Thermal Conductivity of Gases Organic Compounds at Atmospheric Pressure Dipak Roy1 and George Thodos Northwestern University, Evanston, Ill. 60201
Thermal conductivity measurements, k*, available in the literature for organic compounds in their gaseous state and at atmospheric pressure, were used to obtain the product, k*X, where the parameter, X = M1/2Jc1/6/Pc2/3, This product is temperature-dependent and represents the composite contributions of translational, rotational, and vibrational modes of energy transfer. The translational contribution, (k*X),, is identical (k*X), = XI represents the contribution due to vibrational to k*X for monatomic gases. The difference, k*X and rotational effects. Specific relationships of X / X 1 vs. J R were obtained for the alcohols, oxygen-containing compounds (esters, ketones, aldehydes), halides, amines, and cyclics. Group contributions were also developed which permit the establishment of XI, the value of X at TR = l .OO for these classes of compounds. Thermal conductivities calculated for 52 organic compounds were compared with corresponding experimental values to produce an average deviation of 3.0% for 291 points considered.
-
THE
ESTIMATION of thermal conductivities of polyatomic gases a t normal pressures from theoretical deductions (Eucken, 1913; Hirschfelder et al., 1954) has been limited to simple gases. For gases consisting of more than two atoms, considerable disparity is found to exist between calculated and experimental values (Groenier and Thodos, 1961; Kennedy and Thodos, 1961). These differences can be attributed to the incomplete understanding of the actual mechanics associated with the different modes of energy transfer in polyatomic molecules. A rigorous theoretical treatment requires a comprehensive understanding of the steps associated with the individual translational, rotational, and vibrational contributions for the prediction of thermal conductivity. Following a dimensional analysis approach, similar to that outlined by Llathur and Thodos (1965), IC*, the thermal conductivity of a gas a t normal pressures, can be related to temperature by the following relationship :
k*X = C Z Z , ~ T R ~
ments available for neon, argon, krypton, and xenon were used to produce the relationship of (k*X)t us. T Rpresented in Figure 1. This relationship can be expressed in equation form as follows (Roy and Thodos, 1968s) : (k*),)t = 9.96 X 10-5[e0.04642’~ - e-0.2412TR 1 (3)
+
Equation 3 permits the calculation of (k*X), (k*X), as the difference, k*h Since the products @*A), and (k*X), cannot be evaluated individually, their composite contribution will be treated as a function of TRand defined as follows:
+
+ (k*X),
(2)
Present address, Institute of Gas Technology, Chicago, Ill.
60616
- (k*h)t
(4)
(1)
The product (?C*X)~ for polyatomic gases is identical to k*A for the monatomic gases which possess only translational mode of energy transfer. Thermal conductivity measure1
k*X
=
The dependence of X on TR for a polyatomic gas is to be established from thermal conductivity measurements. Information of this type should assist in the development of patterns associated with the general behavior of X on TR for different substances. I
where the thermal conductivity parameter, = M112T,1/6/ P,2’a.I n their study dealing with different diatomic gases, for which z , varies from 0.294 to 0.251, Roy and Thodos (1968a) established that k*X is independent of z, and therefore exponent m in Equation 1 is essentially zero. Hence, for a gas, the product k*h becomes only a function of TR. I n a study dealing with the thermal conductivity of hydrocarbon gases a t normal pressures, Roy and Thodos (1968b) assumed the product k*X to result from the translational, rotational, and vibrational modes of energy transfer as follows : k*X = (k*X)t
+ @*A),
x=
I
I
I
fl-
I I I I I
IC-
II I I I 0,4
0298 o Argon 0291 0 Krypton 0291 4 Xenon 0.290
x
tY
I I1
0.6 0.8 1.0
I
Monatomic Gases
0 Neon
2
I
I
I
I
2
3
4
M h 2018 39.94 8380 131.30
I I 1 1 1 1 6 810
1530 1099 1.558 1.976
I 20
I
30
TR Figure 1 . Relationship between (k*X)$ and TR for gases at normal pressures VOL. 9 NO. 1 FEBRUARY 1970
I&EC FUNDAMENTALS
71
Table 1.
Basic and Related Constants, Sources of Thermal Conductivity Measurements, and Average Deviations for a Number of Organic Compounds XI, Value of X a t r R = 1.00 Sources of No. of M T,, O K Po Atm A Actual Calcd. Exptl. Data Points Dev., %
Alcohols 5.14 X l o - & 5.14 X 10+ Abas-zade (1954), Abas20 zade and Amiraslanov (1957), Lambert et al. (1950), Moser (1913), Shushpanov (1939),Vines and Bennett (1954) Abas-zade (1954), Abas18 8.35 8.35 zade and Amiraslanov (1957), Moser (1913), Shushpanov (1939) Abas-zade and Amirasla- 20 12.60 11.39 nov (1957) Shushpanov (1939) Shushpanov (1939) 11.40 11.40 16 Shushpanov (1939) 15.60 15.57 18 Shushpanov (1939) 14.90 14.90 18 21.20 20.76 Shushpanov (1939) 17 21.00 20.93 Shushpanov (1939) 18
Methanol
32.04 513.2 78.5 0.874
Ethyl alcohol
46.07 516.3 62.96 1.215
n-Propyl alcohol
60.09 537.2 50.2
Isopropyl alcohol %-Butyl alcohol Isobutyl alcohol n-Amyl alcohol. Isoamyl alcohol.
60.09 74.12 74.12 88.15 88.15
Acetaldehyde
Oxygen-Containing Compounds 5.30 44.05 461.2 54.7 1.280 5.30
Acetone
58.08 508.7
9.90
9.90
Methyl acetate Ethyl formate Ethyl acetate
74.08 506.9 46.3 1.885 11.50 74.08 508.5 46.8 1.872 12.00 88.10 523.3 37.8 2.366 16.25
11.50 12.00 16.25
Diethyl ether
74.12 467.2 35.6 2.321 15.90
15.90
Methylamine Ethylamine n-Propylamine Isobutylamine n-Amylamine Dimethylamine Diethylamine
31.06 45.08 59.11 73.14 87.16 45.08 73.14
Amines 3.79 7.55 12.50 18.25 25.50 7.55 17.90
3.79 7.55 12.50 18.25 25.01 7.55 17.73
101.19 550.2 31.0 2.918 27.70 59.11 433.3 40.2 1.802 10.50 101.19 550.2 30.0 2.966 26.80
27.86 10.50 26.80
Di-n-propylamine Trimethylamine Triethylamine
508.8 561.2 538.2 574.0 580.2
430.1 456.2 497.0 526.4 563.2 437.7 496.2
53.0 49.0 44.5 37.4 38.3
1.618 1.552 1.847 1.955 2.458 2.386
46.6 1.663
73.6 55.5 46.8 40.7 35.2 52.4 36.6
0.872 1.280 1.666 2.054 2.498 1.321 2.183
Nitriles 7.00
7.00
Acetonitrile
41.05 547.9 47.7 1.394
Propionitrile Acrylic nitrile
55.08 564.4 41.3 1.786 11.20 53.06 535.9 44.2 1.661 8.90
Methyl chloride
50.49 416.3 65.9 1.190
Halides 2.40
2.40
Methyl bromide
94.95 464.2 83.4 1.420
2.60
2.60
72
l&EC FUNDAMENTALS
VOL 9 NO. 1 FEBRUARY 1970
10.73 9.38
Lambert et al. (1950), Milverton (1935),Vines and Bennett (1954) Abas-zade (1954), Moser (1913), Vines and Bennett (1954) Vines and Bennett (1954) Vinesand Bennett (1954) Moser (1913), Vines and Bennett (1954) Abas-zade (1954), Lambert et a1 (1950), Moser (1913), Senftleben and Gladisch (1949), Vines and Bennett (1954) Hofker (1892) Hofker (1892) Hofker (1892) Hofker (1892) Hofker (1892) Hofker (1892) Hofker (1892), Vines and Bennett (1954) Hijfker (1892) Hofker (1892) Hofker (1892), Vines and Bennett (1954)
2.07
6.10 0.44 0.84 3.81 6.15 9.62
8
2.47
4
1.20
5 2 3
0.91 1.83 1.28
7
2.21
1 1 1 1 1
0.00 0.00 0.85 1.21 3.47 0.68 0.95
1 3 1 1
3
Lambert et al. (1950), Vines 6 and Bennett (1954) Vines and Bennett (1954) 1 Senftleben (1953) 1 Moser (1913), Senftleben (1953), Senftleben and Gladisch (1949), Vines and Bennett (1954) Moser (1913), Senftleben and Gladisch (1949), Vines and Bennett (1954)
2.29 ~-
2.53 0.71 0.59
1,87 4.42 2.02
5
2.29
4
3.59
Table 1. M
Methyl iodide
re,
O K
P,, Atm
X
141.95 528.0 72.7 1.945
(Continued)
X I , Value of X at Actual
TR
= 1.00 Calcd.
Halides 3.90
3.90
Methylene chloride
84.94 510.2 60.0 1.688
4.65
4.73
Methylene bromide Chloroform
173.86 614.1 70.8 2.262 119.39 536.6 54.0 2.231
5.80 7.20
5.80 7.06
Carbon tetrafluoride
88.01
229.0 42.10 1,918
2.40
2.41
Ethyl chloride
64.52
460.4 52.0 1.617
6.70
6.43
Ethyl bromidea Ethyl iodide. Dichloroethane
108.98 503.9 6 1 . 5 1.891 . . . 155.98 562.4 59.2 2.362 . . . 98.97 561.0 53.0 2.025 10.20
9.76
Trichloroethane Ethylidene chloride Trichlorofluoromethane (Freon 11) Dichlorodifluoromethane (Freon 12)
133.42 571.2 45.7 2.603 12.60 99.02 523.0 50.0 2.081 9.10 137.38 471.2 43.2 2.656 7.80
13.09 9.76 8.11
120.92 384.7 39.6 2.553
6.10
6.21
Chlorotrifluoromethane (Freon 13) Dichlorofluoromethane (Freon 21) Chlorodifluoromethane (Freon 22) Trichlorotrifluoroethane (Freon 113)a Dichlorotetrafluoroethane (Freon 114)
104.47 302.0 39.0 2.302
4.20
4.31
102.93 451.7 51 . O 2.044
5.78
5.78
86.47 369.6 48.5 1 ,873
4.10
3.88
Ethylene oxide
... ...
187.39 487.3 33.7 3,681 14.20 (?)
15.07
170.94 418.9
12.40
44.05 468.2
32.3 3.526 12.40
Cyclic Compounds 71.0 1.079 5.30 4.86
18.62 88.10 585.0 50.7 1.982 17.75 Dioxane 20.73 Piperidine 85.15 585.0 46.7 2.058 20.75 14.98 79.10 617.4 60.0 1.693 15.00 Pyridine 14.99 84.13 590.0 48.0 2.011 15.00 Thiophene a Estimated criticals (Hougen et al., 1984); values of X may be somewhat inaccurate.
No. of
Sources of Exptl. Data
Points
Rloser (1913), Vines and Bennett (1954) Moser (1913), Senftleben and Gladisch (1949) Masi&et al. (1964) Lambert et al. (1950) Noser (1913), Vines and Bennett (1954) Lambert et al. (1955), hlasi&et al. (1964) Keyes (1954), Lambert et al. (1950), Noser (1913), Senftleben (1953), Senftben and Gladisch (1949), Vines and Bennett (1954) &loser (1913) &loser (1913) Senftleben (1953), Vines and Bennett (1954) Senftleben (1953) Vines and Bennett (1954) Markwood and Benning (1943) Keyes (1964), hIarkwood and Benning (1943), Masis et al. (1964), Sherratt and Griffiths (1939) Rlasiit et al. (1964)
Dev., %
4
3.30
1
1.27
6 5
0.42 1.17
9
0.54
6
2.71
..
... ...
.. 1
2.12
1 1 1
2.40 5.29 3.77
13
2.02
8
1.79
Markwood and Benning 9 5 . 5 6 (1943), hlasihet al. (1964) Markwood and Benning 8 2.59 (1943), RlasiA et al. (1964) Markwood and Benning . . . . . . (1943) Keyes (1954), Markwood 4 1 . 8 5 and Benning (1943) Senftleben (1953), Vines and Bennett (1954) Vines and Bennett (1954) Vines and Bennett (1954) Vines and Bennett (1954) Vines and Bennett (1954)
4 0.95 2 2.92 1 1.15 1 0.84 1 2.45
Treatment of Thermal Conductivity Measurements
or
The approach adopted for the treatment of thermal conductivities of organic compounds follows that already presented for hydrocarbons. In a similar study involving hydrocarbons (Roy and Thodos, 1968b), the log X us. log TR relationships for the same types of hydrocarbons were parallel. This behavior suggests that the relationship for a specific substance can be expressed in equation form as follows: log X = Slog TR log C (5)
X (7) XI Thus, the relationships of X / X l us. TR for the different members of the same class of hydrocarbons are superimposed into a single relationship which passes through the point X / X I = 1.0 and TR = 1.0. Equation 7 suggests that the exponent, s, be established as a function of T R . However, since any power function can be expressed as a polynomial, it becomes more convenient to define X / X 1 as a function of T R as follows: X - = (YTR OT,' . ~TR' ~ T R ~ (8)
+
where s = f(TR)and C is a constant, specific to the substance. Substituting the value X = XI a t T R = 1.0 in Equation 5, it follows that C = XI. Thus, Equation 5 can be expressed in the alternate form as X log - = log TR' (6) x 1
- = TRS
XI
+
+
+
+.
In their study, Roy and Thodos (1968b) found that for the different types of hydrocarbons, a third-order polynomial VOL. 9 NO. 1 FEBRUARY 1970
I&EC FUNDAMENTALS
73
2c
IC
s E I
Alcohols
**
zg € *A Y
+
!
Methyl Alcohol 0874 Ethyl Alcohol 1215 1618 + $-PropylAlcohol 1552 0 n-Butyl Alcohol 1847 I-Butyl Alcohol 1955 o n-Amyl Alcohol 2458 (-Amyl Alcohol 2386
0
e
0 n-Propyl Alcohol
4 2 5 4 II
X
Figure 3.
i
I
I
I
I
I
I
05
06
07
00
09
10
TR Relationship between
0.90.8-
X/X1
and
514~16~ 835 1260 1140 1560 1490 2120 2100
5 TR
for alcohols
Oxygen Containing Compounds
AI-
P I.c (
o Acetaldehyde
5.30~16'
Acetone Methyl Acetate Ethyl Formate 0 Diethyl Ether o Ethyl Acetate
990
+
xtx-
0.5
0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.5
11.50 12.00 15.90 16.25
0.4, Figure 2. hols
Relationships between X and TE for typical alco-
0.3
adequately expressed this behavior with an average deviation of less than 0.5%. T o use Equation 8, XI was obtained by the use of group contributions involved in the replacement of hydrogen atoms by methyl groups for the synthesis of molecular structures of saturated aliphatic hydrocarbons. For unsaturated aliphatic hydrocarbons, naphthenes, and aromatics, alternative schemes are presented for the evaluation of XI. Thermal conductivity measurements available in the literature for alcohols, oxygen-containing compounds (esters, ketones, aldehydes), halides, amines, and cyclics were collected and their corresponding k*A values were calculated. The basic and related constants of each of the 52 organic compounds used in this investigation and their sources of data are presented in Table I. The critical constants reported by Kobe and Lynn (1953) were consulted for those compounds for which these values are available. Otherwise, these critical values were estimated by the method of Lydersen (Hougen el al., 1954). Alcohols. The available thermal conductivities of the alcohols presented in Table I were used to obtain their k*A values. With Equation 3, the (k*A) values, corresponding t o the temperatures of these thermal conductivity measurements, were calculated in order to obtain the difference, 74
l&EC FUNDAMENTALS
VOL. 9 NO. 1 FEBRUARY 1970
1
0.2 0.2
+
= 10.082T: + O .l 4T :+ ;
0.3
3 T l;i
I
,
0.5 0.6 0.70.80.91.0
0.4
TR Figure 4. Relationship between X/X1 and TR for a number of oxygen-containg compounds
k*A
-
(k*A)t. These differences which correspond to X =
+ @*A),
were plotted against TR,using log-log coordinates, to obtain the relationships presented in Figure 2. These relationships are nearly parallel and linear and indicate that s is essentially constant for alcohols. Extrapolations of these relationships to TR = 1.0 give the value of X1 for each alcohol. These XI values are also presented in Table I and were used to obtain the ratio X/X1 which when related to T g produced the single relationship presented in Figure 3 for alcohols. This relationship is essentially linear when plotted on log-log coordinates, and has a slope, s = 2.0. Therefore, for alcohols, Equation 7 becomes @*A),
-X -x 1
TR2
(9)
I
."
-
I
0.9 0.8 0.7-
I
l
l
Amines 3,
Primary Amines 0 Methyl Amine o Ethyl Amine 0 n-Propyl Amine i-Butyl Amine a n-Amyl Amine
0.6-
3.79~16~ 255 12.5 18.25 25.5
*
-
0.5
xix-
I
0.4-
0'3t
Secondary Amines A Dimethyl Amine v Diethyl Amine D Di-n-Propyl Amine
7,55 179 27.7
09 08 -
Tertiary Amines + Trimethyl Amine x Triethyl Amine
07 -
Alkyl Halides
06 -
p
Q Methyl Chloride, CH,CI
05 -
0 Methyl Bromide, CH,Br
0 Methyl Iodide, CH,I Methylene Chloride, CH,CI, Methylene Bromide, CH,Br, 0 Chloroform, CHCI, 0 Carbon Tetrafluoride. CF, 0 Ethyl Chloride, C,H$ Dichloroethane, CH2CICH,CI Trichloroethane, CH,CCI, Ethylidene Chloride, CH,CHCI,
04 -
11.2 89
I X = 0.633T; XI
+ 0.367T:
+
+
$ 0.3 0.4 0.5 0.6 07 0.80.9 1.0
0.10 0.2
02
04
0 5 06 07 0809 IO
TR
Oxygen-Containing Compounds. Experimental thermal conductivities for acetaldehyde, acetone, methyl and ethyl acetates, ethyl formate, and diethyl ether were used to obtain values of X. These values when plotted against T R produced individual relationships for each of these compounds. These relationships were essentially parallel to each other and when extrapolated to T R = 1.00, the XI values presented in Table I resulted for each compound. A plot of the ratio X/XI us. T R on log-log coordinates produced the single relationship presented in Figure 4.This relationship is linear with a slope of 2.16; however, it has been expressed in the form of Equation 8 as the polynomial, =
+ 1 045T~'+ 0 0 3 7 T ~ ~
-0 0 8 2 T ~
(10)
Amines and Nitriles. The same approach was applied to the thermal conductivities available for three nitriles and 10 primary, secondary, and tertiary amines. These specific compounds are presented in Table I along with their sources of data and related basic constants. For these two classes of compounds, a single X/Xl us. T R relationship was obtained. This relationship is presented in Figure 5, on log-log coordinates, and is essentially linear with a slope of 2.30. It has also been expressed in polynomial form according to Equation 8 to yield the expression:
-X_ x 1
0 633T~'
+ 0.367TR3
2
3
TI7
Figure 5. Relationship between X / X 1 and TR for amines and nitriles
X X1
465 580 720 240 6 70 102 126 910
+
(11)
Halides. Thermal conductivity measurements available in the literature for 12 alkyl halides and seven Freons provided the necessary information to establish the X1 values presented in Table I. The X us. T R relationships for these conipounds were found to be essentially parallel. The resulting X/Xl us. TR relationships for the alkyl halides and Freons are
Figure 6. halides
c
Relationship between X / X l and TR for alkyl
= -0.107TR+1.33OT~-O.223T~
2
xlx-
-
1.0
0.90.8-
Freons
0.60.7
Freon I I , CC1.F Freon 12, CC1;5 Freon 13, CCIF, Freon 21, CHCI,F Freon 22, C H i F , Freon 113, C,CI,F, Freon 114, CC , F,I,
0.5 -
0.40,3
I
presented in Figures 6 and 7 , respectively. The relationships of these figures are basically identical and can be expressed in the form of Equation 8 as follows:
X XI
- = -0.107T~
+ 1.330T~'- 0.223TR3
(12)
Cyclic Compounds. Thermal conductivities available for the five cyclic compounds, pyridine, thiophene, ethylene oxide, dioxane, and piperidine, were used to obtain values of VOL. 9 NO. 1 FEBRUARY 1970
I&EC FUNDAMENTALS
75
I
0.90.8 0.70.60'5
-
o4 -
t
0.3 0.21
1
1
1
1
o Cyclopropane, C,H, o Cyclohexane, C,H,, Benzene,C,H,
560x16' 20.1
m Eihylene Oxide,C,H,O x Dioxane, C4H80z
17.75
?/
Piperidine, C,H,,N 0 Pyridine, C,H,N t Thiophene, C,H4S
2075 15.00 15.00
0
/
:;
+
the replacement of hydrogen is t o be made be identified, as well as the carbon atoms surrounding it. The method of identification is the same as that formulated for hydrocarbons (Roy and Thodos, 1968b). The number of carbon-to-carbon bonds, associated with each carbon atom, has been arbitrarily selected to define the type of carbon atoms involved in these substitutions. Thus
1
Cyclic Compounds 2,-
1.0
-
I
H
#
Structure H-C-
4
Type of carbon atoms
I
%, = -0.354TR+l.501T,'-0.147T~ I
0.2
0.3
I
1
I
I
I
I
1.k
I
0.6 0.8 1.0
0.4 TR
Figure 8. Relationship between compounds
X/X1
were found to be parallel to each other and when extrapolated to TR = 1.00, the X I values presented in Table I were obtained. For these substances, the ratio X/Xl when plotted against TR produced the relationship presented in Figure 8, which can be expressed as the polynomial
X
XI
+ 1 . 5 0 1 T ~ -' 0 . 1 4 7 T 2
(13)
This relationship is identical to that obtained for the cyclic hydrocarbons, cyclopropane, cyclohexane, and benzene (Roy and Thodos, 1968b). Group Contributions for Establishment of XI
The relationships, expressed by Equations 9 through 13, require that XI be established before the quantity X = @*A), (k*A), can be obtained a t a particular temperature. To establish this value of X a t TR = 1.0, the basic approach outlined for the hydrocarbons (Roy and Thodos, 1968b) was used t o develop the group contributions needed to calculate X1 values from the molecular structures of these organic compounds. The establishment of the value of XI for an organic compound requires that this value for the basic hydrocarbon be available. Group contributions and the method for using them to obtain values of X I for different hydrocarbons have been described (Roy and Thodos, 1968b). However, since the XI values for hydrocarbons become the basis for this study, these values are presented for the following hydrocarbons.
+
Methane Ethane Propane n-Butane n-Pentane %-Hexane
x1
0.83 x 10-5 3.10 6.72 10.90 16.08 21.27
These values along with the XI values presented in Table I for the different organic compounds have been used to obtain the group contributions associated with the substitution of hydrogen present in a hydrocarbon by a functional group. These substitutions require that the carbon atom upon which 76
l&EC FUNDAMENTALS
I
I H 2
1
-C-
-C-
I 3
I 4
Alcohols. An analysis of the XI values for the alcohols presented in Table I suggests the following contributions t o be associated with the replacement of a hydrogen atom in an aliphatic hydrocarbon by a hydroxyl group (-OH).
and TR for cyclic
X which when plotted against TR produced individual relationships for each of these compounds. These relationships
- = -0.354T~
-C-
HI
€(
I
H
I
VOL. 9 NO. 1 FEBRUARY 1970
TYPEOF SUBSTITUTION On methane 1+l 2+l 3 4 4+l 1+2+1
AX1 4.31 x 10-5 5.25 4.67 4.04 3.45 (estimated value) 4.68
The carbon atom from which the arrows point away is the one involved in the substitution. Oxygen-Containing Compounds. T o synthesize values of X1 for esters, ethers, aldehydes, and ketones, the proper hydrocarbon is used as the starting compound upon which the necessary oxygen and methyl substitutions are made. An analysis of the X1 values given in Table I for these oxygencontaining compounds suggests the following contributions t o be associated with oxygen and methyl group substitutions : OXYGENSUBSTITUTIONS 0
H II -C-CH H
H H -C-CH H H H H H
-c-c-c-
H H H
2.20
H
0 I1 H
H
H
+-c-c-c-
x
10-6
3.18
0
I/
H H H -C-0-CH+-C-0-CH H H H
0.85
C
H
H
H
H
H
H
-c-0-c-c-.-c-0-c-c
II
0.35
METHYLGROUPSUBSTITUTIONS
H -C-OH H H H -C-O-CH H H
-+
H H -C-0-CH H H
2.80
+
H H -C-O-C-CHx H H
4.75
0
0
I/
C-CH
/I
+
C-C-CHI
4.60
The following procedure is to be adhered to for the synthesis of XI values for aliphatic oxygen-containing compounds.
Synthesize longest possible hydrocarbon chain. For aldehydes or ketones, replace two hydrogen atoms by oxygen substitutions, as necessary. For esters or ethers, from longest hydrocarbon chain, obtain corresponding alcohol, then replace hydrogen or hydroxyl group by a methyl group as necessary; for esters, 0 continue to produce the group C-0-C-C hydrogen atoms by oxygen.
/I
by replacing two
Amines. Analysis of the XI values of the different amines presented in Table I has produced the following contributions to be associated with the formation of primary, secondary, and tertiary amines : FORMATION OF PRIMARY AMINES. Primary amines may be formed by replacing the hydrogen in a hydrocarbon by the -NH2 group. The contributions to be associated with the different types of such substitutions are as follows: AX1 2.96 4.45 5.78 8.93 7.39
On methane l+l 1 -2+l 2-2+1 1 -3+l
x
10-5
FORMATIOX OF SECONDARY AMINES.One of the hydrogens in the -NH2 group of the primary amine is to be replaced by a methyl group for the formation of a secondary amine. The contributions associated with this hydrogen replacement are as follows:
H 4
H H -C-N-CH, H
5.00
FORMATION OF TERTIARY AMINES.The only hydrogen associated with the nitrogen of a secondary amine can be replaced by a methyl group to produce a tertiary amine. The contributions to be associated with this type of a substitution are as follows: AX1
H CH3-N-CH3
CHI +
CH3-Ib-CH3
CH3-CH3 + CH3-CHz-CN H H H H -C=CH+-C=C-CN
2.95
x
10-5
I
-+
-CHZ-N-CHz-
SUBSTITUTIOSS o s ETHANE Fluorine Chlorine
Synthesize longest hydrocarbon chain. Obtain primary amine by replacing a hydrogen atom by the -SHzgroup. Then, obtain secondary or tertiary amine with the successive replacement of hydrogens in the -KH, group by methyl groups. atMethyl substitutions can be made on a methyl / I I tached to nitrogen \-k-CH3 + -N-CH:--CHS) with the contribution AX1 = 5.185 X
10-5
0.66 3.33
Group
-CH2 -CH= -9H-\--0 -
6x1
4.83 3.98 5.48 3.98 4.10 7.97
x
10-5
where these contributions must be associated with the expression
xI = z6xl - 8 . 9 0 x The procedure for synthesizing values of XI for an amine is as follows:
x
In lieu of thermal conductivity measurements beyond ethyI halides, the halogen substitutions found for ethane may be used for the substitution on paraffins beyond ethane. For the synthesis of XI values of mixed halides, such as the Freons, the order of substitution should be fluorine, chlorine, bromine, and iodine. Cyclics. An analysis of the X1 values of all the cyclic compounds available t o t’his study and presented in Table I suggests the following contributions (not substitutions) for the individual groups present in a ring:
=S= 3.72
0.29 1.57 1.77 3.07
SECOND AKD SUCCESSIVE SUBSTITUTIONS O X XETHANE Fluorine 0.43 Chlorine 2.33 Bromine 3.20
i -
CH3 H -CH*-N-CH2
7.15
These AX1 contributions resulted from the XI values of acetonitrile, propionitrile, and acrylic nitrile. Halides. An analysis of the XI values for the alkyl halides and Freons presented in Table I suggests the following contributions to be associated with halogen substitutions on a hydrocarbon.
Fluorine Chlorine Bromine Iodine
I
H
AX1 6 . 1 7 x 10-5 8.10
On methane
FIRSTHALOGEN SUBSTITUTION o s XETHAKE AX1
1
--C--TU” H
Nitriles. Values of XI for the nitriles can be obtained by taking into account the contributions associated with the replacement of a hydrogen atom in a hydrocarbon by the -CN group. The contributions derived from the XI values presented in Table I for nitriles are as follows:
10-5
in order to produce the XI value for the corresponding cyclic compound. This classification includes not only naphthenes and aromatics, but heterocyclic compounds such as thiophene, pyridine, piperidine, ethylene oxide, etc. The group contributions presented in this study were obtained from the measurements of a limited number of organic compounds. These thermal conductivity measurements represent the efforts of a wide spectrum with respect to time, investigator, and type of experimental equipment used. Therefore these group contributions represent the average of all these variables. Until more experimental information VOL. 9 NO. 1 FEBRUARY 1970
l&EC FUNDAMENTALS
77
becomes available with different types of organic compounds, the group contributions of this study can be used to synthesize values of X1 for organic compounds not listed in Table I. T o illustrate the application of this method, typical examples are presented.
EXAMPLE 1. Calculate k* for methyl ethyl ketone (CH3COC'Hs) in the gaseous state a t 150°C and 1 atm. For this compound, 31 = 72.10, T , = 533'K, and P, = 39.5 atm. These values produce the following basic parameters :
TR
-
423.2 (72. 10)1'2(533)1'6 - 0.794 and A = = 2.085 (39.5)2/3 533
The translational contribution, @ * A ) , is obtained from Equation 3,
Thus at 25OC and 1 atm, k* = 6.79 X 10-j/2.302 = 2.95 X loF5cal/sec cm OK. The recent experimental work of illasii et al. (1964) reports for this Freon a t 25OC and 1 atm, a value of k* = 2.90 x 10-5 cal/sec cm OK. EXAMPLE 3. Estimate the thermal conductivity of thiophene (C4HdS) in the gaseous state a t llO°C and l atm. For this cyclic compound, Jf = 84.13, T , = 590°K, and P, = 48.0 atm. These values produce the following parameters for this compound :
TR =
383,2 590 ~
0.649 and X
=
=
From Equation 3, (k*X)$= 1.75
(84. 13)II2 (590)'16 = 2.011 (48.0)2/3
x 1O-j.
From Equation 13
X - -- -0.354 (0.649) + 1.501 (0.649)' -
x1
x
2.11
0.147 (0.649)3= 0.361 10-5
To obtain the sum of the rotational and vibrational contributions, (k*X), (k*X), = X for this oxygen-containing compound, Equation 10 is first used
+
X - --
+ 1.045(0.794)' +
-0 082(0.794)
x 1
HC-CH
I
0.037(0.794)3= 0 612 The value of XI is next synthesized by the procedure outlined and the group contributions available in the section on oxygen-containing compounds. This procedure requires that two hydrogen atoms in n-butane be replace by a n oxygen atom. Thus,
-
%-Butane,CH3 -CH,-CH?-CH3 -CH~-CHZ-CHZ -CH2-CO-CH*-
10.90
x 10-5
3.18 X1 = 14.08 X 10-'
and consequently, X = 0.612(14.08 x lop5) = 8.62 X 10-j. Therefore, k*X = (2.11 8.62) X 10-j = 10.73 X and k* = 10.73 X 10-j/2.085 = 5.15 x cal/sec cm OK. Since no experimental measurements are available for this compound, no comparisons can be made a t this time. EXAMPLE 2. Calculate the thermal conductivity of gaseous Freon 13 (CClF3) a t 25OC and 1 atm. For this organic halide, Jf = 104.47, T , = 30Z°K, and P, = 39.0 atm. These values produce the following basic parameters :
+
298.2 T R = - = 0.987 and X 302
=
The value XI is synthesized from the group contributions for the individual groups present in this cyclic compound. For thiophene,
(104.47)'/*(302)116 (39.0)?13
=
2.302
HC
1
4(-CH=)
(=S=)
=
4(3.98 x 10-5)
CH
28x1 =
x1
-0.107(0.987)
+ 1.330(0.987)20.223(0.987)3 = 0.976
The prescribed order of substitutions of the halogens and the corresponding group contributions have been used to establish the value of X 1 as follows: Methane (base group) First halogen(fluorine) Second and successive halogens ( 2 fluorines), 2 x 0 . 4 3 1 chlorine Therefore X quently, k*X 78
= =
10-5 = 14.99-x 10-5. Thus, X = 0.361 (14.99 X 10-5) = 5.41 X 10-j. Hence, k*X = (1.75 5.41) X 10-5 = 7.16 X 10-5 and therefore k* = 7.16 X 10-5/2.011 = 3.56 x l o v 5 calisec cm O K . Vines and Bennett (1954) report an experimental value, k* = 3.65 x lO-jcal/sec ern OK.
+
Comparison of Results
The approach presented in this study for the calculation of thermal conductivities of gases a t normal pressures has been applied to the calculation of this transport property for all the organic compounds included in this investigation. Thermal conductivities were Calculated for the temperatures for which experimental values are available and used to obtain the average deviations for each of the organic compounds presented in Table I. The maximum and average deviations resulting for each class of organic compounds are summarized as follows: No. of Points
Alcohols Oxygen-containing compounds .imines ru'itriles Halides (including Freons) Cyclics
145 29 14 8 86 9
Max. Av. - . Deviation, Deviation,
%
%
9.62 2.47 3.47 4.42 5.56 2.92
3.96 1.80 1.01 2.21 2.35 1.50
0 . 8 3 x 10-j 0.29
The over-all average deviation of the 52 organic compounds investigated in this study was 3.07, for 291 points examined.
0.86 2.33 4.31
Acknowledgment
x 10-j
0.976 (4.31 X loF5) = 4.21 X lov5. Conse[2.58 4.211 X 10-j = 6.79 X
+
l&EC FUNDAMENTALS
8x1 15.92 X 7.97 23.89 X 10-j
S
The translational contribution at T E = 0.987 is calculated with Equation 3 to be (k*X)$= 2.58 X 10-j. For halides, Equation 12 is used to calculate
-X_ -
=
VOL. 9 NO. 1 FEBRUARY 1 9 7 0
The authors extend their gratitude to the National Aeronautics and Space Administration for the support of this study through Grant KsG-405-14-007-0.003.
literature Cited
Nomenclature = constant in Equation 5
C k*
thermal conductivity of gas at normal pressures, cal/sec cm OK = exponents, Equation 1 = molecular weight = critical pressure, atm = gas constant = exponent, Equation 6 = temperature, O K = critical temperature, O K = reduced temperature, T / T c = rotational and vibrational contribution to k*A, [(k*A), (k*A),l = value of X a t T R = 1.00 = contribution to X 1 in replacement of a hydrogen atom by different functional groups = individual contributions for different groups in cyclic compounds = critical volume, cma/g-mole = critical compressibility factor, PcvC/RTc =
m ,n
M
P, R S
T TC TR X
+
x 1
AX1 6x1 Vc
Abas-zade, A. K., Dokl. Akad. Nauk SSSR. 99,227 (1954). Abas-zade, A. K., Amiraslanov, A. M., Zh. Fiz. Khim. 31, 1459 (1957).
Eucken, A., Physik. 2. 14,324 (1913). Groenier, W. S., Thodos, George, J . Chem. Eng. Data 6 , 240 (1961).
Hirschfelder, J. O., Curtiss, C. F., Bird, R. B., “Molecular Theory of Gases and Liquids,” p. 534, Wiley, New York, 1964. Hofker, Hinrich, Programm-Gymnasium, Piattenscheid, 1892. Hougen, 0. A., Watson, K. M., Ragatz, R. A., “Chemical Process Principles,” Part I, p. 88, Wiley, New York, 1954. Kennedy, J. T., Thodos, George, A.I.Ch.E. J . 7,625 (1961). Keyes, F. G., Trans. Am. SOC.Mech. Engrs. 76,809 (1954). Kobe, K. A,, Lynn, R. E., Jr., Chem. Revs. 52,117 (1953). Lambert, J. D., Cotten, K. J., Pailthorpe, M. W., Robinson, A. M., Scrivins, J., Vale, W. R. F., Young, R. M., Proc. Roy. Soc. (London)A231,280 (19%).
Lambert, J. D., Staines, E. N., Woods, S. D., Proc. Rou. Soc. (London)A200,262 (1950). Markwood, R. H., Benning, A. F., Refrig. Eng. 45, 95 (1943). Nasi&,A. P., Valle Bracero, A., Barrales Rienda, J. M., Ann. Real SOC.Es aii. FZs. Quim.Ser. A , 60 (5/6), 89 (1964).
8.
Mathur, P., Thodos, George, A.I.Ch.E. J . 11,164 (1965). hlilverton, S. W., Proc. Roy. SOC.(London)A150,287 (1935). Moser, E., dissertation, Friedrich-Wilhelms Universitat zu BerGREEKLETTERS lin, 1913. Roy, Dipak, Thodos, George, Can. J . Chem. Eng. 46, 108 (1968a). CY = coefficient, Equation 1 Roy, Dipak, Thodos, George, IND.ENG.CHEM.FUNDAMENTALS C Y , p, y, 6 = polynomial coefficients, Equation 8 7,529 (1968b). = thermal conductivity parameter, 1W1~2Tc1/6/Pc2/aSenftleben. H.. 2.Anuew. Phus.. 5. 33 119531. x Senftleben; H.; Gladikh, H.,Z.’Pkysik. 125; 653 (1949). Sherratt, G. G., Griffiths, E., Phil. Mag. 27(7), 68 (1939). SUBSCRIPTS Shushpanov, P. I., J. Erptl. Theor. Phys. USSR. 9, 875 (1939). Vines, R. G., Bennett, L. A., J . Chem. Phys. 22,360 (1954). r = rotational t = translational RECEIVED for review January 2, 1969 ACCEPTED September 25, 1969 V = vibrational zc
Prediction of Viscosity of Liquid Hydrocarbons S. I. Kreps and M. 1. Druin’ Department of Chemical Engineering, Newark College of Engineering, 323 High St., Newark, N . J . 07109
The liquid viscosity of four series of homologs-n-paraffins, n- 1 -alkenes, n-alkylcyclohexanes, and n-alkylbenzenes-is estimated from density and molecular weight data. An empirical equation for each of the series, n-paraffins to n-alkylbenzenes, gives average errors of 1.78, 1.95,2.39,and 3.46%, respectively.
A
RECEKT review by Reid (1965) indicated the need for methods of computing the viscosity of a liquid in the absence of experimental data. Gambill (1959) and Reid and Sherwood (1958) concisely present the available methods and conclude that none are reliable. Of the methods available, those of Thomas (1946) and Souders (1938) are recommended only for rough estimates, which are usually good t o within 30% but sometimes are in error by greater amounts. The rheochor is suitable for rough approximations of viscosity a t the normal boiling point.
Viscosity of Monatomic liquids
From the kinetic theory of gases it has been shown (Bird
et al., 1960) that the viscosity of a monatomic gas is given by the relationship I* = 1
1/3
iipA
A = (V/N)1’3 I t is further postulated that momentum is transferred from one lattice plane to a n adjacent plane at the sonic velocity, us, for the liquid. This is similar to a model for energy transport proposed by Bridgman (1923) which predicts the thermal conductivity of pure liquids, with a cubic lattice similar to that of the solid state. Energy is transferred from plane t o plane a t the sonic velocity by collisions arising out of molecular vibrations about the equilibrium lattice positions. Bridgman’s equation for the thermal conductivity is given (Bird et al., 1960) as
(1)
Present address, Celariese Research Co., Box 1000, Summit,
S . J . 07901
In adapting this relationship for liquids it is here assumed that the liquid molecules are arranged in a cubic lattice, with center-to-center spacing equivalent to
K = 3(N/V)*/3kv, (2) I n the case of momentum transfer, molecules reaching a VOL. 9 NO. 1 FEBRUARY 1970
I&EC FUNDAMENTALS
79
