32 1
GAS IMPERFECTIOS. I1
(10) MELLON: illelhods of Quantitative Chemical A n a l y s i s , p. 413. The hlncrnillnn Company, S e w York (1937). (11) MICHAELSON A N D LIEBHAFSKY: Gen. Elec. Rev. 39, 445 (1936). (12) SMITH: Pharm. J . 126, 1011 (1930). AND MELLON: J. Optical SOC.Am. 27, 414 (1937). (13) SWANK (14) \'ax DER BURG:Chem. Weekblsd 36, 101 (1939). (15) VAXURK:Pharm. Weekblsd 66, 1246 (1928). (16) \'as URK: Phsrm. Weckblad 66, 157 (1929).
GhS IJIPERFEXTIOS.
11
IES FOK SOME UXATL-RATED.%LIPHATIC HYDRODERIVED FRON THE EQCATIOXS O F ST.iTE
'I"EIlJlODTS.IMlC y U . i
ChHHONS
EDWIS E. ROPER' Depwlment of Chemistry, Haroard University, Cambridge, Massachusetts Ileceiced FebruaTp 21, 1940
In two previous papcw, data and derived equations ha\.e been presented for the gas imperfection terms (16) and for the vapor pressures (IO) of ethene, propene, propndiene, 2-niethylpropene, 1-butene, trans-2-butene, and cis-2-butene. The data wcrc obtained in each case utilizing the identical samples of hydrocarbons and the same platinum resistance thermonieter. The simriltnneous cmploymeiit of both sets of these data for the calculntion of thrrmodyiianiic properties of thc saturated region may be ospccted to yield qLiite self-cotisistent results. Thrrc arr ccrtniii thcviiodynamic quantities derivable only from the IIIOI'LL c x w t cvlri:ition of statc which become of import:incc \vhcn the entiqiics and heat c:tpnciticx which have lieeri obtained by csperimerital mrthods arc to be rompxred with those calculated with thc aid of statist i c d qriantuni mechanics and spectroscopic data. These quantities are tlic difl'crcncr i n thv heat capacities of the gas a t constant pressure and coiistnnt volume, the difference iii thv heat capacities between a given 1)rcxsrirc and zwo prcswrr, and the coniw&xi of the eiitropy of an actual y:is :it n givcii state to thc. ideal statc. In cases nhere calorinictric deterinitiations of the Iient of vnporizatioii :iw riot availabl(~,the gas imperre may l x rom1iiiic:d to calculate. the fc7ctioii niid the vapor p ~ ~ s s i i equations g:is iinpcrfcctioii mrrcctioii to this hc:it at tho normal boiling point. The i,cwlts of t h k rcscnrch I i a i ~a l r c ~ d yIxmi utilized in specific cases (3, 0, 12. 15) to obtain .suc~li quaiititics. 1
Present :dtlress: Stniioliiid Oil and g:is Cuiiipnn)-, 'I'ulsn, Oklahomn.
322
EDWIN E. ROPER
The low-pressure equation of state employed in the gas imperfection work (16) is of the Onnes type
~ v = R T + ~ V where p is expressed in millimeters of mercury, V in cubic decimeters, and T in degrees Kelvin absolute (To = 273.16'K.). The resulting units of the second virial e are dm.6 X mm. Hg per mole? and R = 62.362 dm.a X mm. Hg per mole per degree on this basis. For obtaining the heat capacity difference terms, the following equations were utilized:
SC',j = [Ck,
- C i ] = SC:'
+Q -R
(4)
where the C's are the heat capacities of the gas with the subscripts indicating the condition of restraint and the superscripts the thermodynamic state, the remaining nomenclature being standard. For the calculation of the true (in contradistinction to thc perfect) heat of vaporization, the Clausius-Clapeyron equation is used :
where the superscript a indicates that the state is the actual one and not the perfect (superscript p), ( A V ) a is the volume change upon vaporization equal to V a - u, where Va and u are the actual molal volumes of the gas phase (saturated vapor) and of the liquid phase, respectively, a t 2'. When T i s taken equal to Tb, the normal boiling point, then p becomes 760 mm., dp/dT the slope a t the normal boiling point, and the resulting heat is for vaporization a t Tb under normal atmospheric pressure. The correction for gas imperfection in the absolute entropy of the saturated vapor a t 1 atmosphere and a t Tb was made following the method of Giauque and Wiebe (6). The fundamental equation employed is
323
GAS IMPERFECTION. I1
The total entropy change for proceeding isothermally from the actual gas state a to the perfect state p is given by the expression*
The fugacity, f, as a measure of the escaping tendency, is defined (11) by
or dlnf=
-1 l k RT
Vdp= -K1 T[4E+g]dV
(8)
I
Integrating the last part of equation 8, there is obtained finally
It should be noticed that in all the above equations, having been given the form of the equation of state employed, n o assumptions of any kind have been introduced, so that each relationship is thermodynamically exact. Disregarding experimental errors, the only assumption made which has an effect upon the quantities that may be calculated by means of equations 2 to 9 is that the actual gas may be represented within some restricted range by the Onnes type equation of state as given by equation 1. The good correspondence of the calculated with the experimentally observed molal volumes (16), h0.06 per cent, indicates that this assumption concerning the form of the equation of state is essentially correct. I n equations 2 and 3 the unusual form is adopted, owing to the peculiarities of the specific form of the equation of state utilized, wherefrom certain differentials in V with respect to T and to p ape rather complex. Owing to this fact, it was found simpler to make an approximation for the integration involving V in equation 7 , obtaining ASirnp
P
[(g): pVn [RVn -
+
$1
+
[RTVn 28L
(10)
-R
This approximation will not introduce any serious error. I n the interests of brevity, i t occasionally proves advantageous t o Trite certain nomenclature for the pressure in terms of atmospheres rather than millimeters of mercury.
Employing equations 2, 3, 4, 5, 9, arid 10, in conjunction with the vapor pressure equations (10) thc second virial temperature coefficient equations (16), and data from the literature (1, 2, 7, 8, 14) for the molal volume of the liquid phase, the quantities given in tables 1 and 2 were computed. 'I'IBLE 1 Thermodynamic quantzties at 298 16°K. and 760 mm., calculated with the aid of the eouations of state (16)
calories per mole per degree
i ,I
Perfect gas.. . . . . . . Ethene . . . . . . . . . . . . . Propene.. . . . . . . . . . Propadiene. . . . . . . . . 2-Methylpropene.. . 1-Butene . . . . . . . . . . trans-2-Butene. . . . . cis-2-Butene.. . . . . .
0 -2746 -6456 -6655 - 12262 -12167 - 13645 -13446
, i I 1
24.466 24.317 24.113 24.108 23.787 23.793 23.708 . 23.720
O.Gd206 0.08459 0,08491 0'08300 0.08840 0.08961
1
11
1
I
1.987 2.033 2.111 2.127 2.306 2.306 2.314 2.367
O.Oo0 0.064 0.218 0.253 0.601 0.602 0.597 0.798
TABLE 2 Various thermodynamic quantities at the normal boiling points, calculated with the aid of the equations of state (16) and the vapoi iressure equations (1 __ HYDROCARBON 8 Va f As:,, HF,, 'Simp Tb - __ ~
~
j
'K.
X mm Hg per
m.6
mole2
I
-4378 -9104 Propadiene, . . . . . . . 2-Methylpropene. . 1-Butene.. . . . . . . . trans-2-Butene. . . . .
* A H F ~ ,=
239.52 266.04 266.86 274.07
AH:^, - AH&,;
-9006
- 14930 - 14767 - 15480 - 15500 AH:,,
dm.a per mol e
mm.
13.468 17.832 19.031 20 890 20.971 21.543 21.767
737.3 733.4 736.7 728.6 729.2 729.4 729.9
t
=
!aL.
T. Li.
per
m o r
mde
3204 4386 4827 5116 5195 5358 5636
18.92 19.45 20.15 19.23 19.47 19.55 20.37
d . pe7
E.C.
mde
pm mde
113 183 174 253 253 259 267
0.112 0.180 0.163 0.251 0.248 0.225 0.253
RT2 dp
-.-. P
dT
DISCUSSIOK
There is very little data in the literature with which a comparison can be made. Powell aiM Giauque (15) obtained 4402 f 3 cal. per mole for the calorimetrically detcrmined heat of vaporization of propene at the normal boiling point; this should be compared with the value 4386 found in this paper, a valuc 0.36 per cent lower than the calorimetric figure. Eucken and Parts (5) have determined thc second Tirial coefficient of ethene over
325
G b S IMPERFECTION. I1
the temperature range 181" to 273'K. I n table 3 are given the results of calculations from which some idea can be gained of the correspondence of the values obtained in this research with those available in the literature. Inspection of the calculated quantities in tables 1 and 2 nil1 show that in general the values increase as the molecular structure becomes more complex For non-polar molecules in an isothermal, isopiestic state, as the molecular structure is made more comples the gas imperfection will increase, sinre the imperfection is due to two causes,-the actual volume TABLE 3 Comparisons with other data for ethene
I "",;gD
QUANTITY
TF,= 169.4"K.; p
e..........................................
E.U. per mole
T
OTHERS
/TEIBRlaEARCE
= 760 mm.
. ! -5092(.)
.I,
13.400
-4378 13.468 3204
1
0 165
0.112
V', dm.3 per m o l e . , . . . . . . . . . . . . . . . . . . . . . . AH'.,, calories per mole. . . . . . . . . . . . . . . . . . . AS,,,,
~
= 298.2"K.: P = 760 mm.
I
8 . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Ti', dm.3 per mole . . . . . . . . . . . . . . . . . . . . . (C: - CL), calories per mole per degree . . (C; - C:), calories per mole per degree . .
.I
-2675ta) 24.321 2.032 1 0.076
1
-2746 24.33 (13)
24.317 2.033 0.064
occupied by the molecules arid the intermolecular forces.-both of which increase as a more complex molecular structure is concerned. There are various reasons for believing that in an homologous series the gas imperfection effects will not only increase but will do so in a regular manlier, and, furthermore, that only small differences arc t o be expected between .\-arious related series. I n an attcmpt to correlate these changes in the gas imprfection effects, an examination was made for simple, fundamental molecular constants that' might possibly be used as a measure of the imperfection. The
326
EDIVIN E. ROPER
simplest factors with which these increases might be correlated are the chain length and the gram-molecular w i g h t . It appears, from the limited amount of data available, that the imperfection increases somewhat regularly with increase in the chain length for a n homologous series. I n the final analysis, there are certain more complex molecular constants that are fundamentally influential in determining the magnitude of the gas imperfection; these constants are the dipole moment, the polarizability, the characteristic frequency in the dispersion force of London, and the molecular separation, these constants being involved in fixing the parameters in the law of molecular force for a specific structure. These factors are under investigation a t present.
r--r----
-
--
~
1
,
""\
*3 I
160
180 200 220 240 260 280
Tb,'KK. FIG.1. The second virial coefficient a t the normal boiling point for eight aliphatic hydrocarbons aB a function of the respective normal boiling points, Tb. The diameters of the points have been made equal t o the mean deviation of the observed values of 0 from the temperature coefficient equation as developed by the method of least squares (16). In addition to the seven hydrocarbons studied in Paper I (16), a from the literature (5, 17) has been included. The value for ethane (Tb = 184.5"K.) line has been drawn through the values for ethene, propene, and 1-butene.
It is apparent that the chain length or the gram-molecular weight is not sufficient to account for the experimentally observed differences in the gas imperfection effects of isomers, the butanes behaving in an analogous manner to the butenes. It mas found that the imperfection effects were quite closely allied to the numeriral value of the respective normal boiling points. I n figures 1 and 2 is presented a comparison between some gas imperfection effects and the normal boiling points. In figure 1, the second virial 8 (at TB) is shown plotted against the respective normal boiling point Tb,and in figure 2 the deviation from the perfect gas value of the difference in the heat capacity (C, - C, - R , in calories per mole per degree) a t 298.2"K. and 760 mm. is plotted against Tt,. I n both figures, the addition of the value for ethane (Tb = 184.5'K.) has been made, calculated
327
GAS IMPERFECTION. XI
from the corrected (17) second virial temperature coefficient equation of Eucken and Parts ( 5 ) . The line in both figures has been drawn through the valucs for the compounds ethene, propene, and 1-butene, an homologous series. For all eight hydrocarbons conccrned, the deviations in each figure from a smooth curve are close to or within the respective experimental error involved. DatJafrom the literature for a few other hydrocarbons show about the same type of deviations. Undoubtedly constitutive influences are present, but the available data are so limited both in accuracy and in extent that such influences may not be determined at this timc. Three of the hydrocarbons involved, propene, 2-methylpropene, and 1-butene, have small dipole moments, and one, cis-2-butene, has a very small moment. From these curves and from analogous studies of various other thermodynamic functions, i t is probable that the experimental data for pro@
-
0.4r--
_._ .
'
I
C
0'0.2
I
/'
1
/
/"
0
0
160 180 200
220
240
260
280
FIG.2. The deviation in C,-C, (at 298.2"K. and 760 mm.) from the value for a perfcct gas for eight aliphatic hydrocarbons as a function of the respective normal boiling points, Ta. The diameters of the points have been made equal to 0.01 csl. per mole per degree; the units of the ordinate are calories per mole per degree. The line has been drawn through the values for ethene, propene, and 1-butene.
padiene and for cis-2-butene are relatively less accurate than for the remaining five hydrocarbons (10).
smiiv.inT With the aid of previously developed temperature coefficient equations for the second virials of ethene, propene, propadiene, 2-methylpropene, 1-butene, trans-2-butene. and czs-2-biitene, various thermodynamic quantities haxe been calculated. For the standayd state of 1 atm. and 25"C., these quantities are the second virials, the actual molal volumes, the temperature coefficients of the volume, and two differences in the heat capacities. Utilizing previously determined vapor pressure equations in conjunction with the low-pressure data of state. the second virials, the actual molal volumes, the fugacities, the actual heats and entropies of vaporization, the gas imperfection corrections to the heats of vaporization
328
QEORQ CRONHEIM
and to the absolute entropies, have been calculated for the seven hydrocarbons a t their respective normal boiling points. Comparisons with other data in the literature have been made. A discussion of the correlation of the gas imperfection effects with other molecular quantities has been given, and it has been shown that the numerical magnitude of the normal boiling point may, to a certain extent, serve as an index to the imperfections. Professor E. B. Wilson, Jr., has kindly made several suggestions concerning the preparation of this paper. REFERENCES (1) COFFINAND MAASS:Trans. Roy. SOC.Can. !21,33(1927). (2) COFFINAND MAASS:J. Am. Chem. SOC.60, 1427 (1928). (3) CRAWFORD AND RICE: J. Chem. Phys. 7, 437 (1939). (4) EGAN AND KEMP:J. Am. Chem. SOC. 69, 1264 (1937). (5) EUCKEN AND PARTS:Z. physik. Chem. BSO, 184 (1933). (6) GIAUQUE AND WIEBE:J. Am. Chem. SOC.60, 101 (1928). (7) GROSSE AND LINN:J. Am. Chem. Sac. 61,751 (1939). (8)International Critical Tables, Vol. 111, p. 230. McGraw-Hill Book Company, Inc., New York (1928). (9) KISTIAKOWSKY AND RICE: J. Chem. Phys. 8, 610,618 (1940). (10)LAMB AND ROPER:J. Am. Chem. SOC.62,806 (1940). (11) LEWISAND RANDALL: Thermodynamics, pp. 192-8. McGraw-Hill Book Company, Inc., New York (1923). (12) LINNETTAND AVERY: J. Chem. Phys. 6, 686 (1938). (13) MASSON AND DOLLEY: Proc. Roy. SOC.(London) AlOS, 524 (1923). (14) PALLAND hfaass: Can. J. Research 14B,96 (1936). (15) POWELL AND GIAUQUE: J. Am. Chem. SOC.61, 2366 (1939). (16) ROPER:J. Phys. Chem. 44,835 (1940). (17) ROPER:J. Chem. Phys. 8, 290 (1940).
.
T H E CATALYTIC -4CTIOX OF NATURAL MINERAL WATERS GEORG CRONHEIM ??ew York State Research Institute, Saratoga S p a , Saratoga Springs, New York Received March 81, 1940
Since R. G l h a r d (7), in 1911, discovered the “catalatic” and “peroxidatic” properties of the mineral waters of Vichy (France), a whole series of papers have been published about them. The work of Baudisch and Davidson (2) on the mineral waters of Saratoga Springs, New York, in 1927, gave a new impetus to these investigations. The assumption by these authors that the iron in these waters exists in an “active,” probably
