362
P. HESTERMAXS A X D DAVID JVHITE
T'ol. 65
THE VAPOR PRESSURE, HEAT OF VAPORIZATIOiC' AND HEAT CAPACITY OF METHANE FROM THE BOILISG POINT TO THE CRITICL4L TEMPERATURE BY P. HESTERMMANS AXD DAVIDWHITE Cryogenic Laboratory, Department of Chemistry, The Ohio State University, Columbus 10, Ohio Received iVooemhei 11, 1.960
The vapor pressures, heats of vaporization and heat capacities of methane from the boiling point to the critical temperature have been measured. The vapor pressure data have been represented in the form log P,t, = 3.984667 - 444.6667/ T - 6 ( T ) ,where 6 ( T ) is tabulated at equal intervals of temperature. The normal boiling point of methane is 111.42'K. Critical constants have been calculated from the vapor pressure data. It is shown that the measured heats of vaporization are in, good agreement with those calculated from the above vapor pressure equation and the known liquid and gaseous densities. The heat capacity data, when combined with the measured heats of vaporization, yield entropies for the gas along the saturation curve in excellent agreement with those from statistical calculat,ions.
Introduction The entropy of liquid methane, from the boiling point to the critical temperature, has been determined by Wiebe and Brevoortl from heat capacity measurements along the saturation curve. From these results, the entropies of gaseous methane along the saturation curve were calculated using the vapor pressures and saturated vapor and liquid densities of Keyes, Taylor and Smith.2 If these aseous entropies are compared with those calcuated from spectroscopic data2 (corrected for nonideality3 and pressure) it is found that the agreement is generally poor. The entropies calculated from the calorimetric and vapor pressure data are consistently larger than those calculated from the spectroscopic data. The deviations are approximately 0.1 e.u. a t the boiling point and increase to approximately 1.0 e,u. a t 180°K. This discrepancy cannot be ascribed to any known anomalous behavior of either the saturated liquid or vapor. The heat capacity of the saturated liquid between the boiling point and critical temperature appears normal. There is no evidence of association, or any similar phenomena, occurring in the vapor phase in this temperature range. The reason for the discrepancy probably lies in the uncertainty of the derived heats of vaporization from vapor pressure data. Some considerable improvement in the agreement between calorimetric and spectroscopic entropies can be obtained, if the more recent vapor pressure and saturated liquid and vapor density data of Bloomer and Parent4 are used. The improvement is pronounced from the boiling point to approximately 150°K. Above this temperature, however, the calorimetric values are now lower than the spectroscopic ones. In order to unambiguously resolve this discrepancy, the heat capacity of the saturated liquid from the boiling point to the critical temperature have been redetermined and the heat of vaporization, in this same temperature range, has been measured calorimetrically. In addition the vapor pressures, of the same sample used in the above experiments, were measured in order that a comparison between
f
(1) R. D iebe and .\I J.. Brevoort, J . rim. Chem. Soc., 62, 623 (1930). (2) F. G. Keyea, R. 9 . Ta5lor and L. 13. Smith, J . M a t h . f ' h ? / s , 1, 211 (1922). ( 3 ) F. D Rossmi, Am. Pet. Inst., R.P. 44 April 30 (1957). (4) 0. T Bl(iorn~rand J D. Parent, RP* Bull I n s f . Gas T e c h n , No. 17 (1952)
calorimetric heats of vaporizat,ion and t,hose derived from vapor pressures could he made. The results are reported beIow. Apparatus The calorimeter used in all of the experiments was a modified version of that described by Rifkin, Kerr and Johnston? The thermodynamic temperature scale, upon which the results are based, is that of Rubin, Johnston and Altman .& A standard copper-constantan thermocouple, which had been calibrated by means of a helium thermometer: was used for the temperature measurement. In the vapor pressure determinations, pressures from 1.O to 2.5 atmospheres were measured with an open-end mercury manomet,er. The manometer was read with a cathatometer which was calibrated to 0.02 mm. For pressures greater than 2.5 atmospheres, a calibrated modified M .I.T. type dead weight gauge was used? At the lowest pressures the dead weight gauge has a precision of one part in ten thousand, whereas at higher pressures it is precise to one part in thirty thousand. The experimental procedures for the heat capacity and heat of vaporizations measurements in this research were identical to those already reported in the hydrogen investigations.j,* The vapor pressure measurements were made in a manner previously described by White, Friedman and Johnston.Q Purity of Methane.-The methane used in this research was part of a sample prepared by the late Dr. Eisman of the National Bureau of Standards. The source, purification procedure and method of analysis is given by Eisman and Potter.10 The purit,y of the original sample obtained from NBS was 99.93 mole % the major impurity being nitrogen. Additional purification by distillation brought the sample purity t o 99.96 mole %.
Results and Discussion (a) Vapor Pressure.-The vapor pressure data are given in the first three columns of,',Table I. T and P are the temperatures and pressures, respectively. An attempt was made to represent the data by means of some of t8hecommon three term polynomial equation^.^,^ r It was found that such equations, akhough adequat'ely reproducing the observed pressures, do not yield unique values of the first derivatives, (dP/dT). These a,re import,ant in caIculat.ions of the heats of vaporization. This difficulty can be avoided by the use of higher order ( 5 ) E. B. Rifkin, E. C . Kerr and H. L. Johnston, J . Am. C h e m . Soe., 7 5 , 785 (1963). (6) T. Rubin, €I. 1,. Johnston and H. riltman, ibid., 73,3401 (1951). (7) F. G. Keyes. Ind. Eng. Chem., 23, 1375 (1931). (8) D. JTIiitr, J . H. Hu and H. L. .Johnston, .I. P h y s . C'hem., 63, 1181 (1959). (9) D. White. A . 9 . Friedman and H. L. Johnston, .I.Am. Chem. SO?.. 72, 3927 (1950).
(10) J. H. Eisman and E. A . Potter, J . Research Sntl. Bur. Stnnda i d s , 68, 253 (1957).
T'APOR PRESSURE aF METHANE
Feh., 1961
polynomial equations or, as was done in this case, the generation of a smooth diagonal difference table a t equal temperature intervals and calculation of the derivatives by numerical methods. To simplify the smoothing of the data the following equation was used to represent the data.
363
I
I
TABLE I VAPORPRESSURE OF METHANE T, OK.
P , atm., obsd.
P , atm., oalcd.
109.38 114.34 117.26 119.98 126.50 135.57 141.93 146.54 151.61 155.12 161.05 167.51 172.39 176.44 180.02 183.76 187.24 189.52
0.8470 1.2574 1.5596 1.8941 2.9217 4.9851 6.9641 8.7147 11.006 12.823 16.369 20.995 25.043 28.801 32.461 36.642 40.922 43.953
0.8469 1.2572 1,5630 1 ,8970 2.9208 4.9779 6.9575 8.7156 11.003 12.826 16.373 20,991 25.044 28.805 32.464 36.642 40.915 43.955
log P a t m = 3.984667
Pabad.
-
Penlod.
+o. 0001
+
,0002 - .0034 - .0029 .ooo9 ,0072 ,0066 - ,0009 ,003 - ,003 - ,004 ,004 - ,001 - ,004 - ,003 ,000 ,007 - ,002
+ + + + + +
- 444.6667 ____ - 8 ( T ) T
(1)
l
-4.0
I -
I
L!
-5.0
11-L
I
1
:,
1
-I
1
120
140 160 180 200 Temp. (OK.). Fig. 1.-Comparison of 6(T)'s calculated from observed (present and recent) vapor pressures and eq. 1 with the smoothed values (Table 11).
shown in Fig. 1. In this figure 6(T)'s calculated from equahion 1 are plotted as a function of temperature. It can readily be seen from this plot that the precision of the present results are considerably greater than that of Bloomer and Parent.4 Excepting in the vicinity of the critical temperature (above 170°K.), the magnitude of the vapor pressure a t a given temperature in both investigations, are in good agreement. The normal boiling point and critical constants for methane calculated from the vapor pressure data are shown in Table I11 and compared with those previously reported. In this comparison the results of Armstrong, Brickwedde and Scott,'l obtained from a critical review of t,he literature, are included.
where 6(T) is in essence a deviation function. The constants of equation 1 were arbitrarily chosen so as to minimize the magnitude of 6(T). The function 6(T) was then tabulated at equal intervals of temperature and the fourth difference smoot,hed. TABLE I11 A comparison of the pressure calculated from eq. 1 NORMAL BOILIIUG POINT AND CRITICALCONSTANTS OF and the smoothed 6( T ) table, with the experimental METHANE values, is shown in the last two columns of Table I. ArmThe smoothed vapor pressure data and the derivaThis Keyes,z Bloomer,8 strong,ll research et al. et al. et al. tives (dP/dT) as a funct,ion of temperature are Normal boiling point, given in Table 11. TABLE I1 VAPORPRESSURES OF METHANE. SMOOTHED DATA T. OK.
P , atm.
110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190
0.8914 1,3220 1.9001 2.6551 3.6187 4,8237 6.3043 8.0958 IO. 234 12.757 15.700 19.100 22.995 27.427 32.442 38.116 44.626
log p
-0.04992
+ +
,12124 .27887 ,42408 .55855 ,68338 ,79964 .90826 1 ,01006 1.10575 1.19590 1.28103 1.36164 1.43819 1.51111 1.58111 1 ,64959
dP/dT, 6 ( T ) X 10-2 atm. deg.-l
-0.784 .324 .034 .325 ,560 .746
-
+ +
-
-
.884 ,974 1.016 1.010 0.960 .869 .734 ,552 .319
.005 .527
0.07328 .09994 .I323 .1709 ,2158 .2674 ,3260 .3918 ,4648 ,5456 .6332 .7281 ,8314 ,9432 1.0651 1.2098 1 .4034
A comparison of the vapor pressures of this research with those most recently published* i s
O K . 111.42 111.51 111.71 ... Critical pressure (atm.) 45.41" 46.0 45.47 45.6 Critical temp., OK. (190.55) 191.O 190.55 190.6 a This value was computed using the critical temperature of Bloomer, et aZ.4
(b) Heat Capacities and Heats of Vaporization.The heat capacities of the saturated liquid C,1 are shown in Table I V below. They were calculated from the data using the thermodynamic relation Car =
Q nAT ~
+
(Np~HY)B -VN,'AH,' - N,'AHv' (T')&" AT
(2)
where Q is the energy input to the calorimeter for a temperature rise AT, n the total number of moles in the calorimeter, Ng, the mole fraction of gas in the calorimeter and AHv, the molar heat of vaporization. The superscripts i, f , refer to the initial and final temperature of the run. In the seoond term on the right-hand side of equation 2 with the subscript av., the substituted quantities are those at the average temperature of the run. The heats (11) G. T.Armstrong, F. G. Brickwedde and R. B. Scott, {bid., 14, 39 (1955).
364
P. HESTICRMANS A Y D DAVID WHITE
Iro1. GEi
mined heats of vaporization (Table V) with those calculated from vapor pressure data, the data of Table V were numerically smoothed and interpolated to the same temperature as those of Table 11. These results together with a comparison of heats of vaporization calculated from vapor pressure data are shown in Table VI. I n the last column the V , - VI, the difference in the gaseous and liquid molar volumes, used in the calculation of the data from Table I1 are shown. These are the smoothed ~ a l u e spreviously ~ * ~ ~ referred to.
50 h I
2!40
8
" I
bb
-
-% 30 2
v
..
TABLE V HEATOF VAPORIZATION OF METHANE
O" 20 10
i---100
I
1
A -
120
Fig. 2.-Heat
140 160 180 200 Temp. (OK.). crtpacity of liquid methane along the saturation curve.
of vaporizations used in the calculation were obtained from the measurements given in Table V. The liquid arid gaseous densities necessary to calculate the mole fraction of gas in the calorimeter were obtained by smoothing the data of Bloomer and Parent4 and Matthews and Hurd.12 The smoothing was done with the aid of the rectilinear diameter relation. A comparison of the liquid heat capacities reported here with those of previous investigations is shown in Fig. 2. The results of Wiebe and Brevoortl are somewhat lower than those of the present research, however, both sets of data tie in well with the liquid hea,t capacities a t lower temperatures of Frank and Clusius. l 3 TABLE IV HEAT CAPACITY O F LIQUIDMETHANE R u n no.
Temp., OK.
1
114.50
2 3 4 5 6 7 8 9
125.49 134.92 145.12 155.02 164.97 174.99 182.57 187.48
Csl, cal. deg.-l mole-'
13.11 13.83 14.50 15.05 15.93 17.49 20.17 26.00 49.46
The heats of vaporization of methane, AH,, from the boiling point to the critical temperature were calculated from the data in the same way as previously report>edfor hydrogen.8 These results are shown in Table V. Since the calculated heats of vaporization depend on a prior knowledge of liquid and gaseous densities, specifically the ratio dl/dl - d,), (where d1 and d, are the liquid and gaseous densities, respectively, the values of this ratio used in the c a l ~ u l a t i o n ~are - ' ~included in the table. I n order to compare the calorimetrically deter(12) C . 8. Matthews and C . 0. Hurd, Trans.Am. Insl. Chem. Engrs., 4a,55 (1946). (13) A. Frank and K.Clusios, 2. physik. Cham., B3,41 (1929); B86, 291 (1937); B42, 395 (1949).
di
OK.
T.
Moles collected
d
111.88 111.85 119.96 129.99 140.07 150.00 160.05 170.00 180.15 184.iI
0.1594 .1595 ,1810 ,1474 .I411 ,1662 .1740 .1945 .2354 .2208
1.005 1.005 1.008 1.015 1.028 1.048 1.OS1 1.143 1.282 1.442
3
Total moles vaporized
AHv, cal./ mole
1951 1946 1891 1796 1690 1582 1421 1243 962 i59
0.1601 ,1602 1824 ,1496 ,1450 ,1742 ,1881 ,2209 , 2991 3181
TABLE VI HEATSOF \rAPORIZATION T. OK.
O F hfETIIANE' ARv. cal. mole-' Interpolated ' from Calcd. Wiebe and 1.g - VI Table V Table I1 Brevoort' cc. mole-'
100 2030 105 1997 110 1963 115 1927 120 1888 125 1846 130 ls00 135 1751 140 1698 145 1640 150 1577 155 1507 160 1431 165 1343 170 1242 175 1123 180 961 185 743 190 171 a AH, a t 99.54"IC. of mole-'.
..
..
2048 2015 1983 1950 1917 1883 1847 1808 1767 1721 1670 1612 1546 1470 1385 12i6 1141 939
....
....
1974 622.7 1928 430.5 1883 305.3 221.7 1840 1793 164.4 1740 124.1 1690 95.21 1631 73.92 1572 57.90 1503 45.76 1425 36.20 1332 28.55 1227 22.36 1107 17.20 947 12.72 743 8.54 187 .. 1.80 Frank and C ~ U S ~ U 2036 S . ~3t~2 cal.
It is obvious from the data in Table VI that there is very good agreement between the calorimetrically det,ermined heats of vaporization and those derived from the vapor pressure data of this research. The values of Wiebe and Brevoort4 obtained from the data of Keyes, et a1.,2 are substantially larger than those of this research practically over the entire temperature range from the boiling point to the critical temperature. (c) Entropy of Saturated Liquid and Vapor Methane from 100-190°K. Comparison with Statistical Entropy.-The entropy of the saturated liquid, SI,was calculated fromlthe value of the
KOTES
Feb., 1961
entropy at 100°K. given by Frank and C l ~ s i u s ’ ~ and the data in Table IV from the relation rn
Si = Si(100”K.)
+ J$ dT
(3)
100
The entropy of the saturated vapor S, was calculated from the saturated liquid and the heat of vaporization data obtained both calorimetrically and from vapor pressure data (Table VI).
s, = 81 + AH, -gi-
(4)
The results are summarized in Table VII. Two values for S, are given. The super script “c” refers to the entropy calculated from equation 4 using the calorimetric heats of vaporization (Table VI, column 2). The super script “vp” refers to the entropy calculated from heats of vaporization derived from the vapor pressure data (Table VI column 3 ) . In order t,o check the self-consistancy and accuracy of the various experiments, the entropy of methane in the ideal gas state So has been calculated and compared with those obtained from statistical calculations. The ideal gas entropy has been calculated from the expression
so = sg + R In p - (8, - Si) (5) The term R In p was computed from the data in Table I1 and the last term, the difference between
real and ideal gas entropy, from A. P. I. tables.3 The results are shown in columns 6 and 7 of Table VII. So(cal.) and So(v. p.) mere calculated from Sgcand Spv.p.,respectively. In the last column of Table VI1 the statistical entropy of methane is given. It can he seen that these entropies are in excellent agreement with those calculated from the
365 TABLE VI1
T. OK.
100 105 110 111.42 115 120 125 130 135 140 145 150 155 160 163 170 175 180 185 190
Si,
e.u. 17.43“ 18.07 18.68 18.79 19.27 19.85 20.42 20.97 21 51 22.04 22.56 23.08 23.59 24.11 24.62 25.16 25.71 26.32 27.07 28.42
S,,. e.u. 37.73 37.09 36.53 36.35 36.03 35.58 35.19 34.82 34 48 34.17 33.87 33.59 33.31 33.05 32.76 32.46 32.13 31.6G 31.09 29.32
-(SFSi),
SBv,~.,
e.u.
.. . ...
36.62 36.39 36.04 35.54 35.14 34.76 34.40 34.11 33.81 33.56 33.29 33.02 32.69 32.38 32.04 31.58 31.08 29.40
e.u. 0.09 .12 .17 .19 .22 .28 .34 .40 .49 .59 .68 .78 .93 1.08 1.24 1.42 1.68 1.89 2.30 2.92
so
(cal.), e.u. 35.71 36.07 36.48 36.54 36.80 37.14 37.47 37.77 38.10 38.42 38.71 38.99 39.30 39.60 39.86 40.11 40.39 40.46 40.63 39.79
so
SQ
(v.P.), (Stat), e.u. e.u. 35.72 . 36.10 ... 36.48 36.57 36.59 36.58 36 8 3 36.81 3 7 . 1 0 37.17 37 I49 37.42 37.80 37.71 38.02 38.10 38.39 38.36 38.67 38.68 38.94 38.96 39.28 39.20 39.46 39.57 39.79 39.71 4 0 . 0 3 39.95 40.30 40.18 40.38 40.40 40.62 40.62 40.83 39.87
. .
a Entropy of liquid methane at 100°K. = 17.43 cal. deg.-l mole-1 from Frank and C ~ U S ~ U S . ~ ~
experimental data except for the last point (190’ IC.). This is probably due to the large uncertainty in the extrapolation of the heat of vaporization from 185°K. to the critical temperature. Acknowledgement.-One of the authors (P.H.) is indebted to the “Institut pour L’Encouragement de la Researche Scientifique dans 1’Industrie et 1’Agriculture’’ for a grant which permitted his visit to the Cryogenic Laboratory, to the du Pont Chemical Co. which in part supported the research and to Dr. L. Deffet, Director of the “Institut Belge des Hautes Pressions” for the arrangements which made the visit possible. We would also like to thank Dr. P. K. Walsh and Ah-. A. Brooke for their help and advice during the experimental investigations.
NOTES IONIC STRENGTH EFFECT IN THE
more reasonably consider for the several a-chlorotoluenes differences in the localization of charge in the (somewhat different) transition states,’ with REhCTIOhT resultant differenccs in the degree of solvation. BY RICHARD FUCHS AND ALEXNISBET Another viewpoint would consider differences in Department of Chemistry, The University of Texas, Austin 12, Texas the degree of thiosulfate-carbon bond formation in the transition states for the various a-chloroReceaued July I, I960 toluenes, with concomitant variations in the Changes in solvent composition and dielectric amount of deformation of the thiosulfate solvation constant (D)affect unequally the rates of reaction required to attain these configurations. of a-chloro-p-nitro-, a-p-dichloro-, a-chloro- and a- shell It is usually stated2 that ion-neutral molecule chloro-p-isopropy1tr)luene with sodium thiosulfate, reactions proceed relatively rapidly in solvents of The relative rates (or Hammett p constant) are in low This is not confirmed by dielectric most solvent mixtures a logarithmic function of work with theconstant. a-chlorotoluene-thiosulfate system 1,’D.I The solvent must not, therefore, be acting in 40% ~ a t e r - 6 0 7 organic ~ solvent mixtures,‘ solely by affecting the activity coeffcient of the at- and is definitely contradicted by work involving tacking species, thiosulfate ion, for this would lead mixtures of varying composito uniform rate changes for all the a-chloro- tbutyrolactcne-water i~n.~ toluenes as the solvent was varied. One might
THIOSULFATE-~-CHLOROTOLUENES
(1) R. Fuchs and A. Nisbct, J . Am. Chem. SOC.,81, 2371 (1959).
(2) K. J. Laidler and H. Eyring, A n n . N . Y. Acnd. Sci.. 39, 303 (1940); subsequent citations are numerous.
