Isothermal compressibilities of n-alkanes and benzene

M-786 J. Chem. Thermodynamics 1978,10,19-24

Isothermal compressibilities and benzene

of n-alkanes

M. DfAZ PERA and G. TARDAJOS Departamento de Q&mica Fisica, Facultad de Ciencias Quimicas, Universidad Complutense, Madrid 3, Spain (Received 3 May 1977)

The isothermal compressibilities of benzene and of 16 n-alkanes, from n-hexane to n-hexadecane, have been measured at zero pressure and 298.15, 308.15, 318.15, and 333.15 K.

1. IIltroduction We report compressibility measurements on several pure liquids, including benzene and a series of n-alkanes. This is a continuation in part of experimental work on the thermodynamic properties of mixtures of benzene + n-alkane. Previous papers report excess enthalpies(‘,‘) and excess volumes.13y4) A paper now in preparation will give excess compressibilities of the mixtures.

2. Experimental PROCEDURE The experimental method, including the piezometer-filling technique, described elsewhere.“~ 6, Isothermal compressibility rc is defined as :

K = - v-yav/ap),.

has been

(1)

The quantity determined experimentally is (ah/ap)r., encompassing the effects of pressure on the volume of the liquid being studied, on the volume of mercury used to confine the liquid, and on the glass piezometer. Compressibility is related to all of them through the relations :(5) A:= -(~iVl)(ahia~),-(~,,/~:)~~~+(l +v-dww3w~,, (2) where A denotes the cross-section of the capillary (bidistilled mercury was used in its calibration), Vi the liquid volume, calculated from its mass and density, (ah/ap), the change with pressure of capillary-mercury height, VnII, the volume of mercury, determined from its mass and density (we have used published data),“) rcng,the isothermal compressibility of mercury, evaluated from literaturecs) data at various temperatures, and rcg the isothermal compressibility of Pyrex glass, taken also from published data. @) Isotropy and homogeneity of the glass were assumed. At least 12 measurements, regularly distributed over the 0 to 2 MPa interval, of h against p

M. DfAZ PERA AND G. TARDAJOS

20

were made From that (in practice calculation

in each case. A least-squares adjustment gave practically straight lines. adjustment we obtained by extrapolation values of @h/f@), at p = 0 the slope of the straight line). The maximum error in the compressibility from equation (2) was in every case less than 0.5 per cent.

MATERIALS The sources of chemicals are given in table 1. The only treatment they all underwent was with sodium to get rid of any traces of moisture. Densities at the temperature of interest in this work, together with previously reportedcg) values at 298.15 K, are also given on table 1. We also include in table 1 analytical information supplied by the manufacturer regarding the quality of the chemicals. A stepwise procedure was followed to purify mercury by rinsing it with gasoline, methanol, 10 per cent nitric acid, water, sodium hydroxide, and distilled water. This sequence was followed by drying it at 403 K in an air draft, and ended by distilling it twice under vacuum. TABLE 1. Experimental densities p at various temperatures and comparison with literature data at 298.15 K. Mole-fraction 298.15K Compound

Benzene n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane n-Tridecane n-Tetradecane n-Pentadecane n-Hexadecane

Source

Carlo Erba R.S. Merck p.a. Fluka puriss Merck Z.S. Fluka purum Fluka purum Fluka purum Fluka purum Fluka purum Fluka puriss Fhrka purum Hopkin Williams

102x

98 99.5 98 99 99 98 99 99 99 99

2 > > 2 3 > 3 3 > 2 -

purity x of the liquids 308.15 K 318.15 K 333.15 K

298.15 K

p/g cm+ 0.87367 0.65489 0.67977 0.69861 0.71411 0.72625 0.73645 0.74517 0.75276 0.75915 0.76542 0.76997

Expt. 0.86296 0.85220 0.83594 0.64578 0.63639 0.62210 0.67123 0.66257 0.64937 0.69054 0.68232 0.66988 0.70633 0.69843 0.68652 0.71872 0.71109 0.69955 0.72907 0.72162 0.71044 0.73792 0.73066 0.71966 0.74560 0.73845 0.72770 0.75209 0.74505 0.73445 0.75843 0.75145 0.74102 0.76305 0.75614 0.74582

Lit.(@) 0.87370 0.65481 0.67951 0.69849 0.71381 0.72625 0.73655 0.74516 0.7528 0.7593 0.7650 0.76996

COMPRESSIBILITY All measurements were run twice. The average value is given in table 2. Except for n-hexane at 333.15 K, the experimental results for the n-alkanes are fitted well by a polynomial relation of the type: x/TPa-’

= 5 Ad (3) I=0 where n is the number of the n-alkane carbon atoms. The coefficients of equation (3) and the standard deviation are given in table 3. n-Hexane at 333.15 K was excluded from this polynomial fit because its high compressibility would have required a higher degree polynomial to stay within a comparable standard deviation. It must be remembered that at 333.15 K n-hexane is close to its normal boiling temperature.

ISOTHERMAL TABLE

COMPRESSIBILITIES

2. Experimental

values of isothermal compressibilities

298.15 K .___

Compound

21

OF LIQUIDS

308.15 K

318.15 K

333.15 K

1128 2027 1712 1506 1359 1262 1187 1132 1075 1033 1003 978

1277 2385 1969 1705 1536 1415 1322 1254 1193 1149 1103 1066

KITPa-’ Benzene n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane n-Tridecane n-Tetradecane n-Pentadecane n-Hexadecane TABLE

966 1669 1438 1282 1175 1094 1031 988 948 910 882 857

1044 1831 1570 1385 1266 1178 1108 1053 1006 969 940 917

3. Coefficients Al and standard deviation (S(K) corresponding to equation relating compressibility with n-alkane number of carbon atoms 6
4

6Cn616

298.15 K

A0

308.15 K

5906.7 - 1349.52 146.038 -7.31259 0.13901 _____-. 3.3

Al A2 A3 A4 a(!c/TPa - ‘) CALCULATION

6
6840.6 -1614.16 178.104 -9.10654 0.177169 __~ 3.7

(3),

7
318.15 K

333.15 K

8097.7 -1963.31 217.378 -11.0900 0.214701 ~-.. .-~~ 3.3

8987.4 -2096.22 222.385 - 10.8671 0.201425 4.6

OF (a V/a&

The change of molar volume with pressure has been calculated from K and density measurements. An equation (3) type has been used to fit the experimental results; its coefficients and the standard deviation are given in table 4. The experimental values of (aV/ap), against the number of carbon atoms are plotted on figure 1 for the various temperatures. The curves represent the equation (3) fit. TABLE (aV/ap),/lP

4. Coefficients B, and standard deviation cm3 mol-1 TPa-’

o(aV/ap)T

corresponding

to the equation:

= ,ioB,d where n is the number of carbon atoms in an n-alkane and 6 C n < 16

4

BO Bl BZ B3 B4

u(aV/Cjp)r/103 cm3 mol-’

TPa-’

298.15 K

308.15 K

318.15 K

333.15 K

-485.16 93.2641 -11.1147 0.553415 -0.010382

-604.26 128.259 -15.7951 0.836706 -0.0168426

-712.71 176.QO7 -21.5163 1.14010 -0.0228574

- 1026.63 238.320 -27.8879 1.41416 - 0.0269089

0.53

0.55

0.58

0.82

22

M. DfAZ PERA AND G. TARDAJOS {

- 220

- 240

- 32( I

I

6

I

I _-

10

12

_

I

14

16

n

FIGURE 1. Molar volume variation with pressure against the n-alkane number of carbon atoms. COMPARISON

OF OUR

AND

OTHERS’

RESULTS

This comparison is summarized for benzene in table 5. Very few previous measurements are available for the n-alkanes. Those published are in general for temperatures different to ours. In figure 2 we have plotted the relative discrepancy at 333.15 K between our results and those reported by others. Our values are lower for benzene and higher for n-alkanes. Since our method has been the same for all substances it seems reasonable to assume that any systematic error would affect all measurements similarly. In the case of benzene the great discrepancy occurs with Staveley et aZ.(14) Their measurements were made by determining the adiabatic compressibility. Errors are therefore cumulative. On the other hand their values are consistently higher than any others at all temperatures. Values obtained by Holder and Whalley(“) and Tyrer(13’ are, though slightly higher, consistent with ours. Holder and Whalley carried out their experiments in the 0.1 to 10 MPa range and then they extrapolated to zero pressure. Tyrer also measured adiabatic compressibility. Measurements for n-alkanes by Eduljee et ~1.“~’ and Cutler et ~1.~‘~’ are very different from ours and from those of

ISOTHERMAL TABLE

COMPRESSLBILITIES

OF LIQUIDS

23

5. Comparison of benzenecompressibility values with literature data fc/TPa- ’

T/K

This work -__ 966 1044 1128 1277

298.15 308.15 318.15 333.15

Literature .- .~~ __. - ._.--.. 968 (lo) 967,“” 954,02’ 967@’ &,“” 1036@’ 1132,“” 1155@’ 1296,““’ 1273J6’ 1282,(13’ 131204’

Boelhouwer.(“’ Eduljee et al. went as high as 500 MPa and Cutler et al. up to 1000 MPa. Both measured variation of volume with pressure, at widely separated values of pressure. Cutler et al. did not go below 34 MPa and likewise Eduljee et al. never ran below 50 MPa. In order to obtain compressibility at atmospheric pressure they fitted their results to a Tait’s equation and use it to extrapolate. But either their measurements are in error or Tait’s equation is inadequate to account for the curving of the isotherms at low pressures. In addition both teams’ results lack regularity with n-alkane chain length. Boelhouwer”‘) ran his measurements up to 120 MPa and fitted them to Hudleston’s equation. His results though consistent, within the possible error involved in extrapolation, are slightly below ours. A final check has been based on the thermal pressure coefficient y. This may be obtained from the expansion coefficient o! and the isothermal compressibility through the relation : Y = Ul& (4) (‘a) determined y directly for n-octane and n-hexane at 333.15 K. Orwold and Flory In table 6 a comparison is made of their values with those obtained from equation (4), where CIvalues have been taken from Orwold and Flory”” and K values from Boelhouwer and our own work. Table 6 shows that the best agreement is obtained between ‘;’ 5‘ $ 5 .s 3 3Y 8 3 3 .o .5t

I

I

I

I

I

I

I

I

0

r :

0

I

I

I

0

00

-4-

0

0

-8-

A

D

0

I

B

I

I

I

-

A

-tL - 12“0

I

4-

I

ccccccccccq 6 7 8 9

I

I 10

I 11

I 12

I 13

I 14

I, 15

6

FIGURE 2. Comparison of isothermal compressibility at 333.15 K for benzene (B) and n-alkanes (Cl. This work; 0, Staveley, Tupman, and Hart;‘“) A, Holder and Whalley ;“O) n , Tyrer ;(la V , DIaz’Pefia and Cavero ;@) 0, Boelhouwer;(17) 0, Eduljee, Newitt, and Weale;(16) A, Cutler, McMickle, Webb, and Schiessler.“B)

M. DfAZ PERA AND G. TARDAJOS

24

TABLE 6. Comparison of thermal pressure coefficients at 333.15 K Compound n-Octane n-Hexadecane

--__ Direct measurement Orwell and Floryoe) ___---_._ 0.720 0.855

y/K- l MPa y = a/K B;lhouwerU?) 0.749 0.885

This work 0.739 0.871

y values derived from this work and those obtained directly. Boelhouwer’s data show a somewhat larger discrepancy and those of Eduljee et al. and Cutler et al. would show an excessive one.

4. Discussion It is worthwhile to emphasize once again the smooth change of compressibility against chain length. Density also changes smoothly with chain length but in the opposite direction to that of compressibility, that is, it increases with chain length and it decreases with temperature. The opposite trend of compressibility and density behaviour is a logical one. Any chain increase within a homologous series increases the density by decreasing the intermolecular free space, thereby lowering the ability to be compressed. Correspondingly while compressibility increases with temperature, density decreases. Logically the change in absolute value of (aVlap)r with temperature is similar to that of compressibility. It varies with chain length due to the opposing effects of the molar volume and density, both of which increase with chain length. Increasing the molar volume increases the absolute value of (al’/@), while the opposite is true for density increase. Due to this special combination no definite trend can be predicted regarding (aV,ap), behaviour with chain length. Thus a maximum in the value has been observed in the case of n-alkanes. As can be seen from figure 1 this maximum occurs in the region of n-octane. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Diaz Peiia, M.; MenduiAa, C. J. Chem. Thermodynamics 1974, 6, 387. Diaz Pena, M.; Menduiiia, C. J. Chem. Thermodynamics 1974,6, 1097. Dlaz Peiia, M.; Ntiez Delgado, J. An. Qufm. 1974,70,678. Diaz Pefia, M.; Ntifiez Delgado, J. J. Chem. Thermodynamics 1975, 7, 201. Diaz Pena, M. ; McGlashan, M. L. Trans. Faraday Sot. l%l, 57, 1511. Dlaz Pefia, M.; Cavero, B. An. Real Sot. Fis. Quim. 1964, 1360, 357. Znt. Crit. Tables 1927, 2, 48. Bridgman, P. W. Am. J. Sci. 1925, 10. 359. Rossini, F. D. et al. Selected Values of Physical and Thermodynamic Properties of Hidrocarbons and Related Carbons. API Research Project 44, 1%7. Holder, G. A.; WhalIey, E. Trans. Far&y Sot. 1962, 58, 2095. Gibson, R. E. ; Kincaid, J. F. J. Am. Chem. Sot. 1938, 60, 511. Rogers, K. S.; Burkat, R.; Richard, A. J. Can. J. Chem. 1973, 51, 1183. Tyrer, D. J. Chem. Sot. 1961, 103, 1675. Staveley, L. A. K.; Tupman, W. I.; Hart, K. R. Trans. Faraday Sot. MS, 51, 323. Eduljee, H. E.; Newitt, D. M.; Weale, K. E. J. Chem. Sot. 1%1,3086. Cutler, W. G. ; McMickle, R. H.; Webb, W.; Schiessler, R. W. J. Chem. Phys. 1958, 29, 727. Boelhouwer, J. W. M. Physica 1960, 26, 1021. Orwell, R. A.; Flory, P. J. J. Am. Chem. Sot. 1%7,89,6814.