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Thermodynamic functions of melting for cyclohexane
J. Chem. Thermodynamics 1974,6, 379-386
Thermodynamic for cyclohexane R. H. STOKES
functions
of melting
and R. P. TOMLINS
Department of Physical and Inorganic University of New England, Armidale, N.S. W. 2351, Australia
Chemistry,
(Received 18 July 1973) New determinations of the normal melting temperature Tr, triple-point temperature T,,, pressure coefficient of the melting temperature, volume change Al/I on melting, and cryoscopic constant AHf/RT,2 of cyclohexane are reported. Accepted values of the melting temperature are shown to be about 0.17 K low because of dissolved air. The new values are: T,(101.3 kPa) = (279.87,fO.Ol) K; T,, = (279.83stO.01) K; dTr/dp = (5.361-tO.01) x 10-r K Pa-l; AVf = (5.222kO.007) cm3 mol-I; Al&/RTF = (4.196f0.005) x 10e3 K-l.
1. Introduction Cyclohexane has been one component of a number of liquid mixtures studied in this laboratory. Cryoscopic measurements are at present being made on ethanol + cyclohexane in order to study the association of ethanol at low concentrations in this solvent. The work reported here was undertaken to resolve uncertainties about the melting temperature and enthalpy of fusion of cyclohexane. 2. Purifkation Cyclohexane was shaken in turn with: concentrated sulphuric acid + nitric acid ; concentrated sulphuric acid; acidified permanganate; sodium bicarbonate; water; solid calcium chloride, and fractionally distilled through a 2 m column of Dixon rings of about 80 theoretical plates at a reflux ratio of 80. No impurity peak could be detected by g.1.c. using a 3.6 m column, 1.6 mm in diameter, with Varaport 30 packing. This instrument, used with an automatic integrator, could detect impurities at the 0.01 moles per cent level, other than dissolved air or moisture. The distillate was refluxed overnight with sodium wire, distilled off into a flask containing fresh sodium wire under dry nitrogen, and stored under a slight excess pressure of dry nitrogen in a vessel from which it could be drawn off while maintaining a nitrogen flow to prevent access of moist air.
3. Temperature measurement The temperature standards were provided by a Leeds and Northrup platinum-resistance thermometer calibrated for the IPTS-68 at the National Standards Laboratory
380
R. H. STOKES AND R. P. TOMLINS
of Australia. The bridges used were calibrated, and the “ice-point” resistance was determined at the time of use by means of a water triple-point cell, taken as giving 273.160 K. For the measurements of the triple-point temperature (section 5) the platinumresistance thermometer was used directly. For the melting temperature Tf and (dT,/dp) studies the calorimeter thermistor was calibrated against it at six temperatures in the range 275 to 281 K. The thermistor resistances were read with a thermostatted d.c. bridge with recorder output. The power dissipation in the thermistor was about 20 yW. The resistances were fitted to the three-parameter equation: 1nR = a+b/(T+B) with a maximum deviation equivalent to 0.001 K, i.e. within the limit of accuracy of the platinum-resistance thermometer. Since the thermistor resistance could be read within the equivalent of 2 x 10m4 K, it seems safe to assume that temperature changes are given by the thermistor to better than 0.001 K.
4. Melting temperature Melting temperatures were determined in the dilution calorimeter used for excessenthalpy studies in this laboratory. (I’ ‘) The calorimeter was flushed with dry nitrogen and filled using a syringe with the cyclohexane sample. In this calorimeter the sample is held over mercury, with no vapour space; volume changes during cooling and freezing are taken up by the movement of mercury from an external reservoir bulb. The temperature is measured by a thermistor in a well in the glass calorimeter vessel. Freezing temperature measurements were carried out as follows. The bath was cooled to 279 K and held there until the sample supercooled and finally began to freeze. Supercooling usually amounted to 0.15 K, and the appearance of the solid phase was evident from the reversal of the slope of the temperature-time chart. The bath temperature was then raised to follow the rise of the calorimeter temperature until solid -t- liquid equilibrium was established, and the bath was then set 0.005 to 0.01 K below the calorimeter temperature. A steady current of 4 mA was then passed through the heater, providing a power input of approximately 1.6 mW. The calorimeter temperature rose slowly as melting proceeded, and changed slope at the point when the last solid disappeared. The final melting temperature Tf was taken as the intersection of the two linear regions, as the turning point is somewhat rounded by thermal delays. The value of Tr of cyclohexane recommended by the American Petroleum InstituteC3) is 279.704 K, from the measurements of Glasgow and co-workers at the U.S. National Bureau of Standards.‘4) These workers used a highly purified sample, estimated from analysis of the complete melting curve to have solid-insoluble impurities less than 0.003 mole per cent. They remark, however, that it was in contact with air during the measurements. We were startled to find that our material, mildly degassed by warming in the syringe and applying suction with the needle closed off, gave freezing temperatures already more than 0.1 K higher than the Bureau of Standards value. Our surprise faded, however, on noting the mole fraction solubilities of nitrogen and oxygen in cyclohexane reported by Wilhelm and Battino,(‘)viz: (at 283 K) x(NJ = 7.3 x 10V4
THERMODYNAMIC
FUNCTIONS
OF
MELTING
FOR
CYCLOHEXANE
381
and x(0,) = 12.4 x 10w4, with little temperature dependence. If these gases are solidinsoluble the Tf of the N.B.S. sample could have been depressed by 0.20 K below the air-free value. Furthermore, if the sample was saturated with air, the air concentration in the liquid phase would have remained constant throughout the melting process, and hence would not have given rise to a slope of the melting curve; i.e. it would not have been detected as an impurity by melting-curve analysis. In effect, the eutectic system cyclohexanef air was being studied. This conclusion was verified more directly as follows. The calorimeter mercury-outlet tube was closed. A water-pump was then connected via drying tubes to the outlet tube on the stirrer shaft of the calorimeter, and the inlet tube was placed under the cyclohexane sample. The liquid was thus sucked in a rapid jet through the inlet tube, boiling as it entered the evacuated calorimeter vessel. When the vessel was full, the inlet tube was closed and pumping was continued for 15 min, leaving a vapour bubble at the top of the calorimeter vessel. This was expelled by admitting mercury at the bottom. While we hesitate to claim that degassing was now complete, the content of dissolved gas was certainly far below the saturation level. Melting temperatures at the local air pressure (91 kPa) of samples degassed in this way ranged from 279.86 K to 279.88 K. The rate of temperature rise during melting of these samples was typically 0.0015 K h-l. After the measurement of its melting temperature, one of these samples was saturated with air by opening the valve on the stirrer-shaft outlet and injecting a stream of air through the liquid by a syringe on the inlet tube, while stirring continued. Further mercury was then admitted to expel the air bubble, and the melting temperature was redetermined. It was now 279.738 K, in excellent agreement with the N.B.S. value bearing in mind that Armidale air pressure is 0.89 of that at Washington, D.C. However, it was considered necessary to obtain results for really thoroughly degassed cyclohexane, as follows.
5. Triple-point temperature Cyclohexane purified as described above was first degassed by vacuum sublimation as recommended by Dunlop and co-workers. @) It was then admitted under vacuum (figure 1) into a purification train similar to that used by Marsh,(7) involving no contact between the vapour and greased taps or joints. The vapour was passed repeatedly through Linde 4A molecular sieve by trap-to-trap distillation, using solid CO, + (CH,),CO mixture on the cold traps so that traces of CO, could be pumped off. The purified material was distilled into the evacuated triple-point cell and frozen with solid CO, + (CH&CO mixture. The cell jacket was then evacuated and the solid was allowed to melt. The temperature was followed with the platinum-resistance thermometer. The temperature rise between 50 and 100 per cent melting was 0.003 K, indicating a mole fraction 1 x 10e5 of solid-insoluble impurities, in fair agreement with a mole fraction of 7 x 10m6 obtained in section 7. Four separate fillings of the cell gave triple-point temperatures of (279.83kO.01) K. As the vapour pressure of cyclohexane at this temperature is 5.4 kPa, and (dT,dp) along the fusion curve (see later) is 5.36 x low7 K Pa-l, this triple-point temperature corresponds to a normal melting temperature (at 101.325 kPa) of 279.876 K.
382
R. H. STOKES AND R. P. TOMLINS
FIGURE 1. Triple-point cell and purification train: A is the jacket-evacuation molecular sieve, and C leads to the vacuum-sublimation apparatus.
outlet, B the
6. Change of melting temperature with pressure A sample was partially frozen as for the determination of Tf and the bath temperature was adjusted to 0.005 K below the equilibrium temperature, but no heating current was supplied, so that the temperature remained constant within 1 x 10m4 K. The atmospheric pressure and hydrostatic head of mercury were noted. Gas pressures of up to 200 kPa were then applied to the mercury in the external reservoir bulb of the calorimeter, and measured by a mercury manometer or a Ruska high-precision Bourdontype manometer. The equilibrium temperature rose, and the bath was readjusted to 0.005 K below the new value. Three such measurements gave dT,/dp = (5.36 kO.01) x lo-’ K Pa-“. Deffet@) has reported values at much higher pressures (minimum 6.1 MPa) which can be extrapolated to give 5.3, x lo-’ K Pa- ’ at pressures near atmospheric.
7. Volume change on melting Existing data (14) for the density of solid cyclohexane are of good accuracy, but it was nevertheless considered desirable to determine the volume change on melting directly as this avoids the use of solid and liquid densities from different sources. Complete removal of dissolved gases was necessary as otherwise bubbles formed in the solid. A dilatometer (figure 2) containing a weighed mercury pool was attached at A to the vacuum sublimation apparatus, in which sufficient cyclohexane to fill the bulb was sublimed on to the cold finger (cooled with solid COZ + (CH,),CO). Taps B and C were opened and the dilatometer was evacuated, with tap D closed; then the freezing mixture was removed from the cold finger so that the cyclohexane melted. Slight warming transferred it into the dilatometer. When this was filled to half-way up the upper
THERMODYNAMIC
FUNCTIONS
OF MELTING
FOR CYCLOHEXANE
383
FIGURE 2. Dilatometer for volume change AVf on fusion: A leads to the vacuum-sublimation apparatus, B, C, D are spring-loaded Teflon taps, and M is the reference mark on 2 mm capillary.
bulb, tap B was closed and the dilatometer was progressively lowered into a bath at approximately 278 K. Since tap D was closed (with the mercury level at the reference mark M), liquid was drawn down from the smaller bulb as that in the main bulb cooled and froze. When the main bulb was full of solid, the vessel was put in an icebath, immersed to just below tap C, for several hours. Then tap C was closed, and not opened again until the experiment was finished. Tap D was opened, and the dilatometer was exposed to room temperature briefly so that a film of liquid could form between the solid and the wall. It was then placed in a thermostat at 276 K. Mercury was removed from the side-arm into a weighed syringe to restore the level to the reference mark M. This procedure allowed the solid to expand without strain, the liquid film refreezing round the solid. This process was repeated for other temperatures nearer to the melting temperature. The bath was then raised to 0.05 K above the melting temperature, and the solid was all allowed to melt. Mercury was again removed to the mark. From the known volume of the main bulb (from tap C to the mark M) and the various masses of mercury, it is possible to obtain the volume change on melting at the true freezing temperature. Figure 3 shows the results of one such run; note that the liquid molar volume has been reduced by 5.000 cm3 mol-’ to keep it on the graph. The mass of cyclohexane in the main bulb was determined from the reading at 298.15 K assuming a liquid density of 0.77389 g cmB3 at this temperature, because the problem of drying the components of the spring-loaded taps made a direct determination by weighing
384
R. H. STOKES
100.6( 0
’
I 2
AND R. P. TOMLINS
I
I I 4 7-K-273.15
I 6
I
II 8
FIGURE 3. Molar volumes V of liquid and solid cyclohexane near the melting temperature: line A is for solid, B is (V-5 cm3 mol-I) for liquid, and C is the melting temperature.
difficult. However, uncertainties in the mass of cyclohexane merely result in a small vertical shift of both the solid and liquid curves and do not affect the AVf determination significantly. The solid molar volumes of reference 14 in the range 272 to 278 K give a line parallel to that in figure 3 and 0.08 cm3 mol-r below it. The mean of three runs gave AV, = (5.222kO.007) cm3 mol-‘. In figure 3, the point for the solid at 279.65 K lies 0.042 cm3 mol-’ above the extrapolation of the straight-line results from 273.15 to 279.15 K. This is due to the “premelting” induced by small residual traces of solid-insoluble impurity, and can be used(‘) to estimate the level of such impurities, from the equation: V, - v,o = xA VfRT,2/{(T, - T)AH,], where x is the mole fraction impurity, VSois the molar volume of the pure solid at temperature T, and V, is the measured molar volume of the impure solid at temperature T. This yields a mole fraction of solid-insoluble impurity of only 7 x 10b6, indicating a good level of initial purification, drying, and degassing. 8. Cryoscopic constant and enthalpy of fusion Published values of the enthalpy of fusion AH, of cyclohexane range over 100 J mol- I, references 11 and 13 reporting 2677 and 2629 J mol-I, while reference 12 gives, without details, a value of 2728 J mol- ‘. From the results reported in sections 6 and 7 above, we may use the Clapeyron equation: dp]dT, = AHfI(TAVf), to obtain AH, = (2727_+ 8) J mol-“. This supports the value mentioned in reference 12. As further checking was clearly needed, we
THERMODYNAMIC
FUNCTIONS
OF
MELTING
FOR
385
CYCLOHEXANE
measured the cryoscopic constant by determining the freezing temperatures of dilute solutions of highly purified n-hexane in cyclohexane in the calorimeter. A stock solution containing n-CsH,, at a concentration of 4.969 x lo-” mol cmP3 (280 K) was prepared in the calorimeter using cyclohexane of measured freezing temperature. The procedure in making this stock followed exactly our normal procedure for measuring enthalpies of mixing. ~3’) Some of the stock solution was then withdrawn, without contact with air, into a bulb previously full of mercury, connected to the mercury-filled piston-burette. The calorimeter was then refilled with cyclohexane, and the Tf of the solvent was again measured. Increments of the stock n-hexane solution were then injected, Tf being measured at each step. The lowest volume of stock solution injected was 4 cm3, so that the small uncertainty (about 0.002 cm3) arising from the volume of the inlet tube would not be serious. The results are given intable1.Allthevaluesofx,/AT,liebetween4.191 x 10e3 K-1and4.204x10-3 K-l, TABLE
1.
Freezing temperature depressionsAT* for n-hexane (1) in cyclohexane (2) Series A 103x1 3.321 4.865 6.314 7.747 9.040 10.84 12.665
AT& 0.790 1.160 1.505, 1.848 2.151 2.584
103x1 3.377
4.910 6.568 8.563 10.684 12.606
Series B AT& 0.804
1.171 1.566 2.043 2.548 3.003
3.019
and we may therefore take their arithmetic mean, 4.196 x 10m3 K-l, as the cryoscopic constant, defined by limX,,O(xl/ATf) = AHflRTf.. This gives AH, = (2732+ 3) J mol-I, in excellent agreement with the value from the Clapeyron equation. This work was supported by a grant from the Australian Research Grants Committee. We thank Mrs Marion Adamson and Mrs Carol Burfitt for assistance. REFERENCES 1. Stokes, R. H.; Marsh, K. N. ; Tomlins, R. P. J. Chem. Thermodynamics 2. Ewing, M. B. ; Marsh, K. N.; Stokes, R. H.; Tuxford, C. W. J. Chem.
1969, 1, 211. Thermodynamics
1970,
2,
751. 3. Selected
Values of Properties of Hydrocarbons and Related Compounds. American Petroleum Institute Research Project 44. Texas A & M University, 1965. Table 23-2-(3.1110)-m. 4. Glasgow, A. R. Jr. ; Murphy, E. T.; Willingham, J. C. B.; Rossini, F. D. J. Res. Nat. Bur. Stand. 1946,
37, 141.
5. Wilhelm, E.; Battino, R. J. Chem. Thermodynamics 1973, 5, 117. 6. Bell, T. N. ; Cussler, E. L. ; Harris, K. R.; Pepela, C. N.; Dunlop, P. J. J. Phys. Chem. 1968, 72, 4693.
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R. H. STOKES AND R. P. TOMLINS
7. Marsh, K. N. Trans. Faraday Sot. 1968, 64, 883. 8. De&t, L. Ball. Sot. Chim. Belg. 1935,44,41 & 97. 9. Stokes, R. H. J. Phys. Chem. Solids 1966, 27, 51. 10. Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds. Elsevier Pub. Co.: New York. 1950. 11. Ruehrwein, R. A.; Huffmann, H. M. J. Amer. Chem. Sot. 1943,65, 1620. 12. Ziegler, W. T.; Andrews, D. H. J. Amer. Chem. Sot. 1942, 64, 2482. 13. Aston, 3. G. ; Szasz, G. J. ; Fink, H. L. J. Amer. Chem. Sot. 1943, 65, 1135. 14. Higgins, P. F. ; Ivor, R. A. B.; Staveley, L. A. K.; Virden, J. J. des C. J. Chem. Sot., Supplement 1, 5762.1964.
Thermodynamic for cyclohexane R. H. STOKES
functions
of melting
and R. P. TOMLINS
Department of Physical and Inorganic University of New England, Armidale, N.S. W. 2351, Australia
Chemistry,
(Received 18 July 1973) New determinations of the normal melting temperature Tr, triple-point temperature T,,, pressure coefficient of the melting temperature, volume change Al/I on melting, and cryoscopic constant AHf/RT,2 of cyclohexane are reported. Accepted values of the melting temperature are shown to be about 0.17 K low because of dissolved air. The new values are: T,(101.3 kPa) = (279.87,fO.Ol) K; T,, = (279.83stO.01) K; dTr/dp = (5.361-tO.01) x 10-r K Pa-l; AVf = (5.222kO.007) cm3 mol-I; Al&/RTF = (4.196f0.005) x 10e3 K-l.
1. Introduction Cyclohexane has been one component of a number of liquid mixtures studied in this laboratory. Cryoscopic measurements are at present being made on ethanol + cyclohexane in order to study the association of ethanol at low concentrations in this solvent. The work reported here was undertaken to resolve uncertainties about the melting temperature and enthalpy of fusion of cyclohexane. 2. Purifkation Cyclohexane was shaken in turn with: concentrated sulphuric acid + nitric acid ; concentrated sulphuric acid; acidified permanganate; sodium bicarbonate; water; solid calcium chloride, and fractionally distilled through a 2 m column of Dixon rings of about 80 theoretical plates at a reflux ratio of 80. No impurity peak could be detected by g.1.c. using a 3.6 m column, 1.6 mm in diameter, with Varaport 30 packing. This instrument, used with an automatic integrator, could detect impurities at the 0.01 moles per cent level, other than dissolved air or moisture. The distillate was refluxed overnight with sodium wire, distilled off into a flask containing fresh sodium wire under dry nitrogen, and stored under a slight excess pressure of dry nitrogen in a vessel from which it could be drawn off while maintaining a nitrogen flow to prevent access of moist air.
3. Temperature measurement The temperature standards were provided by a Leeds and Northrup platinum-resistance thermometer calibrated for the IPTS-68 at the National Standards Laboratory
380
R. H. STOKES AND R. P. TOMLINS
of Australia. The bridges used were calibrated, and the “ice-point” resistance was determined at the time of use by means of a water triple-point cell, taken as giving 273.160 K. For the measurements of the triple-point temperature (section 5) the platinumresistance thermometer was used directly. For the melting temperature Tf and (dT,/dp) studies the calorimeter thermistor was calibrated against it at six temperatures in the range 275 to 281 K. The thermistor resistances were read with a thermostatted d.c. bridge with recorder output. The power dissipation in the thermistor was about 20 yW. The resistances were fitted to the three-parameter equation: 1nR = a+b/(T+B) with a maximum deviation equivalent to 0.001 K, i.e. within the limit of accuracy of the platinum-resistance thermometer. Since the thermistor resistance could be read within the equivalent of 2 x 10m4 K, it seems safe to assume that temperature changes are given by the thermistor to better than 0.001 K.
4. Melting temperature Melting temperatures were determined in the dilution calorimeter used for excessenthalpy studies in this laboratory. (I’ ‘) The calorimeter was flushed with dry nitrogen and filled using a syringe with the cyclohexane sample. In this calorimeter the sample is held over mercury, with no vapour space; volume changes during cooling and freezing are taken up by the movement of mercury from an external reservoir bulb. The temperature is measured by a thermistor in a well in the glass calorimeter vessel. Freezing temperature measurements were carried out as follows. The bath was cooled to 279 K and held there until the sample supercooled and finally began to freeze. Supercooling usually amounted to 0.15 K, and the appearance of the solid phase was evident from the reversal of the slope of the temperature-time chart. The bath temperature was then raised to follow the rise of the calorimeter temperature until solid -t- liquid equilibrium was established, and the bath was then set 0.005 to 0.01 K below the calorimeter temperature. A steady current of 4 mA was then passed through the heater, providing a power input of approximately 1.6 mW. The calorimeter temperature rose slowly as melting proceeded, and changed slope at the point when the last solid disappeared. The final melting temperature Tf was taken as the intersection of the two linear regions, as the turning point is somewhat rounded by thermal delays. The value of Tr of cyclohexane recommended by the American Petroleum InstituteC3) is 279.704 K, from the measurements of Glasgow and co-workers at the U.S. National Bureau of Standards.‘4) These workers used a highly purified sample, estimated from analysis of the complete melting curve to have solid-insoluble impurities less than 0.003 mole per cent. They remark, however, that it was in contact with air during the measurements. We were startled to find that our material, mildly degassed by warming in the syringe and applying suction with the needle closed off, gave freezing temperatures already more than 0.1 K higher than the Bureau of Standards value. Our surprise faded, however, on noting the mole fraction solubilities of nitrogen and oxygen in cyclohexane reported by Wilhelm and Battino,(‘)viz: (at 283 K) x(NJ = 7.3 x 10V4
THERMODYNAMIC
FUNCTIONS
OF
MELTING
FOR
CYCLOHEXANE
381
and x(0,) = 12.4 x 10w4, with little temperature dependence. If these gases are solidinsoluble the Tf of the N.B.S. sample could have been depressed by 0.20 K below the air-free value. Furthermore, if the sample was saturated with air, the air concentration in the liquid phase would have remained constant throughout the melting process, and hence would not have given rise to a slope of the melting curve; i.e. it would not have been detected as an impurity by melting-curve analysis. In effect, the eutectic system cyclohexanef air was being studied. This conclusion was verified more directly as follows. The calorimeter mercury-outlet tube was closed. A water-pump was then connected via drying tubes to the outlet tube on the stirrer shaft of the calorimeter, and the inlet tube was placed under the cyclohexane sample. The liquid was thus sucked in a rapid jet through the inlet tube, boiling as it entered the evacuated calorimeter vessel. When the vessel was full, the inlet tube was closed and pumping was continued for 15 min, leaving a vapour bubble at the top of the calorimeter vessel. This was expelled by admitting mercury at the bottom. While we hesitate to claim that degassing was now complete, the content of dissolved gas was certainly far below the saturation level. Melting temperatures at the local air pressure (91 kPa) of samples degassed in this way ranged from 279.86 K to 279.88 K. The rate of temperature rise during melting of these samples was typically 0.0015 K h-l. After the measurement of its melting temperature, one of these samples was saturated with air by opening the valve on the stirrer-shaft outlet and injecting a stream of air through the liquid by a syringe on the inlet tube, while stirring continued. Further mercury was then admitted to expel the air bubble, and the melting temperature was redetermined. It was now 279.738 K, in excellent agreement with the N.B.S. value bearing in mind that Armidale air pressure is 0.89 of that at Washington, D.C. However, it was considered necessary to obtain results for really thoroughly degassed cyclohexane, as follows.
5. Triple-point temperature Cyclohexane purified as described above was first degassed by vacuum sublimation as recommended by Dunlop and co-workers. @) It was then admitted under vacuum (figure 1) into a purification train similar to that used by Marsh,(7) involving no contact between the vapour and greased taps or joints. The vapour was passed repeatedly through Linde 4A molecular sieve by trap-to-trap distillation, using solid CO, + (CH,),CO mixture on the cold traps so that traces of CO, could be pumped off. The purified material was distilled into the evacuated triple-point cell and frozen with solid CO, + (CH&CO mixture. The cell jacket was then evacuated and the solid was allowed to melt. The temperature was followed with the platinum-resistance thermometer. The temperature rise between 50 and 100 per cent melting was 0.003 K, indicating a mole fraction 1 x 10e5 of solid-insoluble impurities, in fair agreement with a mole fraction of 7 x 10m6 obtained in section 7. Four separate fillings of the cell gave triple-point temperatures of (279.83kO.01) K. As the vapour pressure of cyclohexane at this temperature is 5.4 kPa, and (dT,dp) along the fusion curve (see later) is 5.36 x low7 K Pa-l, this triple-point temperature corresponds to a normal melting temperature (at 101.325 kPa) of 279.876 K.
382
R. H. STOKES AND R. P. TOMLINS
FIGURE 1. Triple-point cell and purification train: A is the jacket-evacuation molecular sieve, and C leads to the vacuum-sublimation apparatus.
outlet, B the
6. Change of melting temperature with pressure A sample was partially frozen as for the determination of Tf and the bath temperature was adjusted to 0.005 K below the equilibrium temperature, but no heating current was supplied, so that the temperature remained constant within 1 x 10m4 K. The atmospheric pressure and hydrostatic head of mercury were noted. Gas pressures of up to 200 kPa were then applied to the mercury in the external reservoir bulb of the calorimeter, and measured by a mercury manometer or a Ruska high-precision Bourdontype manometer. The equilibrium temperature rose, and the bath was readjusted to 0.005 K below the new value. Three such measurements gave dT,/dp = (5.36 kO.01) x lo-’ K Pa-“. Deffet@) has reported values at much higher pressures (minimum 6.1 MPa) which can be extrapolated to give 5.3, x lo-’ K Pa- ’ at pressures near atmospheric.
7. Volume change on melting Existing data (14) for the density of solid cyclohexane are of good accuracy, but it was nevertheless considered desirable to determine the volume change on melting directly as this avoids the use of solid and liquid densities from different sources. Complete removal of dissolved gases was necessary as otherwise bubbles formed in the solid. A dilatometer (figure 2) containing a weighed mercury pool was attached at A to the vacuum sublimation apparatus, in which sufficient cyclohexane to fill the bulb was sublimed on to the cold finger (cooled with solid COZ + (CH,),CO). Taps B and C were opened and the dilatometer was evacuated, with tap D closed; then the freezing mixture was removed from the cold finger so that the cyclohexane melted. Slight warming transferred it into the dilatometer. When this was filled to half-way up the upper
THERMODYNAMIC
FUNCTIONS
OF MELTING
FOR CYCLOHEXANE
383
FIGURE 2. Dilatometer for volume change AVf on fusion: A leads to the vacuum-sublimation apparatus, B, C, D are spring-loaded Teflon taps, and M is the reference mark on 2 mm capillary.
bulb, tap B was closed and the dilatometer was progressively lowered into a bath at approximately 278 K. Since tap D was closed (with the mercury level at the reference mark M), liquid was drawn down from the smaller bulb as that in the main bulb cooled and froze. When the main bulb was full of solid, the vessel was put in an icebath, immersed to just below tap C, for several hours. Then tap C was closed, and not opened again until the experiment was finished. Tap D was opened, and the dilatometer was exposed to room temperature briefly so that a film of liquid could form between the solid and the wall. It was then placed in a thermostat at 276 K. Mercury was removed from the side-arm into a weighed syringe to restore the level to the reference mark M. This procedure allowed the solid to expand without strain, the liquid film refreezing round the solid. This process was repeated for other temperatures nearer to the melting temperature. The bath was then raised to 0.05 K above the melting temperature, and the solid was all allowed to melt. Mercury was again removed to the mark. From the known volume of the main bulb (from tap C to the mark M) and the various masses of mercury, it is possible to obtain the volume change on melting at the true freezing temperature. Figure 3 shows the results of one such run; note that the liquid molar volume has been reduced by 5.000 cm3 mol-’ to keep it on the graph. The mass of cyclohexane in the main bulb was determined from the reading at 298.15 K assuming a liquid density of 0.77389 g cmB3 at this temperature, because the problem of drying the components of the spring-loaded taps made a direct determination by weighing
384
R. H. STOKES
100.6( 0
’
I 2
AND R. P. TOMLINS
I
I I 4 7-K-273.15
I 6
I
II 8
FIGURE 3. Molar volumes V of liquid and solid cyclohexane near the melting temperature: line A is for solid, B is (V-5 cm3 mol-I) for liquid, and C is the melting temperature.
difficult. However, uncertainties in the mass of cyclohexane merely result in a small vertical shift of both the solid and liquid curves and do not affect the AVf determination significantly. The solid molar volumes of reference 14 in the range 272 to 278 K give a line parallel to that in figure 3 and 0.08 cm3 mol-r below it. The mean of three runs gave AV, = (5.222kO.007) cm3 mol-‘. In figure 3, the point for the solid at 279.65 K lies 0.042 cm3 mol-’ above the extrapolation of the straight-line results from 273.15 to 279.15 K. This is due to the “premelting” induced by small residual traces of solid-insoluble impurity, and can be used(‘) to estimate the level of such impurities, from the equation: V, - v,o = xA VfRT,2/{(T, - T)AH,], where x is the mole fraction impurity, VSois the molar volume of the pure solid at temperature T, and V, is the measured molar volume of the impure solid at temperature T. This yields a mole fraction of solid-insoluble impurity of only 7 x 10b6, indicating a good level of initial purification, drying, and degassing. 8. Cryoscopic constant and enthalpy of fusion Published values of the enthalpy of fusion AH, of cyclohexane range over 100 J mol- I, references 11 and 13 reporting 2677 and 2629 J mol-I, while reference 12 gives, without details, a value of 2728 J mol- ‘. From the results reported in sections 6 and 7 above, we may use the Clapeyron equation: dp]dT, = AHfI(TAVf), to obtain AH, = (2727_+ 8) J mol-“. This supports the value mentioned in reference 12. As further checking was clearly needed, we
THERMODYNAMIC
FUNCTIONS
OF
MELTING
FOR
385
CYCLOHEXANE
measured the cryoscopic constant by determining the freezing temperatures of dilute solutions of highly purified n-hexane in cyclohexane in the calorimeter. A stock solution containing n-CsH,, at a concentration of 4.969 x lo-” mol cmP3 (280 K) was prepared in the calorimeter using cyclohexane of measured freezing temperature. The procedure in making this stock followed exactly our normal procedure for measuring enthalpies of mixing. ~3’) Some of the stock solution was then withdrawn, without contact with air, into a bulb previously full of mercury, connected to the mercury-filled piston-burette. The calorimeter was then refilled with cyclohexane, and the Tf of the solvent was again measured. Increments of the stock n-hexane solution were then injected, Tf being measured at each step. The lowest volume of stock solution injected was 4 cm3, so that the small uncertainty (about 0.002 cm3) arising from the volume of the inlet tube would not be serious. The results are given intable1.Allthevaluesofx,/AT,liebetween4.191 x 10e3 K-1and4.204x10-3 K-l, TABLE
1.
Freezing temperature depressionsAT* for n-hexane (1) in cyclohexane (2) Series A 103x1 3.321 4.865 6.314 7.747 9.040 10.84 12.665
AT& 0.790 1.160 1.505, 1.848 2.151 2.584
103x1 3.377
4.910 6.568 8.563 10.684 12.606
Series B AT& 0.804
1.171 1.566 2.043 2.548 3.003
3.019
and we may therefore take their arithmetic mean, 4.196 x 10m3 K-l, as the cryoscopic constant, defined by limX,,O(xl/ATf) = AHflRTf.. This gives AH, = (2732+ 3) J mol-I, in excellent agreement with the value from the Clapeyron equation. This work was supported by a grant from the Australian Research Grants Committee. We thank Mrs Marion Adamson and Mrs Carol Burfitt for assistance. REFERENCES 1. Stokes, R. H.; Marsh, K. N. ; Tomlins, R. P. J. Chem. Thermodynamics 2. Ewing, M. B. ; Marsh, K. N.; Stokes, R. H.; Tuxford, C. W. J. Chem.
1969, 1, 211. Thermodynamics
1970,
2,
751. 3. Selected
Values of Properties of Hydrocarbons and Related Compounds. American Petroleum Institute Research Project 44. Texas A & M University, 1965. Table 23-2-(3.1110)-m. 4. Glasgow, A. R. Jr. ; Murphy, E. T.; Willingham, J. C. B.; Rossini, F. D. J. Res. Nat. Bur. Stand. 1946,
37, 141.
5. Wilhelm, E.; Battino, R. J. Chem. Thermodynamics 1973, 5, 117. 6. Bell, T. N. ; Cussler, E. L. ; Harris, K. R.; Pepela, C. N.; Dunlop, P. J. J. Phys. Chem. 1968, 72, 4693.
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R. H. STOKES AND R. P. TOMLINS
7. Marsh, K. N. Trans. Faraday Sot. 1968, 64, 883. 8. De&t, L. Ball. Sot. Chim. Belg. 1935,44,41 & 97. 9. Stokes, R. H. J. Phys. Chem. Solids 1966, 27, 51. 10. Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds. Elsevier Pub. Co.: New York. 1950. 11. Ruehrwein, R. A.; Huffmann, H. M. J. Amer. Chem. Sot. 1943,65, 1620. 12. Ziegler, W. T.; Andrews, D. H. J. Amer. Chem. Sot. 1942, 64, 2482. 13. Aston, 3. G. ; Szasz, G. J. ; Fink, H. L. J. Amer. Chem. Sot. 1943, 65, 1135. 14. Higgins, P. F. ; Ivor, R. A. B.; Staveley, L. A. K.; Virden, J. J. des C. J. Chem. Sot., Supplement 1, 5762.1964.