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Excess enthalpies for (di-n-propyl ether + n-alkane) at 298.15 K
M-2260 J.
Chem. Thermodynamics 1988,20,915-919
Excess enthalpies for (di-n -propyl ether + n -alkane) at 298.15 K LUO WANG, GEORGE C. BENSON, and BENJAMIN C.-Y. LU Department of Chemical Engineering, University of Ottawa, 770 King Edward Avenue, Ottawa, Ontario, Canada KIN 9B4 (Received 26 February
1988)
Calorimetric measurements of excess enthalpies at 298.15 K are reported over the entire compositl”on range for (di-n-propyl ether + n-hexane or n-octane or n-decane or n-dodecane or n-hexadecane). A correlation of the results in terms of the Flory theory of mixtures is described.
1. Introduction Several papers (I-5) from our laboratory have reported excess thermodynamic properties for mixtures of the type (di-n-alkyl either + n-alkane). As a continuation of those investigations, we have measured excess enthalpies at 298.15 K for (di-n-propyl ether + one of the n-alkanes: n-hexane, n-octane, n-decane, n-dodecane, and n-hexadecane).
2. Experimental The di-n-propyl ether, n-octane, n-decane, and n-hexadecane, all with stated purities exceeding 99 moles per cent, were obtained from the Aldrich Chemical Co. The n-hexane (Research Grade) and n-dodecane (Pure Grade) were obtained from the Phillips Petroleum Co. The di-n-propyl ether was stored over Type 4A molecular sieve beads. Apart from this, the component liquids were used without further purification. Their densities P(T = 298.15 K)/(kg.me3), measured in an Anton-Paar densimeter were: 742.77, 654.94, 698.64, 726.25, 745.37, and 770.02 for di-n-propyl ether, n-hexane, n-octane, n-decane, n-dodecane, and n-hexadecane, respectively. Excess enthalpies were determined in an LKB flow-microcalorimeter (Model 10700-l) thermostatted at (298.150+0.002) K. This equipment and its modifications have been described previously. ~3~) Over most of the mole-fraction range, the errors of the excess molar enthalpy Hz and mole fraction x are estimated to be less than 0.5 per cent and 5 x 10e4, respectively. 0021L9614/88/080975+05
%02.00/O
0 1988 Academic Press Limited
976
L. WANG,
G. C. BENSON,
AND
B. C.-Y.
LU
3. Results and discussion The experimental values of HE at 298.15 K for {x(C,H,)~O + (1 - x)C,HZn + l} with n = 6, 8, 10, 12, and 16 are summarized in table 1 and plotted in figure 1. Each set of results was fitted with the smoothing equation: HE/(J*mol-‘)
=
x(1-x)
$J j=l
hj(l-2X)‘-l.
(1)
Values of the coefficients hj, determined by the method of least-squares with all points weighted equally, are listed in table 2 along with the standard deviations s of the representations. Curves calculated from equation (1) are also shown in figure 1, together with a curve representing the smoothed results of our previous investigation of (di-n-propyl ether + n-heptane).‘3’ increases fairly regularly with increasing fC%(C,H,),O + (1 - xW-L+ d chain length of the n-alkane. The curves are nearly symmetrical about x = 0.5, but TABLE
x
1. Excess
ff: J. mole1
molar
x
enthalpies
HE for {x(C,H,),O+(l
HEi
J.mol-’
-x)C.H~.+~}
fE
HEi
’
at 298.15
J,mol-’
’
J.mol-’
K
HE x
J.mol-’
~C,H,),O+(~-~GHI, 0.4991 0.4999 0.5007 0.5486
185.8 186.4 186.5 182.8
0.6004 0.6496 0.7000 0.7502
176.5 166.1 151.7 133.6
0.8000 0.8499 0.9ooo 0.9499
112.5 88.4 60.6 29.2
184.8 203.7 220.4 232.2
4GH,L@+(1 0.4498 0.4994 0.4996 0.5500
-WsH,, 239.0 241.0 241.1 238.6
0.6007 0.6502 0.6995 0.6997
231.2 219.3 202.8 202.9
0.7497 0.7998 0.8498 0.8999
180.5 154.0 121.8 84.7
0.2499 0.3002 0.3504 0.3950
214.1 241.6 260.4 275.1
~(C~H,),O+(~-X)C,,H,, 0.4499 0.5001 0.5009 0.5500
286.1 291.7 292.7 291.9
0.6003 0.6497 0.6999 0.7499
284.9 273.4 254.2 229.1
0.7993 0.8503 0.9002 0.9500
197.8 158.1 112.2 58.3
57.4 115.0 165.9 213.3 211.8
0.2501 0.2999 0.3503 0.3995
252.5 286.8 312.3 330.7
xGH,),O +(I 0.4497 0.4995 0.5009 0.5495
-x)C&,, 344.7 351.9 352.5 353.1
0.5999 0.6499 0.6997 0.7498
346.5 332.9 312.2 282.9
0.7997 0.8500 0.8997 0.9499
245.2 198.4 142.6 75.9
77.3 152.4 220.8 280.9
0.2501 0.3002 0.3501 0.3998
335.4 383.2 422.4 451.2
x(C,H,),O+(l-x)C,,H,, 0.4502 0.4996 0.5002 0.5510
469.5 483.3 482.3 486.9
0.6001 0.6501 0.7002 0.7500
480.3 464.5 437.1 400.2
0.7988 0.8500 0.9001 0.9500
351.2 286.8 208.1 113.1
0.0500 0.1000 0.1000 0.1499 0.2001
36.8 72.0 72.0 101.9 127.8
0.2502 0.2999 0.3502 0.3993 0.4492
146.2 162.6 174.3 182.1 185.5
0.0499 0.0998 0.1001 0.1499 0.2000
44.8 86.7 88.1 124.9 158.2
0.2497 0.2999 0.3498 0.4000
0.0500 0.1000 0.1500 0.2001
49.4 98.3 141.4 180.3
0.0500 0.1000 0.1501 0.2001 0.2002 0.0499 0.0998 0.1500 0.2001
977
FIGURE 1. Excess molar enthalpies Hk for {x(C,H,),O+(l -x)C,,H~~+~} at 298.15 K. Experimental results: 0, n = 6; 0, n = 8; A, n = 10; 0, n = 12; V, n = 16. --, Calculated from equation (1); , n = 7 from reference 3; - - -, calculated from the Flory theory with x12 from equation (2).
there is a slight skew toward x = 1, which becomes more evident for the longer n-alkanes. We are not aware of any directly comparable studies of the present mixtures. IliC and MaksimoviC@) measured the limiting excess partial molar enthalpies H,E,m of several di-n-alkyl ethers at infinite dilution in n-hexane. For di-n-propyl ether, they reported HF a, = (880+40) J. mol-‘. This is about 7 per cent higher than the value (817+4) J. mol-l derived from the representation of our results by equation (1). TABLE
2. Coefficients hi and standard deviation s for least-squares representations {x(C,H,),O + (l-x)C,H,,+,} at 298.15 K by equation (1) n
hl
h,
6 8 10 12 16
745.9 967.0 1172.8 1408.4 1934.2
71.3 14.8 -88.8 - 144.9 - 306.2
h,
114.2 110.0
h,
-73.4 - 134.0
hs
- 142.7
of HE s 1.1 1.0 1.4 0.6 1.0
for
978 TABLE
L. WANG, 3. Component
v, Component (C,W,O
C&L Wh, GH,s CIO% ‘&Hz, GdL
cm3 ‘mol-’ 137.72 131.57 147.45 163.50 195.94 228.55 294.07
properties
and
%
G. C. BENSON,
AND
B. C.-Y.
parameters used in calculations 298.15 K by the Flory theory
__-KT
kK-’
TPa-’
1.261 1.387 1.256 1.164 1.051 0.960 0.883
1436.6 1703.9 1460.6 1302.4 1109.6 987.6 862.0
P* J.Cm3 441.5 424.2 431.9 436.8 447.0 445.2 457.0
V,* cm3.mol-’ 106.03 99.52 113.60 127.70 155.75 184.40 240.41
LU
for
T*
{x(C,H,),O+(l
St2
X 4639.2 4436.1 4648.1 4827.0 5091.4 5351.4 5614.7
-x)C,H~~+~}
xIZl(J.cm-7 Fit of
0.9791 1.0233 1.0639 1.1368 1.2026 1.3137
at
Hi
6.843 7.127 8.187 9.626 11.439 14.937
Eqn.
(2)
6.515 7.344 8.173 9.831 11.489 14.805
However, this discrepancy seems reasonable since our measurements did not extend to very high dilutions of the ether. Previously we found that the excess enthalpies of (diethyl ether + n-alkane)‘4’ and (di-n-butyl ether + n-alkane)@) could be correlated by the Flory theory.“, lo) The same treatment was applied to the present mixtures. The calculations used the molar volumes V,, isobaric expansivities clp, and isothermal compressibilities I+, listed for the components in table 3. These are taken from our previous publications. CL’) The corresponding characteristic pressures p*, molar volumes V,*, and temperatures T*, obtained from the Flory formalism, are also summarized in table 3, together with the ratio sIZ of (ether-to-alkane) molecular surface areas of
FIGURE 2. Interchange-energy alkane molecule. 0, From fit of
Hi
parameter (column
xlz p lotted against 9 in table 3); -,
the number n of carbon atoms plotted from equation (2).
in the
979
contact per segment and the interchange-energy parameter xIz for each mixture. The values of s12 are based on the simple assumption that the molecules are spherical. The values of x12, gr‘ven in the second last column of table 3, were obtained from least-squares analyses in which the Flory formula for the excess enthalpy was fitted to the representations of the experimental results by equation (1). As found previously, (4,5) the parameter xIz increases nearly linearly with the number n of carbon atoms in the alkane molecule. This is illustrated in figure 2, where the line: ~~~/(J.crn-~) = 1.541+0.829n,
(2)
corresponding to a coefficient of correlation r = 99.77 per cent, is shown. Values of xIz calculated from equation (2) are listed in the last column of table 3, and curves obtained from the Flory theory with these values are plotted in figure 1. Although the curves estimated from the theory are slightly more skewed toward x = 1, the agreement with the experimental curves is reasonable, and suggests that the Flory theory in combination with equation (2) can provide useful estimates of HE for (di-n-propyl ether + an n-alkane having chain length between 6 and 16). The authors are indebted to the Natural Sciences and Engineering Research Council of Canada for financial support. REFERENCES 1. Treszczanowicz, T.; Lu, B. C.-Y. Bull. Acad. Polon. Sci., Ser. xi. chim. 1981, 29, 28.5. 2. Kimura, F.; Treszczanowicz, A. J.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1983, 15, 503. 3. Kumura, F., D’Arcy, P. J.; Benson, G. C. J. Chem. Thermodynamics 1983, 15, 511. 4. Luo, B.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1988, 20, 261. 5. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531. 6. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163. 7. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245. 8. Ilit, Z. E.; Maksimovie, Z. B. Bull. Sot. Chim. Beograd 1981, 46, 551. 9. Flory, P. J. J. Am. Chem. Sot. 1%5, 87, 1833. 10. Abe, A.; Flory, P.‘J. J. Am. Chem. Sot. 1965, 87, 1838.
Chem. Thermodynamics 1988,20,915-919
Excess enthalpies for (di-n -propyl ether + n -alkane) at 298.15 K LUO WANG, GEORGE C. BENSON, and BENJAMIN C.-Y. LU Department of Chemical Engineering, University of Ottawa, 770 King Edward Avenue, Ottawa, Ontario, Canada KIN 9B4 (Received 26 February
1988)
Calorimetric measurements of excess enthalpies at 298.15 K are reported over the entire compositl”on range for (di-n-propyl ether + n-hexane or n-octane or n-decane or n-dodecane or n-hexadecane). A correlation of the results in terms of the Flory theory of mixtures is described.
1. Introduction Several papers (I-5) from our laboratory have reported excess thermodynamic properties for mixtures of the type (di-n-alkyl either + n-alkane). As a continuation of those investigations, we have measured excess enthalpies at 298.15 K for (di-n-propyl ether + one of the n-alkanes: n-hexane, n-octane, n-decane, n-dodecane, and n-hexadecane).
2. Experimental The di-n-propyl ether, n-octane, n-decane, and n-hexadecane, all with stated purities exceeding 99 moles per cent, were obtained from the Aldrich Chemical Co. The n-hexane (Research Grade) and n-dodecane (Pure Grade) were obtained from the Phillips Petroleum Co. The di-n-propyl ether was stored over Type 4A molecular sieve beads. Apart from this, the component liquids were used without further purification. Their densities P(T = 298.15 K)/(kg.me3), measured in an Anton-Paar densimeter were: 742.77, 654.94, 698.64, 726.25, 745.37, and 770.02 for di-n-propyl ether, n-hexane, n-octane, n-decane, n-dodecane, and n-hexadecane, respectively. Excess enthalpies were determined in an LKB flow-microcalorimeter (Model 10700-l) thermostatted at (298.150+0.002) K. This equipment and its modifications have been described previously. ~3~) Over most of the mole-fraction range, the errors of the excess molar enthalpy Hz and mole fraction x are estimated to be less than 0.5 per cent and 5 x 10e4, respectively. 0021L9614/88/080975+05
%02.00/O
0 1988 Academic Press Limited
976
L. WANG,
G. C. BENSON,
AND
B. C.-Y.
LU
3. Results and discussion The experimental values of HE at 298.15 K for {x(C,H,)~O + (1 - x)C,HZn + l} with n = 6, 8, 10, 12, and 16 are summarized in table 1 and plotted in figure 1. Each set of results was fitted with the smoothing equation: HE/(J*mol-‘)
=
x(1-x)
$J j=l
hj(l-2X)‘-l.
(1)
Values of the coefficients hj, determined by the method of least-squares with all points weighted equally, are listed in table 2 along with the standard deviations s of the representations. Curves calculated from equation (1) are also shown in figure 1, together with a curve representing the smoothed results of our previous investigation of (di-n-propyl ether + n-heptane).‘3’ increases fairly regularly with increasing fC%(C,H,),O + (1 - xW-L+ d chain length of the n-alkane. The curves are nearly symmetrical about x = 0.5, but TABLE
x
1. Excess
ff: J. mole1
molar
x
enthalpies
HE for {x(C,H,),O+(l
HEi
J.mol-’
-x)C.H~.+~}
fE
HEi
’
at 298.15
J,mol-’
’
J.mol-’
K
HE x
J.mol-’
~C,H,),O+(~-~GHI, 0.4991 0.4999 0.5007 0.5486
185.8 186.4 186.5 182.8
0.6004 0.6496 0.7000 0.7502
176.5 166.1 151.7 133.6
0.8000 0.8499 0.9ooo 0.9499
112.5 88.4 60.6 29.2
184.8 203.7 220.4 232.2
4GH,L@+(1 0.4498 0.4994 0.4996 0.5500
-WsH,, 239.0 241.0 241.1 238.6
0.6007 0.6502 0.6995 0.6997
231.2 219.3 202.8 202.9
0.7497 0.7998 0.8498 0.8999
180.5 154.0 121.8 84.7
0.2499 0.3002 0.3504 0.3950
214.1 241.6 260.4 275.1
~(C~H,),O+(~-X)C,,H,, 0.4499 0.5001 0.5009 0.5500
286.1 291.7 292.7 291.9
0.6003 0.6497 0.6999 0.7499
284.9 273.4 254.2 229.1
0.7993 0.8503 0.9002 0.9500
197.8 158.1 112.2 58.3
57.4 115.0 165.9 213.3 211.8
0.2501 0.2999 0.3503 0.3995
252.5 286.8 312.3 330.7
xGH,),O +(I 0.4497 0.4995 0.5009 0.5495
-x)C&,, 344.7 351.9 352.5 353.1
0.5999 0.6499 0.6997 0.7498
346.5 332.9 312.2 282.9
0.7997 0.8500 0.8997 0.9499
245.2 198.4 142.6 75.9
77.3 152.4 220.8 280.9
0.2501 0.3002 0.3501 0.3998
335.4 383.2 422.4 451.2
x(C,H,),O+(l-x)C,,H,, 0.4502 0.4996 0.5002 0.5510
469.5 483.3 482.3 486.9
0.6001 0.6501 0.7002 0.7500
480.3 464.5 437.1 400.2
0.7988 0.8500 0.9001 0.9500
351.2 286.8 208.1 113.1
0.0500 0.1000 0.1000 0.1499 0.2001
36.8 72.0 72.0 101.9 127.8
0.2502 0.2999 0.3502 0.3993 0.4492
146.2 162.6 174.3 182.1 185.5
0.0499 0.0998 0.1001 0.1499 0.2000
44.8 86.7 88.1 124.9 158.2
0.2497 0.2999 0.3498 0.4000
0.0500 0.1000 0.1500 0.2001
49.4 98.3 141.4 180.3
0.0500 0.1000 0.1501 0.2001 0.2002 0.0499 0.0998 0.1500 0.2001
977
FIGURE 1. Excess molar enthalpies Hk for {x(C,H,),O+(l -x)C,,H~~+~} at 298.15 K. Experimental results: 0, n = 6; 0, n = 8; A, n = 10; 0, n = 12; V, n = 16. --, Calculated from equation (1); , n = 7 from reference 3; - - -, calculated from the Flory theory with x12 from equation (2).
there is a slight skew toward x = 1, which becomes more evident for the longer n-alkanes. We are not aware of any directly comparable studies of the present mixtures. IliC and MaksimoviC@) measured the limiting excess partial molar enthalpies H,E,m of several di-n-alkyl ethers at infinite dilution in n-hexane. For di-n-propyl ether, they reported HF a, = (880+40) J. mol-‘. This is about 7 per cent higher than the value (817+4) J. mol-l derived from the representation of our results by equation (1). TABLE
2. Coefficients hi and standard deviation s for least-squares representations {x(C,H,),O + (l-x)C,H,,+,} at 298.15 K by equation (1) n
hl
h,
6 8 10 12 16
745.9 967.0 1172.8 1408.4 1934.2
71.3 14.8 -88.8 - 144.9 - 306.2
h,
114.2 110.0
h,
-73.4 - 134.0
hs
- 142.7
of HE s 1.1 1.0 1.4 0.6 1.0
for
978 TABLE
L. WANG, 3. Component
v, Component (C,W,O
C&L Wh, GH,s CIO% ‘&Hz, GdL
cm3 ‘mol-’ 137.72 131.57 147.45 163.50 195.94 228.55 294.07
properties
and
%
G. C. BENSON,
AND
B. C.-Y.
parameters used in calculations 298.15 K by the Flory theory
__-KT
kK-’
TPa-’
1.261 1.387 1.256 1.164 1.051 0.960 0.883
1436.6 1703.9 1460.6 1302.4 1109.6 987.6 862.0
P* J.Cm3 441.5 424.2 431.9 436.8 447.0 445.2 457.0
V,* cm3.mol-’ 106.03 99.52 113.60 127.70 155.75 184.40 240.41
LU
for
T*
{x(C,H,),O+(l
St2
X 4639.2 4436.1 4648.1 4827.0 5091.4 5351.4 5614.7
-x)C,H~~+~}
xIZl(J.cm-7 Fit of
0.9791 1.0233 1.0639 1.1368 1.2026 1.3137
at
Hi
6.843 7.127 8.187 9.626 11.439 14.937
Eqn.
(2)
6.515 7.344 8.173 9.831 11.489 14.805
However, this discrepancy seems reasonable since our measurements did not extend to very high dilutions of the ether. Previously we found that the excess enthalpies of (diethyl ether + n-alkane)‘4’ and (di-n-butyl ether + n-alkane)@) could be correlated by the Flory theory.“, lo) The same treatment was applied to the present mixtures. The calculations used the molar volumes V,, isobaric expansivities clp, and isothermal compressibilities I+, listed for the components in table 3. These are taken from our previous publications. CL’) The corresponding characteristic pressures p*, molar volumes V,*, and temperatures T*, obtained from the Flory formalism, are also summarized in table 3, together with the ratio sIZ of (ether-to-alkane) molecular surface areas of
FIGURE 2. Interchange-energy alkane molecule. 0, From fit of
Hi
parameter (column
xlz p lotted against 9 in table 3); -,
the number n of carbon atoms plotted from equation (2).
in the
979
contact per segment and the interchange-energy parameter xIz for each mixture. The values of s12 are based on the simple assumption that the molecules are spherical. The values of x12, gr‘ven in the second last column of table 3, were obtained from least-squares analyses in which the Flory formula for the excess enthalpy was fitted to the representations of the experimental results by equation (1). As found previously, (4,5) the parameter xIz increases nearly linearly with the number n of carbon atoms in the alkane molecule. This is illustrated in figure 2, where the line: ~~~/(J.crn-~) = 1.541+0.829n,
(2)
corresponding to a coefficient of correlation r = 99.77 per cent, is shown. Values of xIz calculated from equation (2) are listed in the last column of table 3, and curves obtained from the Flory theory with these values are plotted in figure 1. Although the curves estimated from the theory are slightly more skewed toward x = 1, the agreement with the experimental curves is reasonable, and suggests that the Flory theory in combination with equation (2) can provide useful estimates of HE for (di-n-propyl ether + an n-alkane having chain length between 6 and 16). The authors are indebted to the Natural Sciences and Engineering Research Council of Canada for financial support. REFERENCES 1. Treszczanowicz, T.; Lu, B. C.-Y. Bull. Acad. Polon. Sci., Ser. xi. chim. 1981, 29, 28.5. 2. Kimura, F.; Treszczanowicz, A. J.; Halpin, C. J.; Benson, G. C. J. Chem. Thermodynamics 1983, 15, 503. 3. Kumura, F., D’Arcy, P. J.; Benson, G. C. J. Chem. Thermodynamics 1983, 15, 511. 4. Luo, B.; Benson, G. C.; Lu, B. C.-Y. J. Chem. Thermodynamics 1988, 20, 261. 5. Benson, G. C.; Luo, B.; Lu, B. C.-Y. Can. J. Chem. 1988, 66, 531. 6. Tanaka, R.; D’Arcy, P. J.; Benson, G. C. Thermochim. Acta 1975, 11, 163. 7. Kimura, F.; Benson, G. C.; Halpin, C. J. Fluid Phase Equilib. 1983, 11, 245. 8. Ilit, Z. E.; Maksimovie, Z. B. Bull. Sot. Chim. Beograd 1981, 46, 551. 9. Flory, P. J. J. Am. Chem. Sot. 1%5, 87, 1833. 10. Abe, A.; Flory, P.‘J. J. Am. Chem. Sot. 1965, 87, 1838.