of the Clapeyron equation:

$$d\ln(p) / dT = \Lambda\_{vap} H\_{\text{III}} / \left(\Delta Z \cdot \mathbb{R} \cdot T^{\text{\textdegree\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\text\}\} \left. \left. \left. \left. \left\{ \begin{array}{c} \mathbf{I} \end{array} \right. \right\} \right| \left. \left. \left. \begin{array}{c} \mathbf{I} \end{array} \right. \right\} \right| \left. \left. \begin{array}{c} \mathbf{I} \end{array} \right\} \right| \left. \begin{array}{c} \mathbf{I} \end{array} \right\} \right| \left. \begin{array}{c} \mathbf{I} \end{array} \right\} \tag{2}$$

with the approximation for *vap mH Z* / :

600 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

reduce the *pT* parameters determination to the precision temperature measurements. The temperature was automatically measured by potentiometer method and the results were displayed on a personal computer [PC] screen with the aid of the AK-6.25 computermeasurement system designed at All-Russia Research Institute of Physico-technical and

An automatic maintenance of the constant pressure was attained by a mercury-contact manometer which was controlled by vacuum pump via an electromagnetic valve (Fig. 1). The pressure of argon fluctuated in the limits from ( 20 to 40 ) Pa. The boiling temperature was measured at the highest pressure in the cycle at the moment of mercury-to-tungsten contact. The manometer was thermostated at the temperature (300.00±0.02) K. The measurements of the boiling and condensation temperatures were conducted after attaining thermodynamic equilibrium in the ebulliometer. To be assured that the liquid under study had not decomposed, the boiling temperature at one of initial points of the *pT* curve was

Errors of temperature *ST* and vapor pressure *Sp* measurements were calculated as:

1/2 2 2 S (t ) (S ) T1 2 *<sup>S</sup> T T*

 d d d d <sup>3</sup> *1/2 22 2 2 S ( p / T) (t S ) ( p / T) (t S ) <sup>p</sup> 1 T1 3 T*

where <sup>1</sup> *t ST* and <sup>3</sup> *t ST* denote the instrumental errors of the temperature measurements ( <sup>3</sup> 5 10 *<sup>K</sup>* ) at the substance research and at graduation of the mercury-contact manometer; *t* is Student's criterion; <sup>3</sup> 3 10 <sup>2</sup> *S K <sup>T</sup>* denotes the error of graduation of the thermometer; and ( / )1 *dp dT* and ( / )3 *dp dT* are temperature coefficients of the pressure for standard and studied substances, respectively. The total uncertainty of temperature measurement was <sup>3</sup> *S K* 6 10 *<sup>T</sup>* . The error of graduation of the mercury-contact manometer by means of water and *n*-decane and the error of determination of the vapor pressure of the substance under study were equal to *S* ( .) *grad p* = (13 to 20) Pa and *Sp* = (20

The accuracy of ebulliometric measurements was checked by determinations of the saturation vapor pressures of substances having significantly different boiling temperatures, namely benzene and undecane. The normal boiling temperatures of the standard substances obtained in this work agree within errors limits 0.01 K with precise values of reference

Comparative ebulliometry was employed for determination a series of saturation vapor pressures in dependence on temperature for some freons; halogen - ethanes and –propanes; alkyladamantanes; *cis-* and *trans-* hydrindanes, *cis-* and *trans-* decalines, and their

The mathematical processing of the observed boiling temperatures and vapor pressures

Radio-technical Measurements [VNIIFTRI].

to 26) Pa, respectively.

(Boublik et al., 1984).

fluoridated counterparts.

were conducted by the semi -empirical equation:

measured several times during the ebulliometric experiments.

$$
\Delta\_{\text{Tamp}}H\_{\text{III}} \mid \Delta Z = \Delta H\_{\text{III}}^{'}(T) = \Delta H\_{\text{III}}(\{T\}) + \alpha\_{\text{2}} \cdot (T - \{T\}) + (1 \,/\.2) \cdot \alpha\_{\text{3}} \cdot (T - \{T\})^2,\tag{3}
$$

where *Z* denotes the difference of compression factors of gas and liquid. Equation (3) in turn was developed by integration of the approximation for ,, , () ( ) ( ) 2 3 *<sup>o</sup> C C g C liq pm pm pm T T* , as a linear function of the temperature. The treatment of the *pT* parameters was carried out by the least-squares method [LSM] using orthogonal functions (Kornilov & Vidavski, 1969). Mathematical processing of the saturation vapor pressures is given in Appendix. A system of normal equations of LSM is a diagonal matrix relative to the orthogonal functions. The latter are mutually independent that allows to evaluate their uncertainties and those ones for the ln{ ( ) *p T* /Pa} and *H T*( ) *vap m* functions and, as a result, to choice of an adequate number of terms of relations (1) and (3) by curtailing or expanding terms to suit the accuracy of the parameters of these relations without a new treatment of *pT* data. Final equations for these functions are set out for compactness, as:

$$\ln(p \mid Pa) = A + B \nmid T + C \cdot \ln(T \nmid K) + D \cdot T \tag{4}$$

$$
\Delta\_{\text{vap}} H\_{\text{m}} = R \cdot \left( -B + \mathbf{C} \cdot T + D \cdot T^{\prime 2} \right) \cdot \Delta Z \pm \left[ \mathbf{s} \{ \Delta H\_{\text{m}}^{\prime}(T) \} + \Delta\_{\text{vap}} H\_{\text{m}} \cdot \Delta(\Delta Z) \right] \tag{5}
$$

where *A*, *B*, *C,* and *D* are constants related to the parameters of equation (1) by linear correlations; *sH T* { ( )} *m* is the uncertainty of *vap mH* value resulting from errors of ( *p*,*T* ) parameters; and ( ) *Z* is the error of the *Z* difference estimation. The *sH T* { ( )} *m* values are evaluated by the law of random errors accumulation on the basis of dispersions of the orthogonal functions (Appendix).

Because the coefficients of equations (4) and (5) are correlated, the numbers of digits in *A*, *B*, *C*, and *D* coefficients were selected so that the calculated *p* values would not exceed the experimental errors of the vapor pressure determination. (Appendix). Statistical analysis of the error of the smallest parameter <sup>3</sup> of the equation (1) (accordingly, D of equations (4) and (5)) was evaluated by the Fisher criterion, *F* . If the inequality:

$$F = a\_{\mathfrak{Z}}^2 / s^2(a\_{\mathfrak{Z}}) \ge F\_{0.05}(1, f)\_{\prime} \tag{6}$$

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 603

denote evaluated and tabulated values of the *F* -criterion, and *f* is a number of degrees of freedom. Comparing the criteria *F* and (1, ) 0.05 *F f* according to (6) showed an adequate fit of

Table 1 summarizes the purity of the compounds determined by gas – liquid chromatography [g.l.c.] and adiabatic calorimetry, the temperature interval, *T* ( *pT* ), and number, *n*, of *pT* -parameters, the coefficients of equations (4) and (5) and mean-square

<sup>2</sup> 1/2 *S pp n* { ( ) /( 4)} *<sup>p</sup> calc*

Experimental determinations of the enthalpies of vaporization were carried out by direct calorimetric methods and by indirect ones, on the basis of the temperature dependences of saturation vapor pressures. The first method is more precise but the second one is more

The enthalpies of vaporization of some compounds under study were determined at *T* = 298.15 K by calorimetric method using a carrier gas (nitrogen) (Wadsö, 1966). The method is based on measuring the energy dissipated in calorimeter for compensation of the endothermic vaporization effect. The carrier gas was employed for hastening an evaporation process and, thus, for increasing an accuracy. A modified LKB 8721-3 setup consists of some commercial parts, namely calorimetric vessel with an air brass jacket and a carrier gas system and three missing parts designed in (Varushchenko et. al., 1977): precise water thermostat, electrical scheme, and an air thermostat. The latter replaced a thermostated room that was provided for operating by this method. The calorimeter is intended for the substances with vapor pressures from 0.066 kPa to 26.6 kPa at 298 K (or normal boiling temperatures from (335 to 470) K). A mass (0.5 to 1.0) g of substance was required for a

The calorimetric experiment was conducted at an adiabatic and, at the same time, at isothermal conditions. The temperature of the calorimetric vessel measured by a thermistor was maintained constant and equal to that of the thermostat (298.15±0.02) K. Electrical energy used for compensation of the energy of vaporization (20 to 40) J was measured by a potentiometer method with accuracy 0.01 per cent. The mass, *m*, of a substance evaporated (0.07 to 0.3) g was determined to <sup>4</sup> 1 10 g as the difference between masses of calorimetric vessel before and after an experiment. As the calorimeter was non-hermetic, the main error in mass determination arose from a loss of substance in weighing the vessel due to connecting and disconnecting it with the calorimetric system. All preliminary procedures such as filling the vessel with liquid, weighing it, and placing into its air jacket were made inside an air thermostat at *T* 298 K. In so doing, we reduced a loss of the substance from

The value of *vapH* was corrected for a small quantity of energy absorbed during the passage of nitrogen through the calorimeter under low pressure. The calorimeter was tested by measuring the enthalpies of vaporization of *n*-alkanes from C6 to C10. Obtained values of

deviation [MSD] of calculated *pcalc* -values from experimental ones, *<sup>p</sup>* ,

often used because of it's applicability for wider series of the substances.

<sup>3</sup> (D) may be accepted as a reliable one. Here *F* and (1, ) 0.05 *F f*

is satisfied, the parameter

**2.2 The enthalpy of vaporization** 

series from 6 to 8 experiments.

the vessel and the temperature over fall of the latter.

the *pT* parameters.


*<sup>a</sup>*Adiabatic calorimetric; *b* DSC.

Table 1. Thermodynamic parameters of comparative ebulliometry for compounds studied: freons; halogen -ethanes and –propanes; 1,3-dimethyladamahtane [1,3-DMA], 1,3,5 trimethyladamahtane [1,3,5-TMA] and 1-ethyladamahtane [1-EA]; perfluorobicyclo(4,3,0) nonanes [*cis-* and *trans*- C9F16], bicyclo(4,3,0)nonanes, [*cis-* and *trans*- C9H16], perfluorobicyclo(4,4,0)decane, [*cis-* and *trans*- C10F18], bicyclo(4,4,0)decanes [*cis-* and *trans*- C10H18]; perfluoro-N-(4-methyl-cyclohexyl)piperidine [C5F10N-C6F10-CF3 ](Varushchenko et al., 2007; Boublik et al., 1984)

is satisfied, the parameter <sup>3</sup> (D) may be accepted as a reliable one. Here *F* and (1, ) 0.05 *F f* denote evaluated and tabulated values of the *F* -criterion, and *f* is a number of degrees of freedom. Comparing the criteria *F* and (1, ) 0.05 *F f* according to (6) showed an adequate fit of the *pT* parameters.

Table 1 summarizes the purity of the compounds determined by gas – liquid chromatography [g.l.c.] and adiabatic calorimetry, the temperature interval, *T* ( *pT* ), and number, *n*, of *pT* -parameters, the coefficients of equations (4) and (5) and mean-square deviation [MSD] of calculated *pcalc* -values from experimental ones, *<sup>p</sup>* ,

$$S\_p = \pm \{ \Sigma(p - p\_{calc})^2 / (n - 4) \}^{1/2}$$

## **2.2 The enthalpy of vaporization**

602 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

Freons and halogen -ethanes and –propanes CFCl2CFCl2 99.30 *<sup>a</sup>* 313–361 12 59.2013 5922.1 6.71105 3.3075 2.1 CF2ClCFCl2 99.80 *<sup>a</sup>* 298-316 7 42.1123 4680.0 3.96897 - 19.0 CF2ClCF2Cl 99.79 *<sup>a</sup>* 178 -277 10 320.3557 10029.4 55.11366 110.0486 34.5 CF2BrCF2Br 99.50 *<sup>c</sup>* 298–320 8 43.4680 4732.1 4.17343 - 10.5 CF2ClCHCl2 99.64 *<sup>b</sup>* 297–345 14 141.7579 7982.7 21.01696 25.5415 15.0 CFCl2CHFCl 99.38 *<sup>b</sup>* 289–346 16 137.9719 7912.3 20.33885 24.3167 11.0 CF3CHCl2 99.83 *<sup>a</sup>* 256–454 45 90.4773 5766.1 12.41706 13.8312 3.8 CF2ClCHFCl 99.51 *<sup>a</sup>* 278-303 9 655.6005 20714.9 111.4046 177.9514 10.0 CF3CHClBr 99.7 *<sup>a</sup>* 297-323 8 45.2236 4950.1 4.37789 - 5.6 CF3CH2CH2Cl 99.90 *<sup>a</sup>* 297-315 8 47.6041 5040.0 4.71465 - 11.9 CF3CH2CHCl2 99.30 *<sup>c</sup>* 302-341 12 133.0670 8026.1 19.24539 21.0475 13.9 CF3CH2CCl3 99.59 *<sup>a</sup>* 321-364 12 243.2798 11578.6 38.06825 48.1087 20.3 CF3CH2CFCl2 99.9 *<sup>b</sup>* 297-333 9 1415.3662 43459.2 241.45741 366.8286 36.8 CHCl2CH3 99.9 *<sup>b</sup>* 294-330 11 135.6402 7511.9 20.10746 25.2571 10.1 CH2ClCH2Cl 99.9 *<sup>b</sup>* 299-356 15 83.3156 6652.5 10.77546 9.2008 6.2 CH2BrCH2Br 99.9 *<sup>b</sup>* 331-426 12 127.1428 8810.4 17.99911 18.0408 23.1 CHCl2CH2Cl 99.9 *<sup>b</sup>* 316-384 11 90.36301 7530.3 11.71063 9.0204 7.1 CHCl2CH2CH3 99.9 *<sup>b</sup>* 312-362 14 89.3533 6827.0 11.8439 10.8245 4.5 CH2ClCHClCH3 99.9 *<sup>b</sup>* 303-368 15 98.1061 7219.8 13.2971 12.6285 14.4 CH2ClCH2CH2Cl 99.8 *<sup>b</sup>* 330-393 14 140.9922 9134.9 20.33477 21.1678 5.1 CH3CCl2CH3 99.72 *<sup>a</sup>* 295-341 12 176.6209 8828.3 27.13786 35.4801 11.6 CH3CCl3 99.99 *<sup>a</sup>* 296-371 18 44.7407 5209.8 4.29370 - 8.0 CH3CCl3 99.95 *<sup>b</sup>* 174-223 8 117.9294 4801.5 18.43752 34.8788 6.3 Alkylderivatives of adamantane 1,3,5-TMA 99.98 *<sup>a</sup>* 385-482 16 130.7579 10220.9 18.22485 15.8278 10.0 1,3-DMA 99.9 *<sup>a</sup>* 352-526 24 101.7980 9034.5 13.50183 10.5779 2.0 1-EA 99.93 *<sup>a</sup>* 387-498 14 115.7566 10147.8 15.57166 11.9069 10.6 Bicyclic hydrocarbons cis-C9H16 99.99 *<sup>a</sup>* 351-442 18 118.1951 9158.1 16.27432 14.2522 9.2 trans-C9H16 99.98 *<sup>a</sup>* 345-435 18 107.7679 8639.8 14.60163 12.5083 11.3 cis-C10H18 99.87 *<sup>a</sup>* 373-470 19 129.3296 10107.8 17.94129 15.3346 7.5 trans-C10H18 99.98 *<sup>a</sup>* 366-461 19 105.6064 9031.6 14.11863 11.3055 5.1 Bicyclic perfluorocarbons cis-C9F16 99.69 *<sup>a</sup>* 316–392 17 160.6582 9773.9 22.20257 21.4086 8.0 trans-C9F16 99.40 *<sup>a</sup>* 314-389 17 153.5136 9444.2 21.06404 20.3262 6.0 cis-C10F18 99.57 *<sup>a</sup>* 315-416 19 218.3225 12353.8 32.91383 34.7585 6.4 trans-C10F18 99.46 *<sup>a</sup>* 313-414 18 195.0918 11539.7 29.04017 29.8875 10.9 C5F10N-C6F10-CF3 99.66 *<sup>a</sup>* 374-461 18 210.0577 13500.8 30.83011 28.0834 5.0

Table 1. Thermodynamic parameters of comparative ebulliometry for compounds studied: freons; halogen -ethanes and –propanes; 1,3-dimethyladamahtane [1,3-DMA], 1,3,5 trimethyladamahtane [1,3,5-TMA] and 1-ethyladamahtane [1-EA]; perfluorobicyclo(4,3,0) nonanes [*cis-* and *trans*- C9F16], bicyclo(4,3,0)nonanes, [*cis-* and *trans*- C9H16], perfluorobicyclo(4,4,0)decane, [*cis-* and *trans*- C10F18], bicyclo(4,4,0)decanes [*cis-* and *trans*- C10H18]; perfluoro-N-(4-methyl-cyclohexyl)piperidine [C5F10N-C6F10-CF3 ](Varushchenko et al., 2007;

*n A -B -C D·*<sup>103</sup> *Sp* ,

Pa

Compounds Purity,

*<sup>a</sup>*Adiabatic calorimetric; *b* DSC.

Boublik et al., 1984)

mol. %

*T* ( *pT* ), K

> Experimental determinations of the enthalpies of vaporization were carried out by direct calorimetric methods and by indirect ones, on the basis of the temperature dependences of saturation vapor pressures. The first method is more precise but the second one is more often used because of it's applicability for wider series of the substances.

> The enthalpies of vaporization of some compounds under study were determined at *T* = 298.15 K by calorimetric method using a carrier gas (nitrogen) (Wadsö, 1966). The method is based on measuring the energy dissipated in calorimeter for compensation of the endothermic vaporization effect. The carrier gas was employed for hastening an evaporation process and, thus, for increasing an accuracy. A modified LKB 8721-3 setup consists of some commercial parts, namely calorimetric vessel with an air brass jacket and a carrier gas system and three missing parts designed in (Varushchenko et. al., 1977): precise water thermostat, electrical scheme, and an air thermostat. The latter replaced a thermostated room that was provided for operating by this method. The calorimeter is intended for the substances with vapor pressures from 0.066 kPa to 26.6 kPa at 298 K (or normal boiling temperatures from (335 to 470) K). A mass (0.5 to 1.0) g of substance was required for a series from 6 to 8 experiments.

> The calorimetric experiment was conducted at an adiabatic and, at the same time, at isothermal conditions. The temperature of the calorimetric vessel measured by a thermistor was maintained constant and equal to that of the thermostat (298.15±0.02) K. Electrical energy used for compensation of the energy of vaporization (20 to 40) J was measured by a potentiometer method with accuracy 0.01 per cent. The mass, *m*, of a substance evaporated (0.07 to 0.3) g was determined to <sup>4</sup> 1 10 g as the difference between masses of calorimetric vessel before and after an experiment. As the calorimeter was non-hermetic, the main error in mass determination arose from a loss of substance in weighing the vessel due to connecting and disconnecting it with the calorimetric system. All preliminary procedures such as filling the vessel with liquid, weighing it, and placing into its air jacket were made inside an air thermostat at *T* 298 K. In so doing, we reduced a loss of the substance from the vessel and the temperature over fall of the latter.

> The value of *vapH* was corrected for a small quantity of energy absorbed during the passage of nitrogen through the calorimeter under low pressure. The calorimeter was tested by measuring the enthalpies of vaporization of *n*-alkanes from C6 to C10. Obtained values of

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 605

Freons and halogen -ethanes and –propanes

CFCl2CFCl2 R-112 366.00±0.01 - 34.98±0.39 31.26±0.33 CF2ClCFCl2 R-113 320.76±0.01 28.61±0.09 28.71±0.41 27.21±0.44 CF2ClCF2Cl R-114 276.65 - - 24.9±±1.1 CF2BrCF2Br R-114b2 320.36±0.01 28.61±0.09 28.63±0.34 27.11±0.32 CF2ClCHCl2 R-122 345.01±0.01 32.91±0.09 32.84±0.40 29.84±0.36 CFCl2CHFCl R-122a 346.34±0.01 33.10±0.06 33.04±0.36 29.95±0.35 CF3CHCl2 R-123 300.981±0.008 - 26.35±0.33 26.14±0.34 CF2ClCHFCl R-123a 303.02±0.01 - 26.82±0.28 26.45±0.32 CF3CHClBr R-123b1 323.41±0.01 29.80±0.09 30.01±0.33 28.36±0.31 CF3CH2CH2Cl R-253fa 318.84±0.01 - 29.86±0.39 28.39±0.40 CF3CH2CHCl2 R-243 345.47±0.01 34.05±0.04 34.40±0.57 31.14±0.47 CF3CH2CCl3 R-233 368.28±0.01 36.76±0.08 37.4±1.4 32.62±0.57 CF3CH2CFCl2 R-234fb 333.74±0.01 - 33.59±0.65 29.80±0.62 CHCl2CH3 1,1-DClE 330.35±0.01 30.62±0.14 31.12±0.34 29.24±0.35 CH2ClCH2Cl 1,2-DClE 356.61±0.01 32.15±0.01 35.36±0.39 32.18±0.35 CH2BrCH2Br 1,2-DBrE 404.55±0.01 41.73±0.02 41.97±0.95 36.23±0.51 CHCl2CH2Cl 1,1,2-TClE 386.98±0.01 40.28±0.10 40.23±0.56 35.09±0.42 CH3CCl3 1,1,1-TClE 347.21±0.01 32.62±0.09 32.58±0.35 29.89±0.34 CHCl2CH2CH3 1,1-DClP 361.53±0.01 35.10±0.11 35.34±0.45 31.85±0.35 CH2ClCHClCH3 1,2-DClP 369.50±0.01 36.20±0.08 36.37±0.49 32.45±0.41 CH2ClCH2CH2Cl 1,3-DClP 393.95±0.01 40.75±0.04 41.18±0.55 35.56±0.38 CH3CCl2CH3 2,2-DClP 342.67±0.01 - 32.22±0.38 29.66±0.37 CH3CFl3 R-143a 225.85±0.01 - - 19.40±0.24

 <sup>0</sup> *H K* (298.15 ) *vap m (calor)*  kJmol-1

 <sup>0</sup> *H K* (298.15 ) *vap m (р-Т)*  kJmol-1

 <sup>0</sup> ( ) . . *vap mH Tn b (р-Т)*  kJmol-1

K

Table 2. Normal boiling temperatures, . . *Tn b* , molar enthalpies of vaporization,

1985; Boublik et al., 1984)

 *H K* (298.15 ) *vap m* , measured calorimetrically and calculated from *pT* data at *T* 298.15 K and . . *Tn b* for some freons and halogen-alkanes (Varushchenko et al., 2007; Majer & Svoboda,

Compounds . . *Tn b*

*vapH* at *T* 298.15 K agree with well established literature values (Majer & Svoboda, 1985) within (0.2 to 0.5) per cent.

A main method of determination of the enthalpies of vaporization is until now an indirect one based on the temperature dependence of the vapor pressure. This is caused by a less complicated technique for precise vapor pressure determinations than direct calorimetric measurements of *vapHm* . The best-accuracy estimations of *vapHm* values are attained for a moderate range of vapor pressure (5 to 150) kPa. The literature data on the enthalpies of vaporization obtained by indirect method are usually published without uncertainties, that can be explained by fitting the *pT* -parameters with ln( ) ( ) *p f T* equations, coefficients of which were correlated. An accuracy determination of the enthalpies of vaporization in indirect method is given in Appendix. The *vapHm* values obtained by indirect method were computed by equation (5) using the *Z* difference which took into account the vapor deviation from ideality and volume changes of both phases. The *Z* values were calculated from formula:

$$
\Delta \mathcal{Z} = \{ p \mid (\mathcal{R} \cdot \mathcal{T}) \} \cdot \{ V\_{\mathcal{W}}(\mathcal{g}) - V\_{\mathcal{W}}(\text{liq}) \}. \tag{7}
$$

The molar volume *V liq m*( ) of liquid was evaluated on the basis of density; an adequate value for the volume of vapor, *V g m*( ) , was calculated from the volume-explicit virial expansion truncated after the second virial coefficient *Bv* . The values of *Bv* were evaluated on the basis of critical quantities (part 4.2) by the Tsonopolous extension of Pitzer and Curl's method (Poling et al., 2001). Comparing two series of *Z* values estimated from experimental and calculated values of *V g m*( ) of hydrocarbons enable us to accept the errors of *Z* evaluation ≤ 1 per cent.

**Freons and halogenalkanes.** Table 2 presents the normal boiling temperatures, . . *Tn b* , and the enthalpies of vaporization at *<sup>T</sup>* 298.15 K and . . *Tn b* for freons and hologenalkanes, calculated from equation (4) and (5), respectively and calorimetric *vapHm* values.

The enthalpies of vaporization obtained both by direct and indirect methods at the saturated vapor pressure, were recalculated to the standard values by means of correction ( ) { ( / ) }. *Hm p T dB dT B v v* The reliability of the calculated *vapHm* values were proved by their agreement with the calorimetric ones within the error limits (Table 2). Due to smaller extrapolation intervals, the errors of the enthalpies of vaporization at the normal boiling temperatures are less than *H K* (298.15 ) *vap m* values. Extrapolation capabilities of equations (3) and (5) were verified by comparison of calculated *vapHm* values at *T* 298.15 K with experimental ones for some well studied alkanes and alkanethiols (Boublik et al., 1984). It has been shown that these equations allowed us to estimate the *vapHm* values with uncertainties 2 per cent in extrapolation intervals *T* 50 K.

Mutual congruence of some thermodynamic properties in set of related compounds (Table 2) can be drawn from comparison of these properties in dependence on some physicochemical characteristics having influence upon intermolecular interactions in liquid state.

Fig. 3 represent critical temperatures,*Tc* , normal boiling temperatures, . . *Tn b* , and enthalpies of vaporization, *H K* (298.15 ) *vap m* , for freons and chloroalkanes C2, C3 depending on the dipole moments, ( ) *liq* , and coefficients of molecular packing, *Km* , in the liquids. The

*vapH* at *T* 298.15 K agree with well established literature values (Majer & Svoboda,

A main method of determination of the enthalpies of vaporization is until now an indirect one based on the temperature dependence of the vapor pressure. This is caused by a less complicated technique for precise vapor pressure determinations than direct calorimetric measurements of *vapHm* . The best-accuracy estimations of *vapHm* values are attained for a moderate range of vapor pressure (5 to 150) kPa. The literature data on the enthalpies of vaporization obtained by indirect method are usually published without uncertainties, that can be explained by fitting the *pT* -parameters with ln( ) ( ) *p f T* equations, coefficients of which were correlated. An accuracy determination of the enthalpies of vaporization in indirect method is given in Appendix. The *vapHm* values obtained by indirect method were computed by equation (5) using the *Z* difference which took into account the vapor deviation from ideality and volume changes of both phases. The *Z* values were calculated

The molar volume *V liq m*( ) of liquid was evaluated on the basis of density; an adequate value for the volume of vapor, *V g m*( ) , was calculated from the volume-explicit virial expansion truncated after the second virial coefficient *Bv* . The values of *Bv* were evaluated on the basis of critical quantities (part 4.2) by the Tsonopolous extension of Pitzer and Curl's method (Poling et al., 2001). Comparing two series of *Z* values estimated from experimental and calculated values of *V g m*( ) of hydrocarbons enable us to accept the errors

**Freons and halogenalkanes.** Table 2 presents the normal boiling temperatures, . . *Tn b* , and the enthalpies of vaporization at *<sup>T</sup>* 298.15 K and . . *Tn b* for freons and hologenalkanes,

The enthalpies of vaporization obtained both by direct and indirect methods at the saturated vapor pressure, were recalculated to the standard values by means of correction

proved by their agreement with the calorimetric ones within the error limits (Table 2). Due to smaller extrapolation intervals, the errors of the enthalpies of vaporization at the normal boiling temperatures are less than *H K* (298.15 ) *vap m* values. Extrapolation capabilities of equations (3) and (5) were verified by comparison of calculated *vapHm* values at *T* 298.15 K with experimental ones for some well studied alkanes and alkanethiols (Boublik et al., 1984). It has been shown that these equations allowed us to estimate the *vapHm* values with uncertainties 2 per cent in extrapolation intervals

Mutual congruence of some thermodynamic properties in set of related compounds (Table 2) can be drawn from comparison of these properties in dependence on some physicochemical characteristics having influence upon intermolecular interactions in liquid state. Fig. 3 represent critical temperatures,*Tc* , normal boiling temperatures, . . *Tn b* , and enthalpies of vaporization, *H K* (298.15 ) *vap m* , for freons and chloroalkanes C2, C3 depending on the

*v v* The reliability of the calculated *vapHm* values were

( ) *liq* , and coefficients of molecular packing, *Km* , in the liquids. The

calculated from equation (4) and (5), respectively and calorimetric *vapHm* values.

*Z p R T V g V liq* { /( )} { ( ) ( )}. *m m* (7)

1985) within (0.2 to 0.5) per cent.

from formula:

*T* 50 K.

dipole moments,

of *Z* evaluation ≤ 1 per cent.

( ) { ( / ) }. *Hm p T dB dT B*


Table 2. Normal boiling temperatures, . . *Tn b* , molar enthalpies of vaporization, *H K* (298.15 ) *vap m* , measured calorimetrically and calculated from *pT* data at *T* 298.15 K and . . *Tn b* for some freons and halogen-alkanes (Varushchenko et al., 2007; Majer & Svoboda, 1985; Boublik et al., 1984)

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 607

Bicyclic perfluorocarbons *cis*-C9F16 391.52±0.01 41.98±0.14 41.95±0.52 34.43±0.37 44.91 *trans*-C9F16 389.02±0.01 41.34±0.05 41.22±0.51 34.11±0.36 46.11 *cis*-C10F18 416.96±0.01 46.19±0.12 46.79±0.62 36.57±0.43 40.30 *trans*-C10F18 414.70±0.01 45.40±0.08 46.02±0.60 36.26±0.43 41.10

Bicyclic hydrocarbons *cis-*C9H16 *a* 440.99±0.01 - 46.34±0.82 38.01±0.44 25.22 *trans*-C9H16 *a* 434.22±0.01 - 44.88±0.78 37.21±0.43 28.84 *cis-*C10H18 *a* 468.93±0.01 - 50.90±0.94 40.46±0.45 21.25 *trans-*C10H18 *a* 460.43±0.01 - 48.45±0.78 39.29±0.43 25.05 Alkylderivatives of adamantane 1,3,5-TMA 483.31±0.01 51.74±0.20 51.50±0.52 40.52±0.50 - 1,3-DMA *a* 476.441 49.71±0.20 49.47±0.54 39.71±0.41 - 1-EA 498.86±0.01 54.96±0.28 54.6±1.3 42.56±0.51 -

. . *Tn b* and *H K* (298.15 ) *vap m* values were calculated from literature data of (Boublik et. al., 1984).

Table 3. Normal boiling temperatures, . . *Tn b* , molar enthalpies of vaporization, *H K* (298.15 ) *vap m* , obtained by direct and indirect methods, and oxygen capacities,

(298.15K), for bicyclic hydrocarbons, perfluorocarbons, and derivatives of

The saturated vapor pressure of bicyclic PFC at temperature (310 K) of the human body, <sup>310</sup> *ps* , is one of the key properties of the blood substitute, which ranges from 0.16 to 2.66 kPa. A stability of an aqueous emulsion of fluorocarbon and its delivery rate from the body depends on <sup>310</sup> *ps* value. Medicine employs bicyclic perfluorocarbon composition with high and low vapor pressures. Perfluoro-N-(4-methylcyclohexyl)piperidine, C5F10N-C6F10- CF3, having the low value of <sup>310</sup> *ps* =0.157 kPa, is a component of "Ftorosan" (Russia) blood substitute in mixture with *cis-* and *trans-* perfluorodecalines, which have higher (1.54 and 1.72) kPa values of <sup>310</sup> *ps* , respectively. Another key property of the blood substitutes is an

vaporization by empirical method developed within a theory of regular solutions (Lawson

Table 3 presents derived thermodynamic values of cyclic compounds. The values of the normal boiling temperatures and the enthalpies of vaporization of *cis-*isomers are more than

(cm3/100 ml), which is defined as a volume of oxygen, dissolved in

values were evaluated on the basis of the enthalpies of

 <sup>0</sup> *H K* (298.15 ) *vap m (р-Т),*  kJmol-1

460.74±0.01 56.56±0.24 56.58±0.88 40.68±0.44 34.30

 <sup>0</sup> ( ) . . *vap mH Tn b (р-Т),*  kJmol-1

( ) <sup>2</sup> (298.15), cm3/100 ml

 <sup>0</sup> *H K* (298.15 ) *vap m (calor),*  kJmol-1

Compounds . . *Tn b*

C5F10N-C6F10- CF3

*a*

( ) <sup>2</sup> 

adamantine

oxygen capacity, ( ) <sup>2</sup>

et al., 1978).

100 ml of the liquid. The ( ) <sup>2</sup>

K

Fig. 3. Variations of thermodynamic properties *Tc* , . . *Tn b* and *H K* (298.15 ) *vap m* in dependence on the dipole moments, ( ) *liq* , and coefficients of molecular packing, *Km* , in series of liquid halogenated ethanes **(a)**: CF3CHCl2 [1], CF2ClCHFCl [2], CF2ClCFCl2 [3], CH3CHCl2 [4], CH2ClCH2Cl [5], CHCl2CH2Cl [6]; and propanes **(b)**: CF3CH2CF2Cl [1], CF3CH2CFCl2 [2], CF3CH2CCl3 [3], CF3CH2CHCl2 [4], CF3CH2CH2Cl [5]

coefficients *Km* were calculated by analogy with (Varushchenko et al., 2007). In spite of the large atomic weight of fluorine in comparison with hydrogen, thermodynamic values of compounds decrease when hydrogen is substituted for fluorine that can be explained by decreasing of the ( ) *liq* and *Km* parameters. Minimum*Tc* , . . *Tn b* , and *H K* (298.15 ) *vap m* values are inherent to completely halogenated 1,1,1-trifluoro-2,2-dichloroethane, which has the lowest values of dipole moment and *Km* coefficient. Maximum values of corresponding properties are observed for the most polar compounds, 1,1,2,-trichloroetane, the *gauche*  conformer of which is stabilized by the dipole interaction in the liquid phase.

Analysis of the data shown in Fig. 3 allows to conclude that the values of critical and normal boiling temperatures and enthalpy of vaporization vary in a series of compounds according to the combined action of the parameters responsible for intermolecular interactions and short range order of the liquid phase, thus proving the mutual consistency of the thermodynamic data in the series of halogenated ethane and propane.

**Cyclic perfluorocarbons and hydrocarbons.** A thermodynamic study of perfluorated cyclic organic compounds has scientific and practical importance. Perfluorocarbons [PFC] have high chemical and thermal stability, absolute biological inertness, and weak intermolecular interactions [IMI]. The combination of these properties can be assigned to high C-F bond strength and the shielding effect of fluorine atoms towards the carbon framework. The weakness of IMI is responsible for the ability of PFC to dissolve and transfer considerable amounts of gases, in particular, oxygen and carbon dioxide. On account of these properties, PFC have found wide application in biology and medicine as efficient gas-transfer media (blood substitutes).

Fig. 3. Variations of thermodynamic properties *Tc* , . . *Tn b* and *H K* (298.15 ) *vap m* in

series of liquid halogenated ethanes **(a)**: CF3CHCl2 [1], CF2ClCHFCl [2], CF2ClCFCl2 [3], CH3CHCl2 [4], CH2ClCH2Cl [5], CHCl2CH2Cl [6]; and propanes **(b)**: CF3CH2CF2Cl [1],

coefficients *Km* were calculated by analogy with (Varushchenko et al., 2007). In spite of the large atomic weight of fluorine in comparison with hydrogen, thermodynamic values of compounds decrease when hydrogen is substituted for fluorine that can be explained by

values are inherent to completely halogenated 1,1,1-trifluoro-2,2-dichloroethane, which has the lowest values of dipole moment and *Km* coefficient. Maximum values of corresponding properties are observed for the most polar compounds, 1,1,2,-trichloroetane, the *gauche* 

Analysis of the data shown in Fig. 3 allows to conclude that the values of critical and normal boiling temperatures and enthalpy of vaporization vary in a series of compounds according to the combined action of the parameters responsible for intermolecular interactions and short range order of the liquid phase, thus proving the mutual consistency of the

**Cyclic perfluorocarbons and hydrocarbons.** A thermodynamic study of perfluorated cyclic organic compounds has scientific and practical importance. Perfluorocarbons [PFC] have high chemical and thermal stability, absolute biological inertness, and weak intermolecular interactions [IMI]. The combination of these properties can be assigned to high C-F bond strength and the shielding effect of fluorine atoms towards the carbon framework. The weakness of IMI is responsible for the ability of PFC to dissolve and transfer considerable amounts of gases, in particular, oxygen and carbon dioxide. On account of these properties, PFC have found wide application in biology and medicine as efficient gas-transfer media

( ) *liq* and *Km* parameters. Minimum*Tc* , . . *Tn b* , and *H K* (298.15 ) *vap m*

( ) *liq* , and coefficients of molecular packing, *Km* , in

conformer of which is stabilized by the dipole interaction in the liquid phase.

thermodynamic data in the series of halogenated ethane and propane.

CF3CH2CFCl2 [2], CF3CH2CCl3 [3], CF3CH2CHCl2 [4], CF3CH2CH2Cl [5]

dependence on the dipole moments,

decreasing of the

(blood substitutes).


*a* . . *Tn b* and *H K* (298.15 ) *vap m* values were calculated from literature data of (Boublik et. al., 1984).

Table 3. Normal boiling temperatures, . . *Tn b* , molar enthalpies of vaporization, *H K* (298.15 ) *vap m* , obtained by direct and indirect methods, and oxygen capacities, ( ) <sup>2</sup> (298.15K), for bicyclic hydrocarbons, perfluorocarbons, and derivatives of adamantine

The saturated vapor pressure of bicyclic PFC at temperature (310 K) of the human body, <sup>310</sup> *ps* , is one of the key properties of the blood substitute, which ranges from 0.16 to 2.66 kPa. A stability of an aqueous emulsion of fluorocarbon and its delivery rate from the body depends on <sup>310</sup> *ps* value. Medicine employs bicyclic perfluorocarbon composition with high and low vapor pressures. Perfluoro-N-(4-methylcyclohexyl)piperidine, C5F10N-C6F10- CF3, having the low value of <sup>310</sup> *ps* =0.157 kPa, is a component of "Ftorosan" (Russia) blood substitute in mixture with *cis-* and *trans-* perfluorodecalines, which have higher (1.54 and 1.72) kPa values of <sup>310</sup> *ps* , respectively. Another key property of the blood substitutes is an oxygen capacity, ( ) <sup>2</sup> (cm3/100 ml), which is defined as a volume of oxygen, dissolved in 100 ml of the liquid. The ( ) <sup>2</sup> values were evaluated on the basis of the enthalpies of vaporization by empirical method developed within a theory of regular solutions (Lawson et al., 1978).

Table 3 presents derived thermodynamic values of cyclic compounds. The values of the normal boiling temperatures and the enthalpies of vaporization of *cis-*isomers are more than

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 609

essential error into the *vapHm* value. But the *dP dT* / or *d p dT* ln( ) / derivatives are determined not enough reliably because the saturation vapor pressure is a weak function of the temperature. Thus, an accuracy of determination of the enthalpy of vaporization is

The temperature dependences of the vapor pressures for the ferrocene derivatives [FD] were determined by a transpiration method elaborated and fully described by Verevkin S.P. and coathers (Emel'yanenko et al., 2007). Here, only the main features of the method are given. The determination of the vapor pressure is based on the measurements of the mass of substance transpired in the stream of carrier gas (nitrogen) and the volume of the gas flowing. The vapor pressure of the substances was obtained by Dalton law for partial vapor pressures of the ideal gas mixture. A sample of the substance (~0.5 g) was placed into the Utube, temperature of which was controlled with accuracy ±0.1 K. A nitrogen flow, controlled by a precision Hoke valve and measured with a bubble gauge, was passed through the tube. The transferred substance was condensed in a cooled trap and was analyzed chromatographically using the external standard (hydrocarbons). The rate of the nitrogen flow was adjusted to ensure that the condensed and vapor phases were in stable

restricted for the compounds with low vapor pressures at about 298 K temperature.

equilibrium. The saturation vapor pressure *psat* was calculated by the formula:

determined from the flow rate and the measurement time.

enthalpy of vaporization was calculated by the formula:

approximated by equation:

that , *<sup>g</sup>*

where *V = V(N2)* + V(DF); *R =* 8.314472; *m* and *M* are the mass of the sample under study and molecular weight of FD, respectively; *V(N2)* and V(FD) are the nitrogen and FD volumes, respectively, *V(N2)* > V(FD); and *T* is the U-tube temperature. The *V(N2)* value was

The *pT* parameters of the solid FD were measured in the pressure and temperature intervals from (0.01/0.11 to 0.44/4.9) Pa and from (311/342 to 341/379) K, respectively. Appropriate pressure and temperature intervals for the liquid FD were from (0.3/1.87 to 7.88/130) Pa and from (298/384 to 358/430) K, respectively. The vapor pressures of FD were

where *a* and *b* are coefficients, () ( / ) *C C* ,, , *g C cr liq pm pm pm* is the difference between the heat capacities of the vapor and condensed phases, and *Tst =* 298.15 K is the standard temperature (arbitrarily chosen). Equation (9) was deduced by integration of the correlation [( ln( )) / (1 / )] ( ) , , *R d <sup>p</sup> d T H C TT vap p m m T st* (Kulikov et al., 2001). The latter was obtained on the basis of Clausius-Clapeyron equation *R d* [( ln( )) / (1 / )] *p dT H vap m* in approximation of / *<sup>g</sup> V RT <sup>m</sup> <sup>p</sup> liq* and derivative ( )/ , *d H dT C vap <sup>m</sup> <sup>p</sup> <sup>m</sup>* by assuming

*liqCp <sup>m</sup>* value is independent on the temperature in the *pT* interval under study. The

obtained by differentiation of equation (9) with respect to 1/*T*. The ideal gas heat capacities of the ferrocene derivatives [FD] were obtained by additive Chickos and Acree method (Chikos & Acree Jr., 2003) that is defined as "an atom together with all of its ligands".

*p mRT VM* / *sat* (8)

ln( ) / ln( / ) *R p abT C TT p m*, *st* (9)

( ) *vap m m p m H H bC T sub* , (10)

those of *trans-*isomers in the series of perfluorobicyclo-nonanes and –decanes and their hydrocarbons analogues. Despite the more molecular mass, the normal boiling temperatures . . *Tn b* and the *vapHm* values of the perfluorocarbons are less than those of the hydrocarbons. On the contrary, the oxygen capacities are two times more in the series of perfluorocarbons which can be explanted by more poor intermolecular interactions of PFC. Fig. 4 presents the critical temperatures, enthalpies of vaporization, and oxygen capacities, ( ) <sup>2</sup> , for *cis-* and *trans-* perfluorobicyclo(4,3,0)nonanes (1 and 2), for components of Ftorosan blood substitute *(*Ries*,* 1991*), n*amely perfluorobicyclo(4,4,0)-decanes (3 and 4), perfluoro-N-(4-methylcyclohexyl)piperidine (5), and for some of their hydrocarbon analogues (6-9), respectively.

Due to smaller energies of intermolecular interactions, the critical temperatures and enthalpies of vaporization of perfluorocarbons are less, but oxygen capacities are more, than appropriate properties of appropriate hydrocarbons.

Fig. 4. Critical temperatures, *Tc* , enthalpies of vaporization, *H K* (298.15 ) *vap m* , and oxygen capacities, ( )(298.15 ) <sup>2</sup> *K* , for perfluorinated compounds 1-5 and their hydrocarbon analogues 6-9

Despite the more molecular mass, the normal boiling temperatures and enthalpies of vaporization of perfluorocarbons are less than those of appropriate hydrocarbon. This can be explained less coefficients of molecular packing, *Km* , and therefore by more intermolecular distances, and as a consequence less intermolecular interactions of perfluorocarbons in comparison with their hydrogen – containing counterparts.

#### **2.3 The vapor pressure and enthalpies of vaporization of the hard-volatile compounds**

The saturation vapor pressures of the solid and liquid substances having *p* < 1 kPa were determined by a dynamic method of evaporating the sample in a stream of the carrier inert gas. In calculation of the enthalpy of vaporization, the volume of vapor is well described by the ideal gas law and the volume of liquid can be easily neglected without introducing

those of *trans-*isomers in the series of perfluorobicyclo-nonanes and –decanes and their hydrocarbons analogues. Despite the more molecular mass, the normal boiling temperatures . . *Tn b* and the *vapHm* values of the perfluorocarbons are less than those of the hydrocarbons. On the contrary, the oxygen capacities are two times more in the series of perfluorocarbons which can be explanted by more poor intermolecular interactions of PFC. Fig. 4 presents the critical temperatures, enthalpies of vaporization, and oxygen capacities,

 , for *cis-* and *trans-* perfluorobicyclo(4,3,0)nonanes (1 and 2), for components of Ftorosan blood substitute *(*Ries*,* 1991*), n*amely perfluorobicyclo(4,4,0)-decanes (3 and 4), perfluoro-N-(4-methylcyclohexyl)piperidine (5), and for some of their hydrocarbon

Due to smaller energies of intermolecular interactions, the critical temperatures and enthalpies of vaporization of perfluorocarbons are less, but oxygen capacities are more, than

Fig. 4. Critical temperatures, *Tc* , enthalpies of vaporization, *H K* (298.15 ) *vap m* , and oxygen

Despite the more molecular mass, the normal boiling temperatures and enthalpies of vaporization of perfluorocarbons are less than those of appropriate hydrocarbon. This can be explained less coefficients of molecular packing, *Km* , and therefore by more intermolecular distances, and as a consequence less intermolecular interactions of

**2.3 The vapor pressure and enthalpies of vaporization of the hard-volatile compounds**  The saturation vapor pressures of the solid and liquid substances having *p* < 1 kPa were determined by a dynamic method of evaporating the sample in a stream of the carrier inert gas. In calculation of the enthalpy of vaporization, the volume of vapor is well described by the ideal gas law and the volume of liquid can be easily neglected without introducing

perfluorocarbons in comparison with their hydrogen – containing counterparts.

*K* , for perfluorinated compounds 1-5 and their

( ) <sup>2</sup> 

analogues (6-9), respectively.

capacities, ( )(298.15 ) <sup>2</sup> 

hydrocarbon analogues 6-9

appropriate properties of appropriate hydrocarbons.

essential error into the *vapHm* value. But the *dP dT* / or *d p dT* ln( ) / derivatives are determined not enough reliably because the saturation vapor pressure is a weak function of the temperature. Thus, an accuracy of determination of the enthalpy of vaporization is restricted for the compounds with low vapor pressures at about 298 K temperature.

The temperature dependences of the vapor pressures for the ferrocene derivatives [FD] were determined by a transpiration method elaborated and fully described by Verevkin S.P. and coathers (Emel'yanenko et al., 2007). Here, only the main features of the method are given. The determination of the vapor pressure is based on the measurements of the mass of substance transpired in the stream of carrier gas (nitrogen) and the volume of the gas flowing. The vapor pressure of the substances was obtained by Dalton law for partial vapor pressures of the ideal gas mixture. A sample of the substance (~0.5 g) was placed into the Utube, temperature of which was controlled with accuracy ±0.1 K. A nitrogen flow, controlled by a precision Hoke valve and measured with a bubble gauge, was passed through the tube. The transferred substance was condensed in a cooled trap and was analyzed chromatographically using the external standard (hydrocarbons). The rate of the nitrogen flow was adjusted to ensure that the condensed and vapor phases were in stable equilibrium. The saturation vapor pressure *psat* was calculated by the formula:

$$p\_{\text{sat}} = mRT \, / \,\text{V}M \tag{8}$$

where *V = V(N2)* + V(DF); *R =* 8.314472; *m* and *M* are the mass of the sample under study and molecular weight of FD, respectively; *V(N2)* and V(FD) are the nitrogen and FD volumes, respectively, *V(N2)* > V(FD); and *T* is the U-tube temperature. The *V(N2)* value was determined from the flow rate and the measurement time.

The *pT* parameters of the solid FD were measured in the pressure and temperature intervals from (0.01/0.11 to 0.44/4.9) Pa and from (311/342 to 341/379) K, respectively. Appropriate pressure and temperature intervals for the liquid FD were from (0.3/1.87 to 7.88/130) Pa and from (298/384 to 358/430) K, respectively. The vapor pressures of FD were approximated by equation:

$$R \cdot \ln(p) = a + b \;/\ T + \Delta C\_{p, \mathcal{W}} \cdot \ln(T \;/\ T\_{\rm sf}) \tag{9}$$

where *a* and *b* are coefficients, () ( / ) *C C* ,, , *g C cr liq pm pm pm* is the difference between the heat capacities of the vapor and condensed phases, and *Tst =* 298.15 K is the standard temperature (arbitrarily chosen). Equation (9) was deduced by integration of the correlation [( ln( )) / (1 / )] ( ) , , *R d <sup>p</sup> d T H C TT vap p m m T st* (Kulikov et al., 2001). The latter was obtained on the basis of Clausius-Clapeyron equation *R d* [( ln( )) / (1 / )] *p dT H vap m* in approximation of / *<sup>g</sup> V RT <sup>m</sup> <sup>p</sup> liq* and derivative ( )/ , *d H dT C vap <sup>m</sup> <sup>p</sup> <sup>m</sup>* by assuming that , *<sup>g</sup> liqCp <sup>m</sup>* value is independent on the temperature in the *pT* interval under study. The enthalpy of vaporization was calculated by the formula:

$$
\Delta\_{\text{vap}}H\_{\text{m}}(\Delta\_{\text{sub}}H\_{\text{m}}) = -b + \Delta C\_{p,\text{m}} \cdot T \tag{10}
$$

obtained by differentiation of equation (9) with respect to 1/*T*. The ideal gas heat capacities of the ferrocene derivatives [FD] were obtained by additive Chickos and Acree method (Chikos & Acree Jr., 2003) that is defined as "an atom together with all of its ligands".

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 611

investigated in this work by low-temperature adiabatic calorimetry (Varushchenko et al.,

The measurements of the heat capacities were conducted in a fully automated setup, consisted of a vacuum adiabatic calorimeter, a data acquisition and control system, AK-9.02, and a personal computer, PC (Fig. 5). The setup was produced in the National Scientific and

Fig. 5. The vacuum adiabatic calorimeter (CA) and cryostat (CR): (1) titanium container (*V*~1 cm3); (2) copper sleeve with the heater of calorimeter; (3) adiabatic shield; (4) bronze lid of the container; (5) the rhodium-iron resistance thermometer; (6) four-junction battery of Cu/Fe - Chromel thermocouples; (7) radiation screen – aluminium- coated Dacron-like film; (8) nylon threads; (9) spring; (10) Teflon tube; (11) plug; (12) vacuum jacket; (13) grooves of the plug 11; (14) valve; (15) and (16) detachable vacuum and cable joists, respectively; (17) steel tubes; (18) coupling nut; (19) charcoal getter; (20) radiation screens. Research Institute of Physical Technical and Radio-Technical Measurements (Mendeleevo, Moscow Region). The main principles of its construction were published in (Pavese &

The calorimetric cell consists of a container, 1, a copper sleeve, 2, in which the container is tightly held, and an adiabatic shield, 3. A bronze brass lid, 4, serves for vacuum-tight sealing the container by means of indium gasket and a simple manifold. To decrease the heat capacity of the empty calorimeter, the miniature rhodium-iron resistance thermometer, 5, ( 50 ) <sup>0</sup>*<sup>R</sup>* was mounted on the inner surface of the adiabatic shield. The thermometer, which was calibrated on ITS-90, is destined for temperature measurements from (0.5 to 373) <sup>К</sup> with accuracy <sup>3</sup> 3 10 K. The temperature difference between the calorimeter and the

1997a).

**3.1 Experimental** 

Malyshev, 1994).


Table 4 lists the purity of ferrocene derivatives determined by adiabatic calorimetry (part 3.2), coefficients *a* and *b* of equations (9) and (10), and enthalpies and entropies of vaporization and sublimation of FD at *T* = 298.15 K.

*<sup>a</sup>* Adiabatic calorimetry; *b* DSC; *c* the value calculated on the basis of correlation *subH HH m vap m m fus* .

Table 4. The purity, coefficients of equations (9) and (10), enthalpies and entropies of vaporization, ( ) *<sup>o</sup> vap mH T* and ( ) *<sup>o</sup> vap mS T* , and sublimation, ( ) *<sup>o</sup> subH T <sup>m</sup>* and ( ) *<sup>o</sup> subS T <sup>m</sup>* of ferrocenylmethanol [FM], benzylferrocene [BF], benzoylferrocene [BOF], propionylferrocene [POF], *n*propylferrocene [*n-PF*], *iso*-butylferrocene [*i-BF*] at *T* = 298.15 K

For testing the uncertainties of transpiration method in applying to FD, a compilation of the literature data on the enthalpy of sublimation of ferrocene were carried in reference (Emel'yanenko et al., 2007). A series of 21 (298.15 ) *<sup>o</sup> subH K <sup>m</sup>* values ranged from (70.3±1.0 to 76.78±0.85) kJ·mol-1 was obtained, the most part of the data being focused in the range between (72 and 74) kJ·mol-1. Uncertainties of these quantities were probably the random errors. Taking into account the uncertainties of the initial vapor pressure data making up from (1.5 to 2) per cent, a total value of the random and systematic errors could be 2 %. Therefore, the errors of the enthalpies of vaporization and sublimation as derivative values of the vapor pressure in the transpiration method were evaluated as ± 2 %.
