INDUSTRIAL A N D ENGINEERING CHEMISTRY
December, 1941
-
= (0.01868) (0.5094) 0.009516 = -(0.02588) (0.5094) -0.01318 = (6.16 X lo4) (0.5094) (0.3249)5 = 1.08 X 10'
a b c
Equation 2 can then be used as an approximate expression of the gas law for most gases in the range specified by Maron in liters and Turnbull, employing the following constants (BO per mole; the prime marks refer to nitrogen) : 3.247 1.253 0.5622 0.4058
-
PLTc Bo = B: 7
0.02346
TP.
The use of the above constants for hydrogen gives slightly better agreement with experimental results than those of Maron and Turnbull a t higher temperatures and pressures and slightly worse agreement a t lower temperatures and pressures.
Literature Cited (1) DeBoer, J., and Michels, A.. Physica,5, 945-57 (1938). (2) Lennard-Jon@ J. E., Ibid., 4, 941-62 (1037). (3) Lennard-Jones, J. E., and Devonshire, A. F., Proc. Roy. SOC. (London), A163, 53-70 (1937). (4) Maron, S. H., and Turnbull,D., IND.ENQ.CHIM., 33, 408 (1941).
For HI
For Other Gaees a = 4.634 fl = 0.669 y 0.5622 6 = 0.4068
1537
P U B L I ~ Hby E Dpermission of the Director, U. S. Bureau of Mines
M Mol M
L
v/sco&l?yCOnStl?~/
comtanr
t-2 0
Viscosity
Nomographs
-40
d Densltv
qms /cc
for
Organic Liquids
r --
__---
D. S. DAVIS Wayne University, Detroit, Mich.
IO0
OUDERS' showed that for a wide range of
S
3
organic liquids the logarithm of the logarithm of the viscosity in millipoises is linear with the density in grams per cubio centimeter according to the expression log (log V ) = ma
- 2.9
FIQWR 1 ~
(1)
where m is a constant characteristic of each liquid. He calculated the viscosity-density constant, m,by the equation 0 m = I/M whey M = molecular weight I = viscosity-constitutional constant ~
1
Souden, Mott, Jr., J . Am. Chsm. 806.. 60, 154 (1938).
(2)
The two equations may be combined to give: log (log 7 ) = I d / M
- 2.9
(3)
The viscosity-constitutional constant, I , may be evaluated from the summation of general atomic and structural constants given in Table I. For example, the value of I for ethyl iodide is 2(50.2) 5(2.7) 110 = 223.9. The use of Figure 1, designed to solve Equation 3 quickly and accurately, is illustrated as follows: What is the viscosity
+
+
1538
Vol. 33, No. 12
INDUSTRIAL AND ENGINEERING CHEMISTRY
FIGURE
of ethyl iodide when the density is 1.925 grams per cc.? Connect 224 on the I scale with 156, the molecular weight, on the M scale and note the intersection with the a axis. Connect this intersection with 1.925 on the d scale and produce the line to the 7 scale where the viscosity is read as 5.5 millipoises. Figure 1 is a general chart for organic liquids and covers wide ranges, but the viscosity scale is necessarily short and crowded owing to the nature of Equation 3. Figures 2 and 3 are less general but permit closer estimation of viscosity, and require reference t o Table I1 which lists compound numbers against the names of the compounds in question. The index line in Figure 2 shows that the viscosity of cyclopentane (compound 25) is 4.54 millipoises when the density is 0.751 gram per cc., and the index line in Figure 3 indicates that isobutyl iodide (compound 84) with a density of 1.614 has a viscosity of 9.5 millipoises. A comparison between results as read from the specific and general charts may be effected by noting that the viscosity of ethyl iodide (compound 89) a t a density of 1.925 grams per cc. is 5.6 when read from Figure 3 as against 5.5 reported in a previous illustration. A small variation in density or in the constitutional constant will result in a considerable change in viscosity due to the log-log function. This oondition is faithfully reflected in the charts.
2
CONSTANTS TABLE I. ATOMICAND STRUCTURAL ATOMICAND GROUPVALUE^ CHz H C 0
N C1 Br I
57.1 90 104.4 80
OH
55.6 2.7 50.2 29.7
coo
COOH N0a
STRUCTURAL VALUES
R, where
X is a negative
R
group
6-C 6-C
-24 -21
ring ring
R
R Side group on 6-C
ring
1
R-C-R
I
\
13
/CHX
R
R Mol. wt.
< 17,
-9
-
H-C-R
It
16
0
Mol. wt. > 16, -17 Ortho and pars 3; meta = 1 CH-C-R
II
0
5
37
60 79 110
December, 1941
INDUSTRIAL AND ENGINEERIN
C H E M ISTRY
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L
FIQURE3
1
NUMBERB LISTEDON FIGURES 2 AND 3 TABLE11. COMPOUND 49
67 23 22 62 48 35 63 51 34 50 60 42 31 16 20 14a 14 28 17 56
46
55 81 83 76 77 80 82
Aoetaldehyde Acetate, ethyl Aoetate ethyl tetradec 1 Aoetati 2-hept 1 nonyr Acetate: methvr Aoetate; n-propyl Acetone Add, acetic Acid, n-butyr:o Aajd, p-oaproio Aoid, 1sobuty:io Acid, propionio Aoid n-valeric Aloohol. allyl Aloohol butyl Aloohol) ethyl Alooho< isobutyl Aloohol: isopro yl Aloohol, methy? Aloohol, n-propyl Aniline Benzene Benzylamine Bromide allyl Bromide' ethyl Bromide' isobutyl Bromide: isopropyl Bromde n-propyl Bromobdnneene
79 77 77 53 68 75 65 60 67 72 70 70 69 20 29
44
12 4
25 6
74 80 20 2 1 46
19 15
11
m-Bromotoluene o-Bromotoluene p-Bromotoluene n-Butyrate methyl Chloride ailyl Chloride' ethylene Chloride: isobutyl Chloride. isopropyl Chloride, n-propyl Chlorobenzene m-Chlorotoluene o-Chlorotoluene Chlorotoluene yolohevane Cyolohexanol Cyclohexanone Cyclohexyldocosane C yolohexylhexaoosane CvoloDentane D;oaSe Diohloroethane Dichloromethane, Diisopropenyl (diallyl) Diisopro yl Dimeth yybutane Dimethylaniline 5-Dooosene, phenyl Dooosylbenaene Dooosyloyolohexane
E-
21 5 31 24 27 30 25 47 40 6
61
64
56 3 8 4 16 5 36 88 89 84 85 90 87 86
53 10 6
-Dooosylnaphthalene 5Ether odeoane ethyl
Ether: ethyl isobut 1 Ether ethyl ropyf Ether: methy? propyl Ether, propyl Ethylaniline Ethylbenzene Ethyltetradeoanol Formate, ethyl Formate, methyl Formate, propyl Heptadeoane Heptane He tylnonanol b-€!exaoosene, phenyl Hexane Hexylna hthalene Iodide, 8 1 ~ 1 Iodide ethyl Iodide' isobutyl Iodide: isopropyl Iodide methyl Iodide: propyl Iodobenaene Isobutyrate. methyl Isoheptane Isohexane
6 26
33 33 32 54 92 10 73 71 6 18 13 24 6
9 59 15 14 37 51 58 43 52 60 5 41 38 39
Isopentane Isoprene Ketone diethyl Ketone' methyl ethyl ' Methyfaniline Ketone' methyl propyl Methylcyolohexane Meth lpentane Nitrogenzene Nitrotoluene Nonane Ootadeoylbenaene Octadeoylo olohexane #-Ootadeoy%mphthalene Ootane Pentane Phenol Phenyldocosane Phenylhexaoosane Propionaldehyde Propionate ethyl Propionate: methyl Toluene o-Toluidine Toluidine ndeoane m-Xylene o-Xylene p-Xylene
-6
