.Tiinp
ISDUSTRIAL A S D ENGIXEERI,VG CHEMISTRY
1R2.i
643
Vapor - Pressures of Glycerol-Water and GlycerolWater-Sodium Chloride Systems' By A. R . Carr, R . E. Townsend, and W. L. Badger U N I W R S I T Y OF
MICHIGAN, ANN ARBOR,M I C H .
I
T H E design of Proper the Pumping tube and the The vapor pressure data and boiling point-composicommercial apparatus for tion diagrams for the systems glycerol-water and thermometer immersed dievaporation and distillarectly into the liqtlid. glycerol-watersaturated with sodium chloride have been In determining the vapor tion,it is necessary to know derived from the Diihring lines. The latent heats of the Properties of the subPressure the dynamic method vaporization for the system glycerol-water have been stances and solutions to be was employed, whereas Gercalculated. The applicability of these data to problems evaporated or distilled. It is lach used the static method. arising in the design of glycerol evaporators or glycerol very apparent, to one Who -4comparison of the results distilling equipment is pointed out. seeks this information, that of the two methods is shown the literature is sadly lacking, in Figure 3. Th, solutions especially in the case of solutions. The present investigation were carefully made up by weight and the composition was undertaken with the purpose of obtaining information checked by grayity from Gerlach's specific gravity ,abies. concerning glycerol-water solutions and solutions of glycerolwater saturated with sodium chloride. Duhring Lines for Solutions Studied The most important work on glycerol-water solutions has Baker and Waite4 have shown that Duhring's rule is apbeen done by Gerlachz and by Jfayer BUgstrom,3 mho determined many of their properties. The writers repeated a plicable to aqueous solutions of inorganic salts siith a considpart of this work and extended it to include solutions of glgc- erable degree of accuracy. Ddhring's rule may bt: most simply expressed by saying that if T1is the boiling point of a given erol-water saturated with sodium chloride. substance at a pressure PI,and T2is its boiling point a t some Apparatus and Method other pressure, Pz, and if tl and t2 are the boiling points of some other substance at these same two pressures, then The apparatus was similar to that of Baker and Waite4 TI with the exception that for salt solutions the pumping tube - -- Tz tl - t 2 could not be used, as the salt plugged the arms of the tube. For these solutions a boiling point tube was substituted for This was long known to be true for organic liquids of a similar 1 Received February 6, 1925. composition. Baker and Waite show that it is true for the 2 Chem I n d , 1, 277 (1884). relation between water as one liquid and an aqueous solution * 2 deut Ol-Felt-Ind , 44, 418 (1924) of an inorganic salt as the other liquid. This paper shows ' C h e m M e t E n g , 26, 1137 (1921), Trans A m I n s t C h e m E n s , 13, 223 (1921).
50
60
70
80
TFMPERAWRE OF WATER Figure 1-Duhring
90
100
TEMPERATUREOF WATER PLG.C.
DEG.c.
Lines for t h e S y s t e m Glycerol-Water
Figure-Z-&hring
Lines for t h e S y s t e m Glycerol-Water Saturated w i t h S o d i u m Chloride
644
I N D L'STRIAL A N D ENGINEERING CHEMISTRY
that the relation also holds both for aqueous solutions of glycerol and aqueous solutions of glycerol saturated with sodium chloride. Duhring's rule may be used as the basis of a graphical representation of a series of such solutions from which many calculations may easily be made. If the boiling point of one substance at a certain pressure is plotted as ordinate against the boiling point of another substance at the same pressure as abscissa, the series of boiling points thus plotted will fall in a straight line. In dealing with aqueous solutions, it is usually most convenient to plot the boiling points of water along the horizontal axis and the boiling points of solutions on the vertical axis. The boiling points of a solution of zero concentration fall on a straight line a t 45 degrees. The boiling points of other solutions are represented by sloping lines more or less parallel to this and a t various heights above it. The elevation in boiling point of a given solution at a given pressure is, then, the vertical distance between the zero concentration line and the line for the solution in question, a t the temperati ;e which boiling water has under the given pressure. Figure 1 shows the Duhring lines for glycerol-water solutions and Figure 2 gives the Duhring lines for glycerol-water saturated with sodium chloride a t the temperatures of the boiling pojhts of each solution. The per cent of glycerol in the solutions shown in Figure 2 is the amount of glycerol in these solutions before saturation with sodium chloride. These figured are plotted as described above. Thus, in Figure 1 solution H boiled a t approximately 80" C. a t a pressure of approximately 185 mm. The boiling point of water at this pressure is about 65" C.; therefore one finds a point in Figure 1plotted for these values (65" c. on the water axis and 80" C. on the solution axis). The elevation of the boiling point of a solution whose composition is H is then the vertical distance between the line for H and the line for pure water, which is line A in Figure 1. The Diihring lines coincide very closely with the experimental data. With few exceptions the deviation is less than 0.1" C. I n the case of the higher concentrations, above 80 per cent glycerol, the deviation is slightly more in some instances. This was due to experimental error caused by the bumping of the solutions. Enough experimental data were taken to secure the exact slope of the Duhring line for each solution. Table I-Amounts
of S o d i u m Chloride in t h e Glycerol-Water Solutions at 25' C.
Solution A
B
C D E
F H G
I J
.
Glycerol before saturation Grams NaCl per Per cent 100-gram solution 24.5 10.45 22.5 20.3 20.5 30.45 18.4 40.15 16.2 50.82 14.3 60.10 12.2 69.90 11.1 75.83 9.4 86.22 8.1 95.64
It is obvious that the Duhring relation would hardly be expected to hold for a solution whose composition changed with change in temperature. Consequently, the boiling points of a saturated solution of a substance which changes rapidly in solution with temperature cannot be expressed by Duhring's rule. It happens that the solubility of sodium chloride in aqueous glycerol changes so little and so regularly with temperature that the solutions of constant glycerol content but saturated with sodium chloride at various temperatures still obey Diihring's law. This is merely the result of the peculiar solubility curve of sodium chloride and cannot be expected as a general rule. Table I gives the amount of sodium chloride necessary for saturating the glycerol-water solutions a t 25' C. Since the amount of sodium chloride necessary for saturation varied with the temperature, the
Vol. 17, No. 6
values in Table I are only approximately true for any other temperature. P o i n t s of S y s t e m Glycerol-Water, Experimental Data -BOILING POINTSGlycerol solutions Water Pressure O c. Mm. 125.11 65.20 189.10 136.72 73.26 268.60 147.48 80.59 363.50 161.99 90.63 538.70 86.00 55.46 120.56 97.49 65.04 187.77 104.45 71.02 244.02 116.07 80.83 367.30 122.39 86.04 451.60 128.55 549 Bo 91.17 .._ 78.35 54.47 114.90 105.80 78.26 330.80 115.50 86,61 461.70 122.50 92.62 080.40 68.22 54.58 115.50 79.24 64.77 185.50 87.84 72.72 262.50 98.32 82.27 389.20 106.81 89.99 525.50 77.85 65.77 193.97 89.57 76.89 312.70 96.95 83.90 415.00 104.33 90.77 541.50 66.64 59.43 145.31 78.88 71.25 246.50 89.05 81.02 370.00 97.72 89.47 515.50 69.34 65.34 190.33 87.09 82.57 393.90 88.67 93.34 499.90 98.85 94.06 612.12 58.77 56.69 127,82 71.23 68.99 223.41 80.71 78.29 331.23 89.53 86.97 468.30 97.61 94.88 631.20 65.32 64.21 180.80 77.08 75.75 298.34 91.42 89.96 525.00 96.84 95.29 640.90 65.87 65.39 190.70 79.58 79.04 341.30 88.79 89.41 502.30 97.37 96.61 672.80
Table 11-Boiling Glycerol Per cent 95.64
89.70
86.22
75.83
69,99
56.80
42.44
28.53
20.05
9.47
c.
Calculation of Vapor Pressures
The experimental data from which the Duhring lines were constructed are given in Tables I1 and 111. From the Duhring lines the data for the vapor pressure curves can readily be derived by interpolation. These calculated data are presented in Table IV for glycerol-water and in Table V for glycerol-water-salt solutions. Boiling point composition curves a t 760 mm. for the solutions studied were also derived from the Duhring lines and are given in Figure 3. The broken curve, A , represents Gerlach's values, and Curve B shows the writers' experimental data for glycerol-water solutions. It will be seen that the agreement is very close. Curve C shows the boiling points for glycerol-water solutions saturated with sodium chloride. Calculation of Latent Heats of Vaporization
I n operations involving the evaporation of solutions, a knowledge of latent heats of vaporization is desirable. A method of calculating latest heats, based on a knowledge of the Diihring curve, has been proposed by Lewis,6who writes the Clapeyron equations for water and the substance or solution, respectively, substitutes for V its value RTIP in both equations and then divides the first by the second and arrives a t the expression where L. and L, are the molal heats of vaporization of the substance and water at the absolute temperatures T. and Tu, respectively. The quantity dTs/dTw is the slope of the Duhring line. L , is known accurately over a wide range of temperatures. L, is therefore readily calculated. 6 Walker, Lewis, and McAdams, "Principles of Chemical Engineering," 1933, p 425. McGraw-Hill Book Company.
INDUSTRIAL AND ENGINEERING CHEMISTRY
June, 1925
Calculations for the latent heats of solutions of glycerolwater are given in Table VI. T a b l e 111-Boiling P o i n t s of S y s t e m Glycerol-Water Saturated with S o d i u m Chloride, Experimental Data BOILINGPOINTS-Glycerol Glycerol solutions Water Pressure Per cent" c. 0 c. Mm.
--
228.5 327.4 451.9 143.3 159.5 302.9 397.0 594.9 121.2 265.8 404.9 519.7
69.49 78.02 86.06 59.12 61.45 76.13 82.77 93.28 55.60 73.02 83.27 89.69
95.64 86.22
a 760-mm. (30-inch) barometer. Exhaust steam a t 2.27 kg. (5 pounds) gage is used for heating all three evaporators. It is obvious that the principal concern of the designer is to supply the proper amount of heating surface. The heating surface needed is determined by the total amount of heat to be transferred, the heat transfer coefficient, and the available temperature drop. Assuming that the coefficient and the total amount of heat to be transmitted can be determined,
90.43 93.22 110.79 118.87 131.58 75.83 74.75 94.23 105.77 113.16 73.37 69.90 93.67 104.04 110.81 71.27 60.10 73.63 82.28 87.80 97.60 103.51 61.44 159.4 73.12 50.80 64.91 186.6 76.69 73.43 270.5 85.83 96.90 83.67 411.4 106.23 92.32 574.0 59.84 148.1 69.85 40.15 83.66 72.91 264.6 94.28 82.86 398.3 102.55 90.83 542.7 93 * 74 605.1 105.97 30.45 67.85 58.92 141.8 94.49 84 * 3s 422.9 101.47 90.76 541.2 150.6 67.82 60.21 20.30 264.2 81.15 72.88 463.7 95.72 86.72 565.9 101.40 91.97 147.5 IO.45 66.43 59.75 82.00 74.38 281.6 97.74 89.40 513.8 94.49 622.3 103.31 ' Represents amount of glycerol in the various solutions before satura-
8-GLYCEROL-WATER
tion with sodium chloride.
PER C m r GLYCEROL
Applications
An instance of the application of these data may be of interest. Waste soap lyes are often concentrated by the following system: (1) concentration in double effect to the point where they are saturated with salt; (2) concentration of the liquor from the double effect (1) to semicrude (35 to 40 per cent glycerol) in a single-effect salting evaporator; (3) concentration of the liquor from the single effect (2) to finished crude (SO to 83 per cent glycerol) in a single-effect salting evaporator. Assume that a light lye containing 10 per cent glycerol and 20 per cent sodium chloride is to be concentrated by this method. The vacuum in the second effect of the double and in both singles will be 650.4 mm. (26 inches) calculated to Table IV-Boiling
Pressure Mm.
Boiling point of water O
760.00 525.80 355.10 233.53 149.19 92.30
C.
Water % 90 Glycerol % 10
100.7 90.6 80.5 70.4 60.3 60.2
100 90 80 70 60 50
Table V-Boiling Boiline
645
Figure 3-Boiling Point-Composition Curves for Glycerol-Water a n d Glycerol-Water-Sodium Chloride S o l u t l o n s at 760 Mm., I.
on the one hand from the information in the designer's possession, and on the other hand from the total quantities to be handled per hour, it remains to calculate the available temperature drop. I n calculating the boiling temperatures in a double-effect evaporator it is necessary to know the concentration a t which the liquid passes from the first to the second effect and also the distribution of available temperature drop between the two effects. It is outside the scope of this paper to outline the calculations necessary for determiningthese two quantities; therefore it will be assumed that the calculations have been made and that they show that when the double effect is run-
P o l n t s of Glycerol-Water Solutions. Calculated from D u h r i n g Lines of Figure 1 (Boiling points in O C.)
80 20 101.6 91.5 81.4 71.2 61.0 50.9
70 30 102.9 92.8 82.6 72.4 62.2 52.1
60 40 104.5 94.2 84.0 73.7 63.5 53.4
50 50 106.7 96.3 86.0 75.6 65.5 55.2
40 60 109.6 99.3 88.8 78.5 68.1 57.6
P o i n t s of S o l u t i o n s of Glycerol-Water Saturated w i t h S o d i u m Chloride. (Boiling points in e C.)
30 70 114.0 103.5 92.8 82.2 71.5 61.0
20 80 121.5 110.3 99.3 88.3 77.3 66.2
10 90 139.8 127.8 116.0 104.0 92.0 80.1
4.36 95.64 175.8 161.1 146.5 132.1 117.6 103.1
Calculated from Duhring Lines of Figure 2
~
Pressure Mm.
Water Yo Glycerol %
100°
90
108.7 98.2 87.7 77.3 66.8 56.5
109.1 9S.5 87.9 77.3 66.6 56.1
80 20 109.8 99.2 88.7 78.1 67.6 57.0
70 30 111.1 100.5 89.9 79.3 68.8 58.2
30 20 10 70 80 90 120.9 129.0 149.8 90 109.8 117.6 137.1 80 98.7 106.0 124.4 70 87.7 94.5 111.6 60 76.7 83.1 98.9 50 65.6 71.7 87.2 Values in this column were interpolated from data for saturated salt solutions taken by Badger and Baker, Chcm. M e t . E R E . 23, , 573 (1920).
760.00 525.SO 355.10 233.53 149.19 92.30 a b
point & water C. 100
Ob
10
60 40 112.5 101.8 91.2 80.6 70.0 59.4
50 50 114.2 103.5 92.8 82.0 71.3 60.6
Represents the amount of glyceiol in solution before saturation with sodium chloride.
40
60
116.8 106.0 95.0 84.2 73.4 62.6
4.36 95.64 179.3 164.7 149.9 135.2 120.5 105.8
IlVDUSTRIAL AND ENGINEERING CHEXISTRY
646
ning regularly the liquid will be passing from the first to the second effect a t about 12.5 per cent glycerol. It will also be assumed that these calculations have shown that the boiling point of the first effect when evaporating water would be 85" C. (185" F.). Steam at 2.27 kg. (5 pounds) gage has a temperature of 108.3"C.(227"F.). A 650.4-mm. (26411.) vacuum corresponds to 51.7" C. (125" F.). Consequently, it might be assumed that all three of these evaporators had a total available temperature drop of 56.6" C. (102" F.). If the evaporators were to be designed on this basis, it would be found that they were too small, as will be shown later. Table VI-Latent Heat of System Glycerol-Water a t 760 mm. Weight per cent Temp. .of solution Latent heat C. calcd./gram of glycerol 100.7 384.8 9.47 101.6 295.3 20.05 249.3 102.8 28.53 105.0 42.44 196.8 56.80 108.6 164.3 114.0 142.1 69.99 117.6 75.83 132.5 121.1 86.22 130.8 138.8 118.7 89.68 95.64 175.8 109.2
The usual method of procedure is to begin operating the double effect with both bodies filled with weak lye. As this concentrates and the level lowers fresh weak lye is fed to the first effect and partly concentrated lye is fed from the first to the second until the second comes up to density. The semicrude and the crude evaporators usually run in batches. If the boiling Doints of the various solutions in these evaporators are calciiated from Table V, the results will be:
Steam temp. Double: Firsteffect Secondeffect Semicrude Crude
O
c.
Vol. 17, No. 6
BEGINNING OF BATCH ENDOF BATCH AVERAGE Useful Useful Useful Boiling temp. Boiling temp. temp. point $op goint drop $rap c. C. c. c. C.
108.3 85.0 108.3 108.3
89.7 55.5 57.8 61.1
18.6 29.5 50.5 47.2
92.8 57.8 61.1 73.3
15.5 27.2 47.2 35.0
17.0 28.3 48.8 41.1
The feed lye to the f i s t effect is not saturated with salt and consequently its boiling point cannot be determined from Table VI. Table VI shows, however, that the presence of 10 per cent glycerol does not increase the boiling point of a salt solution appreciably. Therefore the boiling points of these solutions have been determined from the data for pure sodium chloride solutions given by Badger.E This shows that the double effect will have an average useful temperature drop of only 45.3" C. (82" F.) instead of 56.8" C. (102" F.). When the liquid is fully up to concentration it will have a working temperature drop of 43" C. (77"F,). I n other words, the increase in the boiling point of glycerol solutions has decreased its capacity to about 20 per cent less than it would be when boiling water, in addition to the loss in capacity from the lower heat transfer coefficients for glycerol. The decrease in capacity of the semicrude evaporator is of approximately the same magnitude, and the decrease in capacity of the crude evaporator is considerably more. Many similar calculations will a t once suggest themselves to those familiar with the design of equipment for evaporation and distillation. 6
Chem. M e r . Eng., S T , 932 (1922).
A Stopcock Orifice Flowmeter' By Jonathan Sharp UNITEDSTATESOZONECo., SCOTTDALE, PA.
A
FLOWMETER of variable range was needed in the laboratory for measuring small flows of ozonized air when making rough quantitative determinations of the ozone consumed in oxidation and similar tests on small amounts of organic materials. Since ozone is very destructive to rubber and attacks most metals to some extent, an all-glass construction was necessary. The device illustrated is more easily made than the multiple capillary type, and has other advantages. It has been found reliable for a large range of flow, and should be equally useful for other corrosive gases. The variable orifice, A , is a large bore (6.3 mm. or 0.25 inch) stopcock, notched to close gradually so as to give a full-scale reading, or differential head, of about 41 cm. (16 inches) for any flow from 2.8 liters (0.1 cubic foot) per minute or less to almost 28 liters (1 cubic foot) per minute. A light mineral oil of specific gravity 0.84 was used as the indicating liquid. A small buret cock, B , a t the bottom of the U-tube allows the liquid to be replaced without dismounting the apparatus. To prevent leakage through the drain cock on account of the oil dissolving out the lubricant, a small amount of mercury was drawn in as a seal after filling about half full with oil. A sliding scale (not shown) was made of graph paper pasted on a strip of corrugated fiber to fit between the arms. This requires no clamps and keeps its place after adjusting to the oil level. The stopcock, C, also of large bore and notched, regulates the flow. 1
Received March 26. 192.5
The device is calibrated for a given orifice' setting against a gas meter, using air. With the stopcock C adjustment may be made for the same back pressure that is used in a test. Unlike the capillary type of differential flowmeter, the pressure head varies directly as the square of the flow. This feature, hardly expected for an irregularly shaped orifice such as that of the notched stopcock,. permits close calculation of the flow for any other point on the scale when the same pressure and orifice setting are used. This applied for all but the largest openings, in which case the channel is too s m a l l f o r t h e theoretic square relation to hold rigidly.
=E%= C
€3
