Thermodynamic Properties of Fluorine Compounds Part 15.l-Vapour Pressures of the Three Tetrafluorobenzenes and 1,3,5-Trichlor0-2,4,6-trifluorobenzene BY D. AMBROSE,* J. H. ELLENDER, C. H. S. SPRAKE AND R. TOWNSEND Division of Chemical Standards, National Physical Laboratory, Teddington, Middlesex TW 1 1 OLW Received 11 th April, 1974 The vapour pressures were measured of 1,2,4,5-tetrafluorobenzene from 5 kPa to the critical pressure, of 1,2,3,5-tetrafluorobenzene from 5 kPa to 470 kPa, of 1,2,3,4-tetrafluorobenzene from 7 kPa to 202 kPa, and of 1,3,5-trichloro-2,4,6-trifluorobenzene from 3 kPa to 180 kPa. The results were fitted by Antoine equations (applicable at pressures up to 200 kPa) and by Chebyshev equations. For each compound one of the latter equations is applicable over the whole range up to the critical temp- erature, and it is shown that the variation with temperature of AHlAZcalculated from this equation is similar to that found for other compounds.The vapour pressures, critical temperatures and critical pressures of some highly fluorinated aromatic hydrocarbons have been reported in earlier papers in this ser- ies 2-4 ; extension of the work to the four compounds named in the title is now described. Findlay has already published values of vapour pressure in the range 3 to 30 kPa for two of them, 1,2,3,4-tetrafluorobenzene and 1,2,3,5-tetrafluoro- benzene; the values presented here are more precise, and we believe them to be more accurate. EXPERIMENTAL The samples were from the same batches of material as were used in other investigations in this laboratory; their purities (table 1) had been assessed by low-temperature calor- imetry,6* but as a precaution the samples were re-dried by treatment with calcium hydride or molecular sieve immediately before use.For all the compounds, ebulliometric measurements were made in the range from about 5 to 200 kPa,* and their critical temperatures Tc and pressures pc were determined.g In addition, ebulliometric measurements were made at higher pressures on 1,2,3,5tetrafluoro- benzene and 1,2,4,5-tetrafluoroben~ene,~~ and on the latter compound measurements were made in the range 330 kPa to the critical pressure by both dynamic and static method^.^^ l 1 Temperatures were measured by means of platinum resistance thermometers used with equipment sensitive to 0.001 K, an automatic a.c.bridge (Automatic Systems) linked through a selector and control unit to an automatic typewriter and paper-tape punch for ebullio- metry, and a Mueller bridge (Leeds and Northrup) for the other measurements. Experiments with benzene, including some made with different samples, have shown that by comparative ebulliometry at pressures between 5 and 200 kPa the boiling temperatures of a compound of well established purity that is unaffected by decomposition may be reproduced within 0.005 K. At pressures p above 200kPa measured points obtained by the other methods seldom deviate from the curve best fitting all the points by more than 0.001~ ; this corresponds to an uncertainty in temperature of about 0.03 K near atmospheric pressure, increasing to about 0.1 K near the critical temperature.For benzene, points obtained in two other investiga- tions believed to be reliable as well as those measured in this laboratory all lie within 0.001~ of acurvefitted to the three sets of data. The estimated range of uncertainty in the measure- ments of critical temperatures is kO.05 K. 35TABLE 1 .-PURITIES/MOLES PER CENT ; VAPOUR PRESSURES BELOW 205 kPa ; Ap = Pobs-PcaIc WHERE Pcalc HAS BEEN OBTAINED FROM EQN (I), (11) AND (111). EQN (I) WAS OBTAINED BY FITTING TO THE RESTRICTED RANGE OF OBSERVED VALUES INDICATED BY THE ENTRIES IN THE COLUMN FOR Ap ; EQN (11) AND (111) WERE FITTED TO ALL THE VALUES TABULATED AplPa APlPa TIK plkPa (1) (11) (111) TIK plkPa (1) (11) (111) 1,2,3,4-tetrafluoro benzene (99.85) 1 ,2,4,5 - t e trafluor o benzene (99.94) 300.800 304.567 308.223 3 12.01 8 315.890 3 19.61 6 324.471 328.626 333.357 338.009 342.899 348.275 352.947 356.490 363.273 367.378 368.232 373.020 377.346 382.509 387.449 391.651 7.437 8.945 10.646 12.688 15.095 17.757 21.794 25.823 31.137 37.177 44.535 53.942 63.331 71.305 88.788 100.917 103.593 119,685 135.850 157.351 180.294 201.822 2 -0 0 -0 -1 0 -2 1 -4 0 -4 -0 - 5 -1 -4 -0 5 7 - 5 -5 0 -3 12 7 -4 -1 -7 0 3 -3 1 3 -0 -0 1 1 - 5 -3 -3 -2 -2 4 -8 -10 2 4 -2 15 -14 -24 -8 4 -10 -4 1,2,3, 5-tetrafluorobenzene (99.99) 287.593 291.414 295.169 298.091 303.399 307.963 3 12.406 314.635 318.751 324.852 329.202 334.506 3 3 8.643 343.224 347.715 352.951 356.719 357.291 357.743 362.582 366.716 371.603 376.423 381.524 5.719 6.987 8.457 9.773 12.598 15.541 18.930 20.846 24.802 3 1.779 37.666 46.007 53.501 62.91 1 73.374 8 7.269 98.504 100.305 101.755 118.237 133.926 154.528 177.195 203.907 4 1 1 -1 -1 -1 -1 0 -3 -0 -4 0 -3 1 -3 0 - 3 -0 0 1 2 -0 3 -3 8 -0 1 13 3 4 14 3 0 8 -3 -1 4 - 5 -1 3 -5 7 11 3 3 3 -0 4 -1 2 4 -9 3 6 -16 5 -1 -34 - 5 293.198 296.489 300.519 303.459 308.374 3 13.302 315.839 320.056 324.073 330.275 334.497 339.931 344.142 348.439 353.3 84 3 58.929 362.593 363.049 363.591 368.237 372.427 377.572 382.398 387.568 5.855 6.944 8.505 9.822 12.399 15.524 17.370 20.841 24.655 31.652 37.286 45.699 53.227 61 395 73.237 87.873 98.750 100.1 77 101.896 1 17.566 133.286 154.790 177.330 204.254 3 -0 1 -0 -1 -0 -1 1 -3 1 -3 1 -4 -0 -2 1 -2 -0 -2 -3 4 0 5 -2 2 12 2 -1 10 -3 -2 8 - 5 2 11 0 -1 7 -1 1 8 1 4 11 5 - 4 0 0 0 0 8 1 -6 10 -9 -25 -4 3 -26 -10 trichlorotrifluorobenzene (99.8) 3 64.225 367.951 372.877 377.171 382.099 386.563 391.427 396.136 401.004 405.974 410.718 416.936 422.234 428.262 434.156 440.352 447.167 453.087 459.341 466.122 471.301 472.3 80 478.412 483.851 490.344 2.845 3.360 4.159 4.987 6.104 7.290 8.799 10.498 12.539 14.949 17.604 21.658 25.690 3 1.008 37.048 44.400 -1 53.802 1 63.223 6 74.562 -0 88.653 -1 103.470 - 5 119.561 -6 135.721 -0 100.790 2 157.227 13 4 0 3 0 -2 -2 -2 -0 -3 1 -4 1 -4 2 -7 -1 - 5 1 -7 -2 -2 1 3 2 5 0 9 -1 14 -2 22 2 23 -1 26 2 15 -5 8 -3 4 3 - 4 - 4 -15 1 -21 8 -26 16 496.543 180.149 -2 -61 -18D.AMBROSE, J . H. ELLENDER, C. H. S . SPRAKE, R. TOWNSEND 37 RESULTS Temperatures throughout are expressed as International Practical Kelvin Temp- eratures T6 s , which are treated as interchangeable with thermodynamic temperatures T.The experimental values at pressures below 205 kPa are listed in table 1, those at higher pressures in table 2, and the coefficients of the four equations fitted for each substance, two (I), (11) eqn (l), and two (111), (IV) eqn (2), in table 3. The critical temperatures and pressures have already been reported. T/K p/kPa 104Aloglo(plPa) lY2,3,5-tetrafluorobenzene ebulliometric measurements 385.724 228.28 2 390.810 260.59 1 396.260 299.04 1 402.166 345.46 1 408.935 405.26 1 415.599 471.52 0 1 , 2,4,5- tetra fluoro benzene ebulliometric measurements 392.840 234.88 0 395.913 254.29 0 402.207 297.91 0 408.641 348.26 0 414.978 404.00 0 421.514 468.06 -1 430.210 564.38 -8 437.130 651.79 - 10 dynamic measurements 406.79 333.39 2 413.51 390.65 1 424.26 497.64 2 433.19 602.23 1 447.16 799.04 5 455.93 944.97 5 TIK p/kPa 104Alog~~(p/Pa) 1,2,4,5-tetrafluorobenzene (cont’d) dynamic measurements 464.92 473.82 483.28 492.89 501.94 510.92 520.55 530.70 535.83 538.51 11 14.3 1304.6 1530.3 1792.2 2067.8 2372.1 2736.6 3168.8 3415.5 3544.0 5 6 2 4 3 0 -5 -9 -2 - 6 static measurements 492.10 1770.1 5 496.65 1903.8 4 504.61 2160.0 13 510.81 2369.6 2 516.08 2560.9 -5 526.75 2994.1 -8 53 1.32 3204.1 0 53 1.70 3212.4 - 12 535.07 3374.4 -7 535.22 3385.8 -2 536.29 343 1.7 - 10 539.11 3569.8 - 12 543.35 a 3800.6 a 1 a critical temperature and pressure The values in table 1 were fitted by Antoine equations, both over the full range (11) and also, more exactly, over a restricted range close to the normal boiling point (I).They were also fitted by Chebyshev equations (111),12 (2) (T/K) log,o(P/kPa) = 4 2 + k a,E,(x), s= 1 where Es(x) is the Chebyshev polynomial in x of degree s, and x is defined as [ZT- (T,,, + Tmin)]/(Tmax - Tmin). The values in table 1 and table 2 and the critical temper- atures and critical pressures were also fitted by eqn (2), the values in table 1 being given38 THERMODYNAMIC PROPERTIES OF FLUORINE COMPOUNDS tenfold the weight of those in table 2 (IV). Residuals from eqn (I), (11) and (111) are given in table 1 as Ap = Pobs-pcalc, and from (IV) in table 2 as A log,, p = log,, Pobs - log1, Pcalc, the values of pcalc having been obtained from the appropriate equa- tions.The residuals from (IV) of the values in table l are only marginally larger than those from (111). TABLE 3.-cOEFFICIENTS OF EQUATIONS. (I) SHORT-RANGE ANTOINE EQUATION (1) ; (11) FULL-RANGE ANTOINE EQUATION (l), AND (111) CHEBYSHEV EQUATION (2) FITTED TO ALL VALUES IN TABLE 1 ; (Iv) CHEBYSHEV EQUATION (2) APPLICABLE TO THE CRITICAL TEMPERATURE (1) (11) A - B - C A - B - C 1,2,3,4-tetrafluorobenzene (A) 6.158 54 1291.080 56.617 6.161 07 1292.550 56.453 1,2,3,5-tetrafluorobenzene (B) 6.154 14 1255.781 54.898 6.155 07 1255.981 54.919 1,2,4,5-tetrafluorobenzene (C) 6.173 40 1277.452 56.899 6.177 87 1279.904 56.642 trichlorotrifluorobenzene (D) 6.278 66 1721.246 68.694 6.280 75 1721.899 68.739 - - - - - hexafluoro benzene (El - fluorobenzene (F) - - - - - - A 3 300 392 B 4 287 382 C 3 293 388 D 4 364 497 A 4 300 551 B 5 287 536 C 5 293 544 D 5 364 685 E 5 278 517 F 5 312 561 a0 1167.856 1105.072 1 129.229 1298.238 2246.392 2149.572 2191.684 2599.105 2002.068 2467.161 a1 (111) 324.210 335.195 33 7.09 1 479.339 (IV) 854.391 848.157 858.521 1117.004 823.237 822.894 a2 - 3.256 - 3.662 - 3.676 - 5.71 1 - 8.634 - 8.976 - 9.400 - 13.415 - 10.618 - 5.186 4 0.242 0.283 0.282 0.439 3.721 4.082 4.332 5.236 4.408 3.220 a4 a5 - - 0.238 -0.159 0.025 - 0.341 -0.075 0.075 0.128 - 0.065 0.158 0.071 0.123 Measurements over the whole range up to the critical temperature were made only for 1,2,4,5-tetrafluorobenzene, and where observed values were lacking for the other compounds, estimated values calculated according to the following equation were included (with low weighting) in the sets to which the equations (IV) were fitted, (3) In eqn (3), lOglo(p/kPa)A,t is the value obtained from the full-range Antoine equation (11) for a given value of the reduced temperature T, = T/T, > 0.7 and D is obtained by insertion in eqn (3) of the critical pressure at T' = 1.It has been shown that for non-associated compounds, and in particular for halogenated aromatic hydrocar- b o n ~ , ~ eqn (3) reproduces observed values of vapour pressure in the range 0.7 -= T' < 1.0 within 0.5 %, and this was confirmed in this investigation in respect of 1,2,4,5-tetrafluorobenzene and also, from published 3-1 in respect of hexa- fluorobenzene and fluorobenzene. The equations (IV) detailed in table 3 for the other three compounds included in this study reproduce almost exactly the values given by the corresponding eqn (3).The values of I03D found are: 1,2,3,4- tetrafluorobenzene, 5.65 ; 1,2,3,5-tetrafluorobenzene, 5.87 ; 1,2,4,5-tetrafluoro- benzene, 5.57 ; trichlorotrifluorobenzene, 5.01 ; and for hexafluorobenzene, 5.86 ; log,,(p/kPa) = lOglo(p/kPa)A,t+ D(Tr-0.7) +200D(Tr -0.7)3.D . AMBROSE, J . H . ELLENDER, C. H . S . SPRAKE, R . TOWNSEND 39 and fluorobenzene, 6.09 : they correspond for all the compounds to the critical pres- sure being 7 to 8.5 % above the Antoine value, a usual amount. Properties calculated from the fitted equations are reported in tables 4 and 5. TABLE 4.-vAPOUR PRESSURES AND VALUES OF dp/d T CALCULATED FROM EQUATIONS DETAILED IN TABLE 3 276.91 298.15 367.510&0.001 385.58 429.69 464.75 506.17 533.73 550.83 a 2 6.509 101.325 171.33 500 1000 2000 3000 3791 0.121 0.331 3.116 4.707 10.75 18.21 30.86 42.14 50.55 (111) 274.33 2 (111) 298.15 7.556 (111) 363.413 kO.002 101.325 (111) 380.34 167.43 (IV) 424.50 500 (IV) 459.04 1000 (IV) 499.84 2000 (IV) 526.76 3000 (IV) 543.35a 3800 0.123 0.381 3.172 4.708 10.94 18.47 31.41 43.52 53.74 1,2,3,5-tetrafluorobenzene trichlorotrifluorobenzene 269.39 298.15 357.610+0.002 374.68 418.24 452.45 492.83 519.58 535.25 a 2 9.80 1 101.325 168.69 500 1000 2000 3000 3747 0.125 0.479 3.197 4.771 11.02 18.66 31.71 43.54 52.02 (111) 298.15 (111) 356.63 (111) 471.519-0.004 (111) 479.40 (IV) 549.37 (IV) 592.81 (IV) 643.65 (IV) 677.30 (IV) 684.85 a 0.0651 2 101.325 122.36 500 1000 2000 3000 3270 0.0047 (111) 0.095 (111) 2.474 (111) 2.875 (111) 8.642 (IV) 14.76 (IV) 25.24 (IV) 34.55 (Iv) 36.92 (IV) a Critical temperature ; b Tr = 0.7 ; C normal boiling point with maximum difference that may arise from use of eqn (I), (11) or (IV).TABLE 5.-ACENTRIC FACTOR cr) AND PROPERTIES AT THE NORMAL BOILING POINT: SECOND VIRIAL COEFFICIENT, MOLAR VOLUME OF LIQUID AND ENTHALPY OF EVAPORATION - B/dm3 mol- AH/kJ mol-I VLI 0 a b dm3mol-' a b 1,2,3,4-te trafluorobenzene 1,2,3,5-tetrafluorobenzene 1,2,4,5 - t et rafluoro benzene trichlorotrifluorobenzene hexafluorobenzene fluorobenzene pentafluorotoluene pentafluorophenol 0.345 0.347 0.356 0.427 0.396 0.243 0.416 0.50 1.21 1.19 1.20 1.72 1.29 1.50 1.04 1.12 1.44 1.89 1.32 0.117 33.0 0.117c 32.1 0.117 32.9 0.166 42.9 0.126 31.9 31.68 0.100 31.3 31.20 l3 0.143 35.3 34.74 l8 0.128 40.8 w = loglogc-loglop-l at 7'' = 0.7.16 -B: aestimated by use of w ; bcalculated from ob- served value of AHand eqn (4).A H : a calculated from estimated value of B and eqn (4) ; b observed value. VL : c assumed to be identical with that of 1,2,3,4-tetrafluorobenzene. The enthalpy of evaporation AH was obtained from the equation for which the second virial coefficient B was estimated by the method proposed by Pitzer and Cur1,l6 and the molar volume of the liquid was obtained from measured AH = T[RT/I> + B- VJ dI>/dT, (4)40 THERMODYNAMIC PROPERTIES OF FLUORINE COMPOUNDS densities.l4* 15* l7 Included in table 5 are entries for hexafluorobenzene, fluoro- benzene [for both of which equations (IV) are detailed in table 31, and for pentaflouro- toluene,s together with observed values 2* 3* of AH and values of B calculated from them to indicate the accuracy for this class of compound that may be attributed to the method of estimating these properties.Included also is an entry for pentafluorophenol which supersedes that given for this compound previously. DISCUSSION Equations (1)-(111) are offered as the most convenient (11) or the most accurate (I), (111) expressions for representation of the measured values, and (111) is recommended as the most reliable for extrapolation to lower temperatures. Equations (IV), however, while being convenient and accurate representations of the values, have been chosen so that in addition they conform in their behaviour to a known characteristic of the vapour-pressure line over a long range, as will now be discussed.0.4 0.5 0.6 0.7 0.8 0.9 1.0 TI. FIG. 1.-Plots of AH/AZ; for clarity some of the lines are displaced vertically from their true posi- tions by the amounts stated in parentheses ; A, 1,2,3,4-tetrafluorobenzene (- 5 kJ) ; B, 1,2,3,5- tetrafluorobenzene (- 5 kJ) ; C, lY2,4,5-tetrafluorobenzene ; D, trichlorotrifluorobenzene ; E, hexafluorobenzene (5 kJ) ; F, fluorobenzene ; G, water (12.5 kJ). Waring l9 drew attention to the fact that for water if AH/AZ (A2 = Zv-ZL, the difference in the compression factors of the co-existing vapour and liquid phases) is plotted against T,, a curve is obtained of distinctive shape with a minimum at Trw0.85, and similar curves have been shown for other compounds.20 These curves were plotted from thermal measurements, but the quantity AH/AZ may also be obtained from vapour-pressure measurements by means of the Clapeyron equation written as (5) The curve for AH/AZ may therefore be obtained by differentiation of a vapour- pressure equation, and any such equation that does not give a result qualitatively similar to the usual curve should be suspect.Fig. 1 shows curves for AH/AZ ob- tained from the equations (IV) in table 3 and from an eleventh order Chebyshev equation for water ; 22 they are all of satisfactory shape according to this criterion although the flatness near T, = 1 of curves A, B and D for 1,2,3,4tetrafluorobenzene, 1,2,3,5-tetrafluorobenzene, and trichlorotrifluorobenzene suggests that the estimated AH/AZ = RT2 d lnp/dT.D.AMBROSE, J . H . ELLENDER, c . H . s. SPRAKE, R . TOWNSEND 41 vapour pressures of these three substances may be slightly in error. Curves obtained in the same way from the equations already published for other halogenated aromatic compounds are of a shape similar to those in fig. 1. When the quantity A = Tlog@/atm)/(T-T,,), where Tb is the normal boiling point, is plotted against T, a curve of more pronounced parabolic shape than those in fig. 1 is obtained, again with a minimum at Trz0.85. This A is a variable in the Cox vapour-pressure equation, and Thomson called the characteristic shape of its curve the " Cox criterion " that must be satisfied by reliable data or a valid equation 21 ; the " Waring criterion '' used here seems to be preferable since it is related to the defined thermodynamic quantities AH and AZ. We acknowledge the assistance in the experimental work of Miss R.F. Anthony and Mr. S. W. David, and computational help given by Mr. E. B. Lees. Part 14, R. J. L. Andon and J. F. 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