J . I?. CONSOLT~Y
1082
method of least mean squares is D g./cc. = 9.077 - 8.006 X T'K. zk 0.011 Thus, the liquid density is 7.992 g . / ~ m at . ~ the melting point (1356OK.) and 6.792 g . / / ~ ma.t~the boiling point (2855'K.). This is equivalent to a change in liquid density with temperature (dDldt) of -8.006 X loF4. Extrapolation of the solid density reported by Sauerwald4.j gives a solid density of 8.350 g./cc. at the melting point. Therefore, the volumetric expansion on melting, AVlV,, is 4.51%. The atomic volumes were calculated for various temperatures from the smoothed density values obtained from the liquid copper density equation. They are summarized in Table I together with the cubical coefficient of expansion values calculated from the equation
- do dt
pDt
where dD/dt is the change in density with temperature, p is cubical coefficient of expansion, and Dtis the density at temperature t. Estimate of the Critical Constants.-A method of estimating the critical constants of metals has been described lately by Grosse.I5 From this method, the critical temperature was calculated to be 8900 + 900'K. while the critical density and atomic volume are 1.04 zk 0.2 g./cm.3 and 61 + 10 ~rn.~/mole, respectively. The rectilinear diameter DS = 4.538 - 4.003 X TOK. in g . / ~ m . ~ . (1;) A. \ . Grosse, J . Inorg. & .Yuclear Chem., 2 2 , 23 (1961).
Vol. OG
AA.TOiVICVOLUMES BND
TABLE I EXPANSION COEFFICIENTS
OF
LIQUID
COPPER
Temp., OK.
Density, g./cm.a (smoothed values)
Atomio volume, cm.a/mole
7,992 7.956 7.797 7,636 7.476 7.316 7.156 6.792
7.952 7.990 8.152 8.324 8,503 8,688 8.883 9.359
1356 (m.p.) 1400 1600 1800 2000 2200 2400 2855 (b.p.)
Cubical expansion coefficient P x 105, OK.-
100,2 100.6 102.7 104.8 107.1 309.4 111. 9 117.9
Figure 2 shows the whole liquid range diagram from melt'ing point to critical t'emperature. The densities of the liquid copper above the normal boiling point are presented in Table 11. TABLE I1 THELIQUIDDEXSITY OF COPPER ABOVE IXG POIKT Temp.,
O K .
ITS
NORMAL BOIL-
Liquid density, g./cm.3
3000 4000 5000 6000 7000
6.675 5.87 5.03 4.16 3.2
Acknowledgment.--We wish to thank Dr. A. V. Grosse for his helpful advice and Lucia Streng for the analytical determinations.
IDEALITY OF YZ-BUTANE :ISOBUTANE SOLUTIOSS BY J. F. CONNOLLY Research and Development Department, American Oil Company, Whiting, Indiana Re~eibedDecember 9, 1962
Gas compressibilities were measured for the isobutane: i-butane system up to the saturation pressures, in the temperature range 70 to 170", and 2nd and 3rd virial coefficients were derived. Mixed 2nd virial coefficients calculated on the basis of Amagat's law agreed with the experimental values to 1 cc./mole on the average. Phase boundaries were meaeured for the same system from 70" t o the critical temperature of i-butane. The phase-boundary pressures computed using the idealsolution laws and the virial coefficients agreed with the observed values within 0.2%.
Introduction Solutions of compounds as closely related to one another as n-butane and i-butane might well be expected to form nearly ideal solutions as long as the critical region is not approached too closely. Redlich's vapor-liquid equilibrium measurements, made near atmospheric pressure, have shown that a number of isomers come close to forming ideal solutions1 below a reduced temperature of 0.7. Because of the higher saturation pressures at temperatures nearer the critical, an accurate knowledge of gas compressibilities mould be a necessary addition to vapor-liquid equilibrium data in testing the ideal solution laws. The present work was done in the reduced temperature range from 0.8 to near 1 in order to ascertain whether or not ideality continued to hold at higher temperatures. Phase-boundary pressures (1) 0. Redlioh and A. T. KiEter, J . A m . Chem. Soc., 71, 505 (1949).
mere measured for both compounds and three mixtures in the temperature range 70' to near the critical temperature of i-butane. Gas compressibilities were measured from 4 atm. to close to the saturation pressures for both compounds and a 50: 50 mixture in the temperature range 70 to 170'. Experimental The n-butane and i-butane were Phillips research grade materials with stated purities of 99.99 and 99.96 mole 70. They were not purified further except to remove the air present by distillation in oarno. The purities of the resulting products were confirmed by the small pressure rises, 0.01 atm., observed beta een the two phase boundaries, i.e., between the dew (first trace of liquid) point and the visual bubble (last trace of gas) point. In the experimental method,2 a sample was confined above mercury in a calibrated glass capillary and stirred with a magnetically driven steel ball. Volumes were determined by measuring lengths tr-ith a cathetometer. Pressures were measured with a dead weight gage; temperatures with a (2) J. F. Connolly and G. A. Kandalic, Phys. Fluids, 3, 463 (1960).
June, 19G2
1083
IDEBIJTE' O F n-BUT24NE-ISOBUTANE SOLUTIOSS
platinum-resistance thermometer. Critical points were determined visually. Dew points were determined by noting the discontinuity in the pressure-volume isotherm. Bubble points mere determined both from the discontinuity in the pressure-volume isotherm and by visual observation of the disappearance of the last trace of vapor. The bubble and dew point determinationsvare illustrated in Fig. 1 for the 160°F. isotherm of the 50-50 n-butane:ibutane mixture. The pressure usually rose sharply by about 0.01 atm. as the last trace of vapor disappeared. Because this rise oixurred with the pure substances also, it presumably was due t o traces of volatile impurities. The true bubble point was taken as the discontinuity defined by a short linear extrapolation of the isotherm. The observed vapor pressures of n-butane and i-butane are listed in Table I. The dew and bubble points of the three mixtures are listed in Table 11.
TABLE I
U'
+ by2 + cy?
+ b'xz +
VISUAL BUBBLE POINT 9 576 ATM. TRUE BUBBLE POINT
9.562ATM.
95
i
+-a W
IL
LT
a
&Butanea
Liquid and Vapor Compositions.-In order to obtain both liquid and vapor compositions a t the same temperature and pressure, interpolation with respect to complosition is necessary. Because the variations of the bubble and dew point pressures with composition were not far from linear, they were represented within experimental error by quadratic equations such as
p =
-
W ln
&BUTANE (ATM.)
71 11 8 20 11.00 87.78 11.79 15 52 104.44 16.42 21.29 121.11 22.28 28.56 133.72 27.67 35.32 ... 35.85' 134.62 137.78 29 62 .... 151.97 37. 35' a The vapor pressures of both compounds agree with Sage and Lacey's values3t4 to about 0.1%. b Critical state. Comparing these critical constants with the values selected by Kobe6shows them t o be lower by 0.0" and 0.1 atm. for nbutane and 0.3" and 0.2 atm. for i-butane.
for dew points and
I
I
v)
VAPOR PRESSURE O F ?%-BUTANE AND Temp., "C. n-Butane5
p =a
96
94
5 0 7 MOL% n-BUTANE 49.3 MOL% I - B U T A N E
9:
I
I
1.0
2.0
V 0 LU M E, LI TERS/MOLE
Oo5
r-l
N * 0.04
W
-J
0
5 003 \
-
N.
"-002
n - BUTANE i-BUTANE A 50:50 M I X T U R E
(1) 001 0 8
C'Q~
.
isotherm in the two-phase rcgion.
Fig. 1.-Pressure-volume
(2)
09
I I
1.0
T R I , T R Z(, T R I
for bubble points; where p is the pressure in atin., Fig. 2.-Third virial coefficients. and yz and 2 2 are mole fractions of i-butane in the vapor and liquilct. phases. The constants in eq. 1 (3) and 2 along with closeness of fit to the data are given in Table 111. Values of xZ a t each dew where v is molal volume, and B and C are the 2nd pressure and of yz a t each bubble pressure were and 3rd virial coefficients of the mixtures calculated from these equations. They are listed B = 1/i2Bii 2yiyzBiz 1/z2B2z (4) in Table I [. C = ~ 1 ~ C i i i 3 ~ 1 ~ ~ z C i i3~1~2Cizz z Y Z ~ C ~ Z ~ (5) The critical temperatures of the mixtures were reB1l and Clll being the virial coefficients of n-butane; presented with a maximum deviation of 0.02O by Bzz and CZZZ the virial coefficients of i-butane; and E o ( O C . ) = 151.97 - 16.58~2- 0.76~22 B I Z , C112, and Clzz "mixed" virial coefficients that and the critical pressures with a maximum devia- depend on the forces between unlike molecules. tion of 0.01 atm. by To obtain C, eq. 3 was fitted to the experimental data by least squares. I n Fig. 2 the values for np,(atm.) = 37.35 - 1 . 0 3 ~ -~0 . 4 6 ~ ~ ~ butane, i-butane, and the 50 : 50 mixture are plotted Virial Coefficients.--To represent the gas com- against the reduced temperatures of n-butane and pressibilities in the density range of this work the i-butane, and the geometric mean of the reduced virial equation (of state, terminated after the 3rd temperatures. The points scatter below a reduced virial term, is sufficient. The equation is temperature of 0.9. Such scatter is to be expected (3) R. H. Olds, H. €1. Reamer, B. H. Sage, and W. N. Laoey, Ind. because the density that may be reached without Eng. Chem., 86, 282 (1944). exceeding the saturation pressure is small a t the (4) W. M. Morris, B. H. Sage, and W. N. Laoey, Trans A m . I n s t lower temperatures. Because this makes the Mznzng Met. Engrs., 186, 158 (1940). measured deviations from ideality very small, the ( 5 ) K. A. Kobe and R. E. Lynn, Jr., Chem. Rev.,5 2 , 117 (1953).
+
+
+ +
+
TABLE TI COMPARISON OF OBSERVEI) I'IIASE-BOEND.~RY PRESSVRES IVITII THOSE CAI,C~JI,ATEII OS THE BASIS O F I h v points Temp., OC
71.11
87.78 104.44
121.11
133.72b
2/2
P (atm.)
0.246 .493 .750 .246 .493 ,750 ,246 .493 .750 .246 .493 ,750 ,246 .493 .750
8.76 9.40 10.17 12 54 13.41 14.42 17.44 18.56 19.88 23. 60 25.06 26.76 29.31 31.07 33.16
1 n i c . k ~SOLUTIONS
1OO(p 52a
0 202 ,435 . 706 ,207 ,442 ,712 ,213 ,450 ,719 .221
010/61
020/01
1 012 1 026
0 955
1.043 1,015 1 ,032 I 051 1.018 1.040 1 ,067 1.023 1.050 1.083 1.027 1.061 1 107
,461
,726 ,230 .472 .735
968 ,983 .948
,962 ,980 ,939 ,9RR
.977 ,927 .947 .971
I
I1 1.002
In 0.990
1.005 1.008 1 003 1.006 1.010 1.004 1.009 1.014 1.006 1.012 1.020 1 .no7 1.015 1.025
,993 ,996 ,987 .991 ,995 .983 .!E38 .993 .976 .984 .%I2
%
3
.1
.I .2 .2 .2 .I
... 3
.I .I .I .2
100(p
$in"
+10/91
QZQ/dt
0,296 0.057 1 015 ,551 1 ,030 .9il 1 046 ,985 ,788 .950 ,289 1.018 ,966 ,544 1.036 1.057 .784 .983 ,942 1.021 .282 .959 1.044 ,536 .979 1.071 .779 .929 1.025 .273 .950 1.054 .526 1.087 .974 .772 1.029 .264 1.065 ,514 1.110 ,764 0 too close to the critical temperature 6 2 0 and 12. Therefore, p was calculated from: p = 71.11
0.246 8.88 ,493 9 . Ti6 ,750 10.29 12.68 87 I78 .246 .493 13.60 14.56 .750 104.44 .246 17.59 18.77 .493 20.04 .750 121.11 23.76 .246 25.26 ,493 26.91 ,750 133.72b 29.39 ,246 31.25 ,493 33.26 .750 From eq. 1 and 2. b This temperature is
I1
I2
ideal)/p
0.1 .2
Bubble points (at:.)
x2
-p
.-3
.2
- P iJeal)/p, 7G
0.991 1.003 0.2 .994 1.006 .I .997 1,000 .1 1.004 .988 .1 .992 .2 1.007 ,996 1.011 *I 1.005 .984 .1 1.010 .989 .1 1.015 ,994 .2 .977 .2 1.007 1.013 ,985 .1 .993 1.021 .I 1.008 .o .0 1.016 - .4 1.026 of i-butane t o permit the calculation of
TABLE IT1
-
CONSTANTS FOR EQUATIOSS 1 AND 2 -
7
D
,-----------Bubble
~ points----. ~
Max. dev.,
points
Max. dev.,
Temw.. _ ."C.
a
b
C
atm.
a'
b'
c'
atm.
71.11 87.78 104.44 121.11 133.72
8.200 11.792 16.421 22.285 27.675
2.088 2.833 3.845 5.027 6.236
0.714 0.906 1.025 1.248 1.407
0.00 . 00 .01 .01 .01
8.200 11.792 16.420 22,286 27,676
2,729 3.587 4.679 5.838 6.880
0.073 ,142 ,193 .434 .760
0.00 .00 .01
values of B and C, particularly C, will be more uncertain a t these temperatures. The uncertainty in the low temperature C's has very little effect on the calculation of fugacities because of the lour saturat.ion pressures a t these temperatures. Values of B, as well as C, were obtained in the course of fitting eq. 3. However, in order to obtain slightly better values of B at the lower temperatures, the values of C from eq. 3 were smoothed graphically (Fig, 2) and the least squares process mas repeated using the equation _pv
RT
- 1 - C(smoothed) ..____ 212
0
.01
.01
bility factors with a standard deviation of about O.OS~o. It gave values of E which were the same as those from eq. 2 a t high temperatures, and differed by only 2 or 3 cc. per mole at the lower temperatures. Values of E from equation 6 are plott,ed in Fig. 3 and listed in Table IV. Values of the mixed 2nd ririal coefficient, calculated by means of eq. 4 from B for the 50 : 50 mixture, also are listed in Table IV under B12. Amagat's law6would require a B12 for which
(6)
Equation G rerJroduced the exnerimenl a1 compressi-
The experimental values agreed with this equation
IDEALITY OF ~-BUTANE-~SOBUTANE SOLUTIONS
June, 19G2
1085
TABLE IV VIRIALCOEFFICIENTS -----n-Butanea----T%mp.,
C.
-
CI11,
BII, cc./mole
I.a/molea
Max.c density, mole/l.
,...---
i-B u tanea----
-Bza, cc./mole
0.507 n-Butane i-Butane-?
---0.493 Max. 0 density, mole/l.
Cazz
l.z/mdlez
C,
--B, cc./mole
1.x/molea
Max.* density rnole/l.'
0.41 (0.0270) 485.8 0.50 457.2 (0.0240) (0.0300)* 0.35 517.0 71.11 ( ,0325) .60 0.73 438.6 412.7 ( .0305) ( .0355) .52 87.78 464.7 .87 .0360 1.08 396.9 374.0 ,0335 ( .0380) .75 418.6 104.44 1 29 361.7 .0370 1.68 .0345 341.1 .0395 1.08 381.3 121.11 1.84 337.8 ,0365 318.3 .0340 1.70 .0390 1.46 356.1 133.72 1.72 330.0 .0360 311.5 ,0335 1.70 1.65 348.6 .0385 137.78 274.1 .0310 1.82 ,0290 1.70 259.6 1.58 289.8 .0340 171.11 a Virial coefficients of n-butane and i-butane, in the ranges 0 to 300" and 140 to 300", respectively, have been c Maximum density used in fitting eq. 6. b Values in parentheRs are uncertain.
to 1 cc./mole on the average and 3 cc./mole a t the maximum. Such agreement is within experimental error. Ideality of the Liquid Phase.-A concentrated solution is said to be ideal when its activity coefficients, as defined by a particular choice of reference states, are unity. Except near atmospheric pressure, it is not possible to choose the same liquid reference Btates for both components, unless one is willing to countenance hypothetical states with somewhat indeterminabe properties. Therefore, the reference state for n-butane was taken as pure n-butane and that for i-butane as an infinitely dilute solution of i-butane in n-butane. The chemical potentials in the liquid phase then are given by plL = pzL =
-*0°
483.7 437.9 396.9 361.7 338.1 329.5 273.1 reviewed.?
&
-300
W -1
0
\z.
-400
0
u
ai
+ +
PP(P,T) RT In YIZI RT In YZXZ
pz'(p,T)
-Bn, cc./mole
-500
where yl and yz are activity coefficients of n-butane and i-butane, for which lim y1 = lim yz = 1. Therex1-1
XI-1
fore, the chemical potential of pure n-butane is equal to fils whereas the chemical potential of ibutane in its standard state is given by
- 600
p z 8 ( p , T ) = lim [pzL - RT In zZ]
os
xz-0
For the gas phase we have piG =
Fi(T)
+ RT lnfic
09 TR,
Fig. 3.-Second
(7)
where f is a fugacity and F ( T ) is the chemical potential of the pure gas in the ideal gas state at 1 atm. By equating chemical potentials for each species in the two phases at equilibrium, and making use of the expressions
1.1
I .O
R E D U C E D TEMPERATURE.
virial coefficients of n-butane and i-butane.
pure 1 (n-butane), l f 2 * is the partial molal volume of 2-butane at infinite dilution (xz = 0) in 1, and the superscript 0 denotes the value of the property for the pure substance at its vapor pressure. For ideal solutions y1 = yz = 1 over the whole composition range and we have f>G = S i j i O I i
or l/ipFhi = Sipio+ioIi
wc obtain
(11)
wherc (9)
for n-butane, and.
for i-butane; where V Iis the liquid molal volume of (6) J. A. Beattie, "Thermodynamics and Physics of Matter,"
F. D. Rossini, Ed.. Princeton University Press, Princeton, N. J., 1955, 'p. 305.
(7) H. G. David and S. D. Hamrtnn, "Proc. Joint Conf. Thermodynamic and Transport Properties of Fluids," Inst. Mech. Engrs., London. 1957, pp. 74-78.
and cp is a gaseous fugacity coefficient. Before eq. 11 can be applied to the calculation of phase boundary pressures at a particular temperature, liquid volumes must be known as a function of pressure, and must be known as a function-of pressure and composition. Values of VI and Vz*B -
-
(8) For ideal solutions Vs* Va only when P 2 pzo. and in the present case p < pea. However, the pressure is short enough 80 that Vz* at paQ can be used from pzQ to p .
-
J. M. THORP
1086
are available9 and the virial equation of state in combination with eq. 7 gives6an expression for cpi 3 s2 (YLZCI11 + 2YLY2C11, + Y,2CLJ]
(12)
Vol. 66
activity coefficients with deviations in boundary pressures may be obtained for a 50 :50 mixture (zl = 0.5) as follows: Because the ratio I14z/I~41 varies very slowly with pressure and vapor composition, which in turn are close to the ideal values, we may use eq. 9 and 10 to write
(;*)
Y1 = _Y I_ Y 2 0 2_ lfP Table IV gives all of the virial coefficients needed yZ y2r?fi0 241 Ideal in eq. 12 except the mixed 3rd virial coefficients C112 and Clzz. However, Clll and C222 are so close If the deviations from ideality are and together that it makes little difference what com- independent of pressure, then In y1 = and In bining rule is used to obtain these mixed virial co- (rz/yzo) = AzL2,yielding y1yz0/y2 = 1 for a 50:50 efficients. Therefore, it was assumed that mixture. Therefore, for a 50: 50 mixture, (yl/yz) = (yl/gz)ideal and eq. 9 gives 2Cn1 c222, - Clll 2C222 ( 13)
Cll2 =
+
3
+ 3
Equations 13 in combination with eq. 5 predict exactly the values of C for the 50 : 50 mixture listed in Table IV. To calculate ideal dew point pressures, equations 3, 11, and 12 were solved simultaneously by iteration at each dew point composition and temperature. Analogously for the bubble points, bubble point pressures were calculated. The ideal pressures agreed with the experimental ones within 0.1570 on the average. A detailed comparison is is made in Table 11. It is pertinent to ask what the differences between observed and ideal phase-boundary pressures mean in terms of the activity coefficients y1 and y2. An approximate expression relating deviations in (9) B. H. Sage and W. N. Lacey, “Thermodynamic Properties of the Lighter Paraffin Hydrocarbons and Nitrogen,” Am. Pet. Inst., New York, N. Y., 1955.
P - p(idea1) P
YI - ( I 1/41)ideal/(I1/@1) Y1
c 14)
Although 41 is more sensitive to pressure than 41,’ 42, the variation is slow enough and p is close enough to p(idea1) that the approximate equation of state pv = RT Bp may be applied to eq. 14. Then
+
y1--l=a
p
- p(idea1) I;
where a! g 1 -p(Vi - Bll)/RT, which varies from 0.8 to 0.5 for this system in the temperature range 70 to 130’. Thus the activity coefficients of the 50 : 50 mixture are ideal to roughly the same degree as the phase boundary pressures. Acknowledgments.-The author thanks G. A. Kandalic for his aid in making the measurements and W. A . Junk for his advice. (10) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” Reinhold Publ. Carp., New York, N. Y., 1950, p. 35, 131.
THE DIELECTRIC BEHAVIOR OF VAPORS ADSORBED O X POROUS SOLIDS BY J. IT.THORP Chemastry Department, Unzversity of Auckland. Buckland, S e w Zealand Reeezted December 11, 2961
An investigation has been made of the dielectric behavior (at a frequency of 0.5 Mc./sec.) of water adsorbed on alumina, and of benzene adsorbed on both alumina and silica gel, at 25’. Isosteric heats of sorption, and data relating to pore size distribution, were obtained from the determination of sorption isothermals. For water adsorbed on alumina, the plot of capacitance increment against the amount adsorbed was found to be reversible, for both adsorption and desorption, throughout the entire sorption range. The absence of dielectric hysteresis was considered t o be due to strong adsorbate-adsorbpte interaction, Evidence was obtained for the physical adsorption of a layer of orientated water molecules onto an alumina surface modified by initial chemisorption. The evaluated dielectric constant, €2, for benzene adsorbed entirely in the capilthe literature value for the normal liquid. In lary condensed state, on both alumina and silica gel, compared well with an adsorbed benzene monolayer, el was lower than e l l q on silica gel, but higher (and equal t o e,,lld) on al>mina. The former was considered t o be due t o the interaction of the r-electrons in the benzene monolayer with the silica hydroxyl groups. It was assumed that this interaction was absent v ith alumina, the higher value of el observed with the latter being due to close-packing of the benzene molecules on the surface. Dielectric hysteresis was observed for benzene on alumina, but not o h silica gel. .4n explanation has been given in terms of the uneven electron density in the benzene molecule, together wlth the different polarizing influences of the two adsorbent surfaces.
X previous paper’ reported an investigation of the dielectric behavior of water, methyl alcohol, and ethyl alcohol sorbed on three porous powdered adsorbents: silica gel, alumina, and a mixed silicaferric oxide gel. These systems were chosen primarily with the object of investigating whether the hysteresis phenomena observed in the sorption isotherms also occurred in the plots of incremental (1) J. 11. Thorp. Trans. Faladug Soc., 56, 442 (1959).
electrical capacitance against the amount adsorbed. Such a hysteresis loop was in fact observed, the start coinciding with that of the corresponding loop in the isotherm, indicating the onset of capillary condensation. The hysteresis in the capacitance plot was attributed to the different electrical properties of the polar molecules adsorbed in orientated multilayers, built up simultaneously with capillary condensation during adborption, from those in the
