Ethylene Gas Equation State

8/12/2019 Ethylene Gas Equation State

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XN E Q U AT I O X O F STATE; FOR E T H Y L E S E GAS*

B Y LOUIS J GILLESPIE

I n th e present p aper th e eq uation of sta te of Beattie and Bridgeman'iutilized t o smooth and t o correlate, as f a r a s is possible, th e pressure-volurrrr,-temperature data for ethylene gas. Th e available d at a are those ofAmaga t?which extend over a large range of pressure and temperature into the liquidphase; the 24.95' isotherm of Masson and Dolleyj3and abou t four points o neach of four isotherms by hlath ias, Crommelin an d Watts . ' D at a on thf:norm al volume of ethylene atoo and I atmosphere are collected and reviewvedb y B la nc ha rd a n d P i ~ k e r i n g . ~

K Oequ ation of sta te ha s appa rently been presentedfor ethylene, with theexception of virial p v expansion s. Aside from the general usefulnessofequ ations of sta te, especially for gases of considerable chemical ac tiv ity , anequation for ethylene is especially desirable in viewof the work on mixturesof ethylene and argon by Masson and Dolley, which have permitted the cal-cu latio n of pa rtial m olal free energies of th e con stitu en ts of thes e bina rymixtures.6 Th e present work was in fact undertaken witha view toward amore com plete therm ody nam ic investigation of these data th an h as beenhith erto possible.

Interpolation of the Isothermals

For each temperature the v products of Xmagat were graphicallysmoothed asa function of the density, using an app ropriate deviation fun ctionan d large scale coordinate pa per , and values of the p ressure were interpolatedfor even values of the density in moles per liter 0.5, 1 . 0 ~ .5, etc . ) . Thetransfe r from Aniagat unitsof density to moles per liter was effected throughth e norm al density given by B atuccas ' and chosen by Blanchard an d Picker-ing,; namely 1.2604 grams per liter.

By a similar procedure, the da ta of hIasson and Dolley and of the Leidenlaboratory were interpolated to the same even density values, thus per-mit t ing a com parison of d at a. I n th e forme r case th e transfe r of den sity

units required a knowledge of the rat io of'the volum e at24.95 t o t h a t a t o oboth volunies a t I atmosphere. From Xm agat 's dat a this rat io,V /Vo wascalculated to be 1.0936, from >\lasson and Dolley's data,1.0932. The mean

* Contribution from the Research Laboratory of Physical Chemistry, MassachusettsInstitute of Technology, S o . 216.

J. A . Beattie and Oscar C . Bridgeman: J. Am. Chem. Soc., 49 1665 (1927).Ann. Chim. Phys., 16) 29, 68 (1893).Ppoc. Roy. SOC., 03-4 j24 1923).

4 Cinquihme C0ngrt.s International d u Froid, Rome; Premiere commission interna-

5 Sci. Paper U. S . Bureau of Standards, S o . j29 11926).

7 J. Chim. phys., 16, 322 (1918).

tionale de 1'Institut Internationale du Froid, Rapports et Communications. Leiden, 1928.

Gibson and Sosnick: J. .im. Chem. Soc., 49 2 1 7 2 (1927).


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A S EQU.4TION OF STATE F O R E T H Y L E K E GAS 3 5 5

value 1.0934 was chosen. At a subsequent period it was found tha t thehigher ratio was yielded by the equationof state finally derived, butit wasfound that the effect of the difference, 0 . 0 0 0 2 , was practically negligible inall relations un de r consideration.

I t was observed in this isothermal interpolation t ha t thev d a t a a t 24.95'do not approach R T at low pressures in a perfectly smooth way around Iatmosphere. Th e da ta are smo other a t al l higher pressures. These da tawere already sm oothed once before publication,* bu t probably without th eaid of a value of R T, which in fact could not be obtained without knowledge

F I G . I

Typical plot of an unsmoothed isometric 2 . 5 * showing the isothermally smoothed

points due to hma ga t (circles), Masson and Dolley (square), and Mathias, Crommelin an dWatts (crosses). The plot shows the value of the deviation,-p 34 0 . 2 7 j 16t rn afunction of the temperatur e Centigrade. The line is furnished by the equation of s ta tefinally selected. Th e circles centered on this line are drawn with radii equal to O . j ofthe calculated pressures.

of the ra t io 1125,/T 0. h ike situation obtained with reference to the Leidenisotherms; no wa y being discovered of sm ooth ing these together withR Tvalues without assum ing in this case rather large experime ntal errors.

Th e interp olated v alues of th e pressures, which are hereafter describedas the observed pressures, were now grouped as isometricsfor the next s tep .

Representation of the IsometricsFor each density, the pressure was plotted a s a function of th e abso lute

temperature . Fig. I shows a typical plot , that for 2 . 5 moles per liter. T h eline, shown fo r comparison only, was calculated from the final equation.It

liter

8 See Fig. 2 , ref. S o 3 , where irregularities in the original data are obviously not en-

tirely removed in the smoothing.


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356 LOUIS J GILLESPIE

is clear th a t the results of Masson and Dolley,of the Leiden Laboratory, an dof Am aga t differ too much to p ermit utilization of all da ta in the final smooth-ing. Only the Amagat d at a are extensive enough to determine an equationof st at e; such an equation mus t be based on Aniagat 's d ata alone.It is also

clear from the l ine drawn that the equation does not include a certain trmdin the A m agat da ta. Th is tre nd , evidenced by a n inflection of th e isometric.,suggests at f irst a discordance between the high temperature(137', 198.; )and the low temperature (0-100 ) data. Exclusion of the high temperatureda ta would however leave d2 p/ dt 2 ositive, whereas thisis as a rule negative(above th e critical volume)Q.t seemed best therefore to include all temp era-ture s an d to assume such a c urvatu re of the isometrics as would keep themwithin about 0.5 percent of the measured pressures. Following the pro-cedure of Be attie an d B ridgem anlo a va lue ofc was found which would securethis, at least from a density of zero to abou t 7 moles per liter, with some

difficulty as regards the highest temperature-pressure cornerof the field.Th e oth er con stants of th eir eq uat ion were th en determined a s described bythem.

The constants so determined are given in TableI.

TABLE 1Co nstan ts in Beatt ie-Bridgeman E qua tion of Sta te for Eth ylen? .

R A0 a B o b C Mol n-to 0 8 2 0 6 6 1 5 2 o 04964 o 1 2 1 5 6 o 3 5 9 7 2 2 68 IO^ 2 8 0 3 1

T he equation is p RT(I e).(v B ) / v 2 A / v 2Where A A, I a /v )B Bo I b / v )E c / v T 3v = volume in liters of a molep = pressure in international atmospheresT 273.13 t C.

Th e agreementof the equation with the observed pressuresof Am agat i sexhibited in Table 11, which lists the observed pressures and the deviationA p (observed minus calculated pressure) in atmospheres. T he averagedeviation (taken without regard to sign) over the entire range considered is0 . 4 j per cent. Th is range goes to a density 8 mols per liter, slightly higherthan the cri t ical density. The agreement is fair. Th e equ ation holds verywell indeed u p t o 7 mols per liter, the average deviation being0.36 er cent.

Tab le I11 shows th e magn itude of th e disagreem ent, already noted b yMasson and Dolley, between their results and thoseof Am agat . There isagreement only at low densities. It is however precisely a t such low densi-

9 Onnes and Keesom: Encyklopadie der mathematischen Wissenschaften, Art. V IOpage 756 1912); lso Communications from the Phys. Lab. U n i v . of Leiden, 11, Supple-ment 23, p. 142, eiden 1g12).

'OProc. Am. Acad. Arts Sei., 63, 229 1928).


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AN EQCATIOS O F STATE F O R ETHYLENE GAS 3 5 7


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3 58 LOCIS J . GILLESPIE

ties (1 .1 to 2 3 ) tha t the Leiden data differ, and a t al l temperatures. from th eequation, as is shown in Table Is, for which the unsmoothed Leiden datawere utilized. Th e da ta devia te more strongly th an those of M asson andDolley an d in th e opposite direction. If the percentage d eviation is plotted

as a func tion of th e den sity, it is found not t o approa ch zero asym ptoticallya t zero pressure. This is not at tr ibutable to a defect in the equation. Eve ntho ugh th e pur ity of Am agats ethylene was notso great as it is now possiblet o obtain , the fact is imp ortant t ha t the equation furnishes numbers, smoothin two dimensions, which must be considered to approach correctness, insm oot h fashion, as the pressure approacheszero.

There exist relations in which the disagreement between Masson andDolley and Amagat, which reaches4 6 5 up to a density of 8 > s not so im-portant as might appear from TableI11 alone. Co m par e th e discrepancy of3 7 c a t a density of 4.5 wi th t he error of 8 jTCj hich is the percentage deviatio n

of th e perfect gas law from th e observed value. At a d ens ity of6 , th e perfectgas law is in error by 1 2 2 .TABLE 11

Com parison of Calculated an d Observed (M asson and Dolley) Isotherm s at24 95O

obs calc,calc.

p , = I O 0

Density p calc. Ah Density p cnlc A PI - 0 . 0 2 7 6 6 . 7 4 . 6

0 . 5 11 . 4 1 - 0 . 2 7 5 6 8 . 7 4 2

I 2 1 . 2 ; O 8 7 1 . 2 3 . 1

2 3 6 . 7 7 0 . 6 9 77 8 0 . 32 5 4 2 . 7 1 1 . 0 9 . 5 8 2 . 4 2 . 53 4 7 . 6 3 1 . 5 I O 8 7 . 9 4 7

4 5 4 . 9 2 j I 1 1 0 2 . 8 8 . 74 . 5 j 7 . 6 3 . 1 1 . ; 11 2 . 3 - 1 0 . 0

5 5 6 1 . 7 4 . 0 1 2 . j 1 3 6 .6 - 1 0 . 56 6 3 . 3 4 . 6 I 3 1 5 1 . 6 9 . 0

6 . 5 6 5 . 0 4 . 6

TABLE sPercentage d eviations betu-een Leiden experimental values an d the values

Temp./Serial order I 2 3 4

. 36C 1 . 3 1 . 4 I . 6 2 . o0 . O 0 0 . 9 I . o 1 . 2 1 . 5 1 8

2 0 . 1 8 ~ I . o I . o 1 . 2 1 4

1 . 5 2 9 . 6 6 + 0 . 3 8 . j 7 4 . 1 I . 6

3 5 5 1 . 7 1 . 9 1 0 . 5 9 4 . 7 6 . 9

5 9 . 8 3 . 7 I 2 123 5 - I O . j

calculated. T he calculated pressure is always grea ter.

_ _

I O . 170 1 . 1 I . o 1 . 3 I . 6 ~_ _

Dens i ty a t 2 0 . 1 8 ~ I . I 4 1 4 1 . 3 3 5 6 1 . 6 4 7 4 2 . 2 6 4 4 ~


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AN E Q C AT I O N O F STATE FOR ETHYLESE GAS 359

Calculation of t h e Normal Density

Th e equ ation does not necessarily fu rnish upon calculation the same valueof the density at oo and I atmosphere as that which was used t o ob ta in i t )but m ay give a better value.

Tab le V shows the summary of Blanchard and Pickering 5) with theadd ition of th e value calculated from the eq uati on .

TABLE

Norm al Density of Ethy lene, in grams per l i terSource Density Source Density

Leduc I 2 6 0 5 Batuecas I . 2604

Stahrfoss I . 6 1 0 Equat ion 1.2599

Blanchard and Pickering selected the valueof Batuecas. T his selection issupp orted by th e value here found.

Calculation of Critical Data

In the i sothermal smoothingof the p u values und er th e cri t ical tempera-tu re it was noticed th at the calculated pressures became almost a zero func-tion of th e density and indeed, without great care in the sm oothing, t 'hepressures actually decreased with increasing density. K h e n the equ ationwas derived it was thought interesting to see whether it would exhibit thist rend. It was found tha t the equat ion gave a7 j isotherm with an inflec-tion at abou t moles per liter. By a succession of trials it was foun d th a t aninflection occurred at as high a temperature as8.5 , but no t a t 8. 5 , whenthe pressures were calculated with a precision of0 0027c The critical tem-perature is therefore given by the equation as8.5', to the neares t 0.1 .Pickering selects th e value9. o difference of 0 . 4 7 ~ n th e absolute tempera-ture, which is of course the qu anti t y calculated by the equ ation. Since thisselection, Masson and Dolley (3) obtained 9.35', the lowest recent experi-men tal value.

The critical pressure calculated is49 .19 atmospheres against 50.9 selectedby Picke ring, a differen ce of 3.4yc. The critical density calculated is6 .4to 6 . 5 , selected value 7 . 9 in moles per l i ter. Here the errors seem to accumu -late, making a positive disagreement.

Equations Tvhich represent the measured pressures are not generally ex-pected to furnish correct critical constants (nor do those which are derivedfrom critical constants represent the m easured pressures),so th at the successof t h e equat ion for ethylene in furnishing at least the cri tical temp eratureissurprising. Th e agreement mayof course be accidental.

l Sci. Papers, U. S. Bureau of Standards, ?To. 54 (1926).


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360 LOUIS J GILLESPIE

summary

The constants in the equat ionof s ta te of Beattie and Bridgeman havebeen determined for ethylene gas from the data of hm ag at. Using atmos-pheres, liters per mole,T = 273 .13 t C , R 0.08206, th ey areA, = 6.152,

a = 0 .04964 , Bo 0 . 1 2 1 5 6 , b = o.o3j97$ an d c 22.68 I O?Th e representation of Am agat's d ata is goodup to a density of 7 molcs

per liter and fair t o 8, slightly above the critical density; the average devia-tions being o 36 and o 45 per cent respectively.

The equ ation does not rep resent closely th e isotherm of Masson an d Dol-ley, except at low pressures, in accordance w ith the ir statem ent t ha t t hi siso-therm does not agree with interpolations from Am agat's data

Th e cri t ical temperature calculated from th e equ ation agrees too 4y0 withthat observed, the difference being 1 . 2 ; the critical pressure calculated is3.4Yc in error.

The normal density calculated from the equation,1 2 599, supports thevalue of Batuecas as against tha tof Stahrfoss, being lower tha n eith er.

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Ethylene Gas Equation State