INDUSTRIAL A N D ENGINEERING CHEMISTRY
482
Vol. 19. N o . 4
Condensation of a Gas Mixture to Form an Ideal Solution' By J. H. Simons NORTHWESTERN UNIVERSITY, EVANSTON, ILL
T
H E condensation of a liquid from a two-component gas phase is a fairly simple problem if the solubility relations are known. For three or more components the problem becomes quite complicated and, unless the solution formed is ideal, the quantity relations can only be obtained by direct experiment. A knowledge, however, of the limiting case where the liquid formed is ideal is valuable for conditions which approach the ideal in the same way that the ideal gas law is useful. Solutions of oxygen in nitrogen2 approach the ideal, and we would expect a solution of other fixed nonpolar gases in this mixture also to approach the ideal. Solutions of closely related members of a homologous series of organic compounds also approach the ideal so1utionl3and so this knowledge is useful for the condensation of the vapors of a material like 3.0 gasoline. Equations for + 2.6 the condensation of a gas of two and of three comf 2.4 c 1% ponents have 'El 2.2 been derived by 4 Dodges4 He has i 2.0 also pointed out L" that as the equa+ 2 1.8 t i o n s derived >2 29 1.6 seem to fall into a series with an1.4 other t e r m for 2 .E g 1.2 e a c h additional .-0 component, t h e $ 1.0 additional terms a in the equation 0.8 may be written 5 % 0.6 from t h e symestablished. The general equation may be simply derived with somewhat more rigor by the method to be described. Temperature--o K. Figure 1
If the total pressure of the gas system is P,and the partial pressures in the entering gas are TI, 7r2, 7r3, etc., and the partial pressures in the escaping gas are p l , pz, pa, etc., then p = HI T2 533 . . . a m = p1 f i 2 f i 3 - k . . . . . .fin (3) By representing the vapor pressures of the pure components by p l o 1 p2", pB0, etc., from Raoult's law is obtained
+ +
+ + +.
nl
A" 7 = p1 (4) and similar expressions for the other components. As the total quantity of any component entering will be distributed between the condensed phase and the escaping gas, E E L = u -fi- ' + n 1 (5) P P and similar equations for the other components. In the foregoing equations P, E , TI,m,m.. . .rnand PI', p Z 0 , pa'. . . . . . . p n o are known variables and C, U , nl, 122, n3.. . . . .nn,and PI, p2, p 3 . . . . . .pm are unknown. There 2 unknown variables and 2n independent are 2n equations. Equation (1)is not independent of the sum of the equations represented in ( 5 ) combined with equation (3). The equations may then be solved for 121, n2, n3, etc., in the following manner: Solving equation (4)for C,
+
+
100
'J
P
75
9 'CI
s
* 60 0
Derivation of Equationss
5a
A gas of n components is permitted to pass through a chamber at constant temperature sufficiently slowly so that temperature equilibrium is maintained. If E represents the total number of mols of gas entering the chamber in a unit of time, C the total number of mols condensed, and U the total number uncondensed that pass out through the exit, then E = C+ U (11 If the number of mols of each component condensed is nl, n2,n3, etc., then C = nl
+ nz + + . . . . . . . . . .nn n3
(2)
Received December 27, 1926. Baly, Phil. M a g , 49, 517 (1900). 3 Hildebrand, "Solubility." A. C. S. Monograph Series, The Chemical Catalog Co., Inc., 1924. 4 THIS JOURNAL, 14, 1062 (1922). 5 The nomenclature of Dodge is not used, but one more consistent with general chemical practice. 1 2
-g
25
0 81
85 86 84 83 Temperature' K. Figure 2-Quantity of All Components Condensed
82
By eliminating C and U from equations (l), (B), and (8), Ep1 = E m
++
nl(p1:
E ~ =z E H ~ n&
- P) - P)
(9a)
(9b)
and similar expressions for the other components. the separate equations of (9) for all components
By adding
and combining with equation ( 3 ) to eliminate and PI, m,~ 3 etc., ,
p2,
PI,
p3,
etc.,
INDUSTRIAL A N D ENGINEERING CHEMISTRY
.4pril, 1927 Table I-Vapor
K. 75 76 77 78 79
0.12 0.14 0.17 0.21 0.24 0.28 0.32 0.37 0.42 0.48 0.53 0.60 0.66 0.73 0.81 0.90
80
81 82 83 84 85 86 87 88 89 90
n l ( p l o- P )
Atmosbheres 0.18 0.22 0.26 0.31 0.37 0.43 0.50 0.55 0.63 0.71 0.80 0.89 0.98 1.08 1.18 1.28
483
Pressures of Oxygen, Argon, a n d Nitrogen a n d Terms of Equations (15) a n d (18)
0.75 0.85 0.95 1.06 1.19 1.33 1.47 1.63 1.78 2.00 2.20 2.43 2.67 2.92 3.22 3.50
1.750 1.500 1.236 1.000 0.876 0.750 0.657 0.568 0.500 0.438 0.396 0.350 0.318 0.288 0.2595 0,2345
0.0528 0.0432 0.0365 0.0306 0.0257 0.0221 0.0190 0.0173 0.0151 0.0134 0.0119 0.0107 0.0097 0.0088 0.0081 0.0074
1.040 0.919 0.822 0.736 0.656 0.588 0.531 0.479 0.438 0.390 0.354 0.321 0.292 0.267 0.242 0.223
+ n2(p2"- P ) + n3(p3' - P ) + . . . . .
2.843 2.462 2.094 1.767 1.558 1.360 1.207 1.064 0.953 0.841 0.762 0.682 0.620 0.564 0.510 0.465
0.0252 0.0294 0.0357 0.0441 0.0504 0.0588 0.0672 0.0777 0.0882 0.0988 0.1113 0.1260 0.1386 0.1532 0.1701 0.1890
0.00171 0.00209 0.00247 0.00294 0.00352 0.00408 0.00475 0.00522 0,00598 0.00676 0.00760 0.00845 0.00931 0.01026 0.01120 0,01218
0.612 0.695 0.780 0.874 0.983 1.101 1.220 1.355 1.482 1.667 1.836 2.031 2.230 2.441 2.693 2.934
0.685 0.664 0.742 0.827 0.929 1.038 1.148 1.272 1.388 1.561 1.718 1.897 2.082 2.278 2.512 2.733
nn(pno- P ) = 0 (io) From equations (7a), (sa), and -(9b) by eliminating p l and p2 and simplifying,
At the point of total condensation n.1 = E;.c and combining this with equations (3) and (12),, Tipi' + Tzpz" T3p3' , . . . . . Hnpn' = P2
and similarly
or as r1 = -, P rlplo
+
+
T1
+
~292'
+
~3P3'
+ ..
,
. . .rnpno
=
P
By combining equations (10) and (ll),
Equation (12) contains only one unknown quantity, n, the number of mols of one component in the condensed phase, and so is solvable for that unknown when the vapor pressures and compositions are substituted. For convenience in using, TI T2 T3 xn let E = 1 and = rl - = 1-2, B = r3!.. . . . . F = rn,where P ' P r1, r2, 13, etc., are the fractional compositions of the components in the entering gas. Then
T e m p e r a t u r e o K. Figure 3-Composition of Liquid a n d Gas Phases i n Oxygen
Also at the point of total condensation by eliminating nl from equation (9a),
PI
At the dew point, or the temperature of the first drop, n = 0, and combining this with equations (3) and (12) TI T2 T 3 = 1
p+a+a+.....~a $2
or
0
(19)
p1
$9
pPI
$1
$. $!
-
P1' - ? I T
(30)
and similar expressions for the other components.
-+;+'?+ 71 PI0 p2
rn - 1 _ pn0 - P
_ ,
pso
(15)
Also a t the dew point, P I = T I , p~ = TZ,pa = ~ 3 etc., , and , etc., combining with equation (4) and eliminating p l . p ~ ps, ! 3 = l
c
P1°
and similar expressions for the other components. As nl nz n3 ~t
p
and similar expressions for the other components. The limiting mol fraction of the exit gas at the point of total con. . . will densation, which will be represented by be given by
Pn
P3
=
ZJ etc., are the mol fractions in the liquid NI, N2, N3,
etc., N1 -
AT* =
TZ
7 3
N3 = etc. (16) Pz P3 Equation (16) gives the limiting composition of the liquid at the dew point or the composition of the first drop. -o, Pl
-o,
Application to Experiment
Fonda, Reynolds, and Robinson6 have conducted experiments on the partial condensation of air over a range of temperature and have given the composition of the liquid and gas phases in nitrogen, oxygen, and argon. These experimental data may be used for comparison with this theory by taking the first three terms of the equations. Letting oxygen be component 1, argon component 2, and nitrogen component 3, we have r1 = 0.21, ra = 0.0095, and r3 = 0.7805, the composition of air. The pressure a t which the experiments were conducted, P , = 1.395 atmospheres. For convenience E = 1. The vapor pressures are obtained by plot6
THISJOURNAL, 17, 676 (1925).
INDUSTRIAL AND ENGIiVEERING CHEMISTRY
484
ting the values given in the Physical Chemical Tables of Landolt, Bornstein, and Roth on a large-scale graph and interpolating. They are given in Table I. The first step is to obtain the range of temperature over which there will be partial condensation. Above this range there will be no liquid phase formed and below it all the gas phase will be condensed. The dew point is obtained by plotting the values for the sum of the compositions divided by the vapor pressures against temperature; the temperature where this value equals the reciprocal of the total pressure will be the dew point, as indicated by equation
Vol. 19, No. 4
culated by the use of equation (11) and pl, p,, and p3, by equation (9). At the dew point (85.5' K.), N1, N1, and Na are calculated with equation (16), and at the point of total condensation (82.3' K.),
Fp
j;
and
are calculated with
equation (20). The results are given in Table 11. Table 11-Values
of Composition of Condensed Liquid a n d Escaping Gas, Calculated from Equations
85.0°K. 8 5 . 5 ' K .
82.3'K.
83.0°K.
0.21 0.0095 0.7805 0.21 0.0095 0.7805 0.0579
0.183 0.00778 0.479 0.6698 0.273 0.012 0.715 0.0822
0.1197 0.00449 0.1875 0.3117 0.384 0.014 0.602 0.1317
0.0513 0.00174 0.0564 0.1094 0.469 0.016 0.515 0.1780
0.521 0.016 0.470 0.21
@ P
0.0039
0.0062
0.0073
0.00878
0.0095
@ P
0.937
0.9127
0.8618
0.8131
0.7805
nl
n2 n3
Fraction condensed N1 Na Na
PI P
1.0000
84.0'K.
0.0000 0.0000 0.0000 0,0000
100
I 84
I
1
a5
86
T e m p e r a t u r e o K. Figure 4-Composition of Liquid a n d Gas Phases in
Argon
(x) See footnote to Table I11
(15). The values are given in Table I and the plot in Figure 1. I n the figure the ordinate gives the value of the equation and so by taking the point on the curve where the ordinate is equal to the reciprocal of the total pressure the abscissa of that point will be the temperature of the dew point. The point of total condensation is obtained in a similar manner where the sum of the products of the vapor pressures and compositions equals the total pressure, as indicated in equation (18). These values are also given in Table I and Figure 1. In this manner the dew point is found to be 85.5' K. and the point of total condensation, 82.3' K., for the pressure a t which the experiments were performed. The next step is to calculate the variation of the amount condensed with the temperature over this range and also the composition of both the liquid and escaping gas phases. n1 is calculated with equation (13). Then n2 and n3 are calTable 111-Comuarison
OK.
Expt.
1
4.2 4.5 6.2
81.2 81.0
10.94
... ...
... ...
... ...
...
... ... ... ... ...
... ...
19.0 18.3 17.2 17.7
6 6 :98
...
14.3
100:00
...
55.4 61.8
71 4
71.8 80.3
... ... ...
...
...
...
... ...
21.00 17.80
19.8 19.7
10.8
...
I
0.00
15.0
...
11.6
9.6 10.1
...
9.0 8.5
ARGON
Calcd.
Mol aer cent
Per cent
3 i : 17
12.7 14.5 21.0 26.4 37.0 41.5
I
Expt.
...
8.2 5.5
81.8 81.6
81.3
... ...
Calcd.
LIQUIDPHASR OXYGEN
ARGON
OXYGEN
ATURE
85.5 85.0 84.2 84.2 84.1 84.0 83.9 83.9 83.8 83.7 83.5 83.2 83.0 82.5 82.4 82.3
of Exuerimental a n d Calculated Values
UNCONDZNSE~ GAS PHASE
AIR CONDENSED
TEMPER-
A comparison of the theory with the experiments of Fonda, Reynolds, and Rob- a 75 inson6 is given i n Table I11 and shown 4 graphically in Figures f 2, 3, and 4. The full *$ 50 lines are calculated by % the equations and the $ points obtained from the experiments. I n 25 Figures 5 and 6 a comparison is made of the experimental v a l u e s and the theory, by 0 25 60 76 plotting them against Mol per cent the per cent Of Figure +Composition of Liquid a n d condensate. Thefull G a s Phases of Oxygen Compared w i t h Total Condensate lines a r e o b t a i n e d by plotting the theoretical values of the amount of the total air that is condensed against the theoretical percentage of the argon or oxygen in both liquid and gas and the circles are values obtained by plotting the experimental amount of condensation against the experimental composition in both
M o l p e r cent
... ... ...
0.88
... ...
0.84
... ...
... ...
I 1
... ... 0.52 ... ...
...
...
0.73
... ...
8.22
... ... 5.79 ... ...
0.95 0,876
...
... ...
46.8
...
... ... ... ... ... ...
42.5 38.5
... 33.8 ...
0.39 1. 17a (0.50)
Mol per cent 52.1 46.9
...
.... ..
...
29.7 27.0 26.0
:::
... ...
1
...
... ... 38.4 ... ... ... ... ... ... 27.3 ...
I j
1
2.35 2.21
... ... ... ...
2.05
... ...
... ... 1.12
1.44 1.34
2i:t)
...
... ...
:::
Mol per cent 1.6 1.6
... ... ...
0.98 0.84
I
0:ii
... ... ... 1.4 ... ... ... ... ... ...
1.2
... ... ... ...
0.95
... ... ...
This value 1.17,as given in Table I1 of Fonda Reynolds and Robinson's article e does not seem reasonable for the gas phase should become less and less rich in argon as the temperature is lowered, Calculating'back from their Table i I I the value 0.50 is obtained and so the value given in Table I1 is probably in error.
INDUSTRIAL AND ENGINEERING CHEMISTRY
April, 1927
485
liquid and gas. These data are given in Table 111. Very good agreement is obtained.
may be more or less in error. This shows that the approach to the ideal is close, and also that the ideal law may be used for calculations for first approximations or for the limiting Discussion case. The errors in the experiments themselves may account for more or less of the discrepancies. The curves agree very well with the experimental points Equation (12) cannot be easily solved literally for nl, in form and by shifting them one degree lower in temperature, as this quantity appears in part of the denominator of each the fit is exceedingly term. When the values are substituted the equation be100 good. I n Figure 4 the comes first order in nl for two components in our system, curves and points for second order for three, third order for four, etc. The equat h e composition of tions become more difficult to solve as the number of comargon in the liquid ponents increases, but as all but nl are expressed in figures the .= 75 seem to have a differ- solution is readily obtained. Any number of terms of the 0 ent trend a t the upper equation can be readily mitten from inspection of the first 9 V part, but that is in two or three. 8 the region of a small Equations (16) and (20) give the limiting compositions of *$ 50 amount of liquid con- the first drop of liquid a t the dew point and the last trace * densed, which would of gas a t the point of total condensation. This establishes E cause greater error in the limits of the fractionation. Used in conjunction with k t h e e x p e r i m e n t s . Figure 1 the range of temperature for fractionating and the i 25 This discrepancy of limiting compositions is calculated without the labor of the one d e g r e e i s v e r y solution of equation (12). As the composition of the liquid small when we con- a t the point of total condensation and that of the gas a t the sider t h a t we h a v e dew point are the same and equal to the composition of the 0 calculated the curves entering gas, with the other limits calculated, we have an 1 2 with an ideal law and approximation of the trend of the process. Figure 1 gives Mol per cent Figure &Composition of Liquid a n d using vapor pressure us the range of temperature for any pressure, for it is plotted Gas Phases of Argon Compared w i t h Total m e a s u r e m e n t s that independently of the total pressure. Condensate Wl
L
Volatility of Acetone-Benzene Paint and Varnish Removers’ By John Morris Weiss WSISS AND DOWNS, 50 EAST41sr Sr., NEWYORK,N. Y.
Preliminary experiments on the volatility of acetone-benzene-waxpaint and varnish removers indicate that, under reasonable conditions of ventilation in the practical use of properly proportioned removers of this type, the concentration of vapors in the atmosphere will not become suficient to constitute a hazard approaching that of industries where the benzene evaporation is a necessary feature of the operation.
T
HE recent findings of the Benzol Committee of the
National Safety Council showing the danger from benzene poisoning when used under conditions which allow its evaporation in substantial amount in the workroom air, has caused a general review of industries employing benzene in this way, in the hope of minimizing such hazard as far as possible. One of the large uses of benzene is in the manufacture of paint and varnish removers, and the preliminary experiments described herein were conducted to learn the extent of the toxic hazard involved in the use of these removers. I n the ordinary use of such removers, where a solvent for the paint or varnish film is the active agent, the practice is to brush the remover on the surfaces from which the film is to be removed, allow it to remain for about 15 minutes to penetrate, cut, and soften the film, and then scrape the softened film from the wood with a suitable tool. Benzene alone, or benzene simply mixed with another solvent, would not be satisfactory, as it would not adhere sufficiently to vertical surfaces and it is so volatile that it would not remain on the surface long enough to accomplish the necessary softening and cutting.
* Presented before the North Jersey Section of the American Chemical Society, Newark, N . J., January 10, 1927.
Paint and varnish removers have been developed which meet the practical requirements, the most widely used type being a mixture of benzene, acetone, and paraffin wax, in such proportions that there is always a phase of solid paraffin in the finished mixture. The proportions of ingredients in the various commercial removers of this type differ, but in the majority of formulas the proportions of solvents vary from around 50 to 55 per cent benzene and 50 to 45 per cent acetone by volume with the addition of from 3 to 5 per cent by weight of wax. The wax is dissolved in the benzene and the acetone stirred in slowly, in this way precipitating the wax in a fine state of division. Both pure and 90 per cent benzene are used in commercial removers. Raw Materials
The following raw materials were used: TT’uxes SOLIDIFYING POINT
c. A-Commercial white paraffin B-Commercial ceresin (canary yellow) C-White crude scale (119/122) D-Refined paraffin (121/123) E-Refined paraffin (136 min.)
55 53 47.2 48 55.4
F. 131 128 117 118 132
O
