INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1929
mate size and shape has been discontinued a t the recommendation of the AMERICAN CHEMICAL SOCIETY,together with all other 150-cc. sizes in conical or round flasks except one round extraction flask with an extremely wide neck. The position chosen for the location of the temperaturemeasuring device is such that temperatures may be obtained less than the hottest portions of the flask area. This is especially true if the bottom of the flask is located close to the bottom of the iron pot. With this distance cut down to inch (6 mm.) or slightly less, the temperatures existing at the center of the bottom of the flask may be 10" to 15" C. higher than would he shown a t the location advised in the specifications. It would seem that measurements of temperature should be taken to show results not less than the highest igniting-surface temperatures which may be obtained. Moreover, in order that some degree of uniformity can be obtained, the minimum distance from the bottom of the flask to the bottom of the iron pot should be specified. Furthermore, a standard method should contain a definition of autogenous ignition temperature. For example, if the temperature is to be determined by the appearance of flame, then the user should look for the flame and disregard any puffs of smoke which may be obtained a t lower temperatures. Conclusions
1-Copper is not suitable as an igniting surface for general test work. 2-A chromium-plated apparatus has many advantages, but the results are not the same nor are they in proportion to those obtained with steel. 3-Steel has the most universal practical application for its results. However, an apparatus made of steel, or any other metal of sufficient volume to give low results, must be made to order in the machine shop. Such an apparatus is not so easily or quickly cleaned as one in which glass is used as the igniting surface. 4-Fksults can be duplicated more exactly with glass than with any of the other materials tried. There is little to be gained by increasing the size of the ignition chamber over 125 cc. A decrease in the size of the flask mouth lowers the temperature of auto-ignition. The temperature conditions are more uniform when using a solder bath if R round flask is used rather than one of Erlenmeyer shape. Consequently, for test work with glass, Pyrex boiling flask KO.3, capacity 125 cc., is recommended; and temperatures should be meas-
139
ured under the center of the bottom of the flask as close to the flask as is practicable (within '/16 inch or 1.6 mm.). 5-The lowest ignition temperatures are obtained with quantities of fuel such as to give a rich mixture in the ignition chamber. In very few instances does ignition take place with quantities of fuel calculated to give mixtures leaner than the theoretical combining proportions, except a t temperatures much higher than the values presented in the tables. Therefore, it is concluded that relatively lean mixtures of flammable vapor and air cannot be ignited by hot metals a t the temperatures commonly prevailing a t burner boxes or electric heating units in japan ovens; but when vapors have accumulated to a rich concentration, ignition can and does occur with generally disastrous results. Bibliography 1-Krause and Meyer, Ann., 264, 85 (1891). 2-Askenasy and Meyer, Ibid., 269, 49 (1892). 3-Freyer and Meyer, Z . physik. Chcm., 11, 28 (1893); B n . , 26,622 (1892). 4-Gautier and Helier, Compf. rend., 122, 566 (1896). 5-Helier, Ann. chim. fihys., [71 10, 521 (1897). 6--Bodenstein, Z . phystk. Chem., 24, 665 (1899). 7-Falk, J . A m . Chem. Sac., 28, 1517 (1906); 29, 1536 (1907). 8-Dixon and Coward, J . Chem. SOC.,96, 514 (1909). 9-Holm, Z. angew. Chem., 26, 273 (1913). 10-Constam and Schlapfer, Z. Ver. deuf. In&, 67, 1489 (1913). 11-H. Moore, J . SOC.Chem. I n d . , 36, 110 (1917); J.Inst. Petroleum Tech., 6, 186 (1920~; Automobile Eng., 8, 245 (1918). 12-McDavid, J . Chcm. Sac., 111, 1003 (1917). 13-Anonymous, Engineering, 104, 692 (1917). 14-Sinnott and B. Moore, J . Soc. Chem. Ind., 89, 72 (1918). 16-Alilaire, Compf. rend., 168, 729 (1919). 16-White and Price, J . Chem. Soc., 116, 1248 (1919). c 17-Wollers and Ernke, K r u p p . Monatsh., 2, 1 (1921). 18-Ddiber, 2. Ver. deut. Ing., 65, 1289 (1921). 19-Tizard and Pye, Phil. Mag., 44, 79 (1922). 20-White, J . Chem. Sor., 121, 1688 (1922). 21-Alt, 2. Ver. deut. Ing., 67, 686 (1923). 22-Wartenberg and Kannenberg, Z . physik. Chem., 106, 205 (1923). 23-Tausz and Schulte, Mitt. chem.-tech. Inst. tech. Hochschule Karlsruhc 2 (1924); 2. Ver. deut. Ing., 68, 574 (1924). 24-Mason and Wheeler, J . Chem. Sac., 126, 1869 (1924). 25-Wheeler, Ibid., 125, 1858 (1924). 26-Ormandy, J . Inst. Petroleum Tech., 10, 335 (1924). 27-Underwriters' Laboratories, Miscell. Hazards, Repf. 1130 (1924). 28-Ormandy and Craven, J . Inst. Pefroleum Tech., 12, 650 (1926). J . Soc. Chem. I n d . (Japan), 29,266 (1926). ag-Tanaka-Nagai, 30-Garner and Saunders, Trans. Faraday Soc., 22,281 (1926). 3l--Brown, Univ. of Mich., En&.Res. Bull. 7 (1927). 32--Callendar, Engzneerrng, 123, 147, 182, 210 (1927). 33-Egerton and Gates, J . Inst. Petroleum Tech., 18, 244 (1927). 34-Masson and Hamilton, IND.END. CHBM.,19, 1335 (19271. 3S-Weerman, J . Inst. Petroleum Tech., 18. 300 (1927).
Correlation of Freezing Points and Vapor Pressures of Aqueous Solutions b y Duhring's Rule' Carl C. Monrad UNIVERSITY OF MICHIGAN, ANN ARBOR,MICH.
ARIOUS equations have been proposed for expressing the relationship between the temperature and pressure of saturated vapors. Of these by far the most useful is the generalization known as Duhring's rule. This rule states that, if the temperature of one substance is plotted against the temperature a t which another substance has the same vapor pressure, the curve produced is a straight line. Duhring expressed the relationship mathematically as Ti-- Tz el - ez
V 1
Received August 2, 1928.
This was found to hold for a large number of substances with fair accuracy. The advantage of this rule over others, such as the RamsayYoung equation, is that the curve is a straight line. Two points are sufficient to determine the line completely. If additional data are determined, they are of use merely as checks. The reference substance should preferably be one that is chemically similar to the one under consideration. Thus, alcohols are best plotted against water, benzene against toluene, etc. For most purposes water is a suitable standard
I N D U S T R I A L A N D ENGINEERING CHEMISTRY
140
and has the additional advantage that its vapor-pressure curve is known more exactly than that of any other substance. Tables are available that may be easily interpolated. I n 1920 Baker and Waite2 extended Diihring's rule to aqueous solutions and found that it held quite well-in fact. better than any other simple relationship. The experimental points generally fell not farther than 0.1" C. from the line, and this represented the probable error in the data. These authors showed that this rule amlied to all solutions, dilute or concentrated, electrolytes or- ;on-electrolytes. The only limitation is that the concentration must be constant for any one line. The slopes of the lines for various concentrations are, in general, not the same and the lines do not intersect a t any definite point. In 1925 Leslie and Carra extended the investigations to systems in which the solute and solvent both exert appreciable vapor pressures, such as solutions of benzene and toluene, hexane, and heptane. The rule was found to hold equally well in these cases. It has thus been shown that Duhring's rule is applicable to all solutions and pure substances. It is necessary to know only two points on the vapor-pressure curve, and from these the entire curve may be calculated. No simple rule has been stated by means of which the freezing point of a concentrated solution may be correlated with its boiling point. If the solute exerts no appreciable vapor pressure, it is known that the vapor-pressure curve of the solution falls below that of the liauid solvent and continues until it intersects the solid-vapor iine for pure solvent. The temperature of this intersection is the freezing point of the solution, provided that the separating phase at this point is pure solid solvent.
Vol. 21, No. 2
temperature axis a t a point a. The line through the origin at a 45 degree angle is the Duhring line for pure water. Figure 2 shows the phase diagram for the system water a t low pressures. The point 0 is the triple point for liquidsolid-vapor, and the lines OL, OP, OM, and ON are the respective equilibrium lines for solid-liquid, liquid-vapor, supercooled liquid-vapor, and solid-vapor. OR is the liquidvapor curve of any solution as in Figure 1. R is the freezing point of the solution. L
P
0
t
0 Temperature, D e g r e e s Centigrade. Figure 2-Phase Diagram
Since in Figure 1 b is the temperature difference between water a t 0" C. and the solution a t the same vapor pressure, it must also be the distance shown as b in Figure 2. Similarly, a is the temperature difference between water and solution a t the same vapor pressure when the solution is a t 0" C. The solution vapor-pressure curve continues until iinally it intersects the ice-vapor a t R. Let this temperature be F degrees and x the difference between isobaric temperatures of ice and supercooled water. The vapor-pressure curves of ice and supercooled water have been determined experimentally, and formulas are available for accurate extrapolation. If a curve is made of the isobaric temperatures of ice and water plotted against one another, the Duhring line of a solution intersects this curve a t its freezing point. In other words, the freezing point determines one point on the vapor-pressure curve and hence on the Duhring line. From the Duhring line diagram it is apparent that the slope of the line is represented by
-
+
Since - ( F z) is the temperature of supercooled water corresponding to ice a t -F": and since an accurate plot may be made of F versus z on ordinary cross-section paper from the data in Table I, whereas a plot of F against F x is not nearly so accurate, the former was used in this investigation.
+
Figure 1-Duhring
Line
Table I-Vapor Pressure of Ice and Water DIPFERENCB TEMP.WATER TEMP.ICE
PRESSURE
Duhring's rule has been applied to such cases in this investigation and checked against experimental data on aqueous systems. The relationship has been found to hold very well, certainly within the limits of error in most of the experimental data. Method
Figure 1 shows the typical Duhring line for any aqueous solution plotted against water as a standard. The line intersects the solution-temperature axis a t a point b and the water
*
Truns. Am. Ins;. Ckem. Eng., 13, Pt. 11, 139 (1820); Chcm. Met. Eng., 86, 458 (1921). I IND. ENO. CHSM., 17, 810 (1825).
Mm. Hn
4.579 4.216 3.880 3.568 3.280 3.013 2,765 2.537 2.326 2.131 1.960 1.785 1.632 1.490 1.361 0.6077 0.3825 0,1429 0.04383
c.
c.
0.0 1.1366 2.2666 3.396 4.516 5.641 6.762 7.8S5
0.0
O
9.000
10.117 11.231 12,336 13.439 14,558 15.658 25.0 30.0 40.0 50.0
1.0
2.0 3.0 4.0 5.0 6.0 7.0 8.0
9.0 10.0 11.0 12.0 13.0 14.0 22.521 27.116 36.500 45.965
X
0.0 0.1355 0.2666 0.396 0.516 0.641 0.762 0.885 1.000 1.117 1.231 1.336 1.439 1.558 1.658 2.479 2.884 3.500 4.035
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1929
Calculation of Freezing Point from Duhring Line
If the Diihring line of a solution is known from two or more vapor pressures, the freezing point is determined by producing the line to meet the curve of F and F x. It may be more accurately found by using the F vs. 2 curve. The slope of the line is
+
K = -b = u
or
x =
-
F+x-u
( KT -) 1
F
Calculation of Slope of Duhring Line
If only one vapor pressure is known for a solution but the freezing point is also available, the Duhring line is easily constructed. One point is determined as usual from the known vapor pressure The x corresponding to the freezing point is read from the F vs. z curve. The slope of the line is
R =
in most cases from Volume 111, International Critical Tables, checked by reference to the original literature where possible. The Duhring line for a solution was plotted and its slope determined. This was checked by calculating the slope of the Duhring line joining the freezing point to the boiling point a t some pressure, usually 1 atmosphere. In all cases the freezing point was also checked for some of the concentrations, but in general it was found simpler to check the slope.
+a
Hence, if a line is drawn on the F vs. x curve of slope -(K - 1)/K and intercept a on the x axis, the intersection of the curves is the freezing point of the solution.
+F Ta + F + x Tm
where T,,and Tw, are the temperatures of water and solution a t the known vapor pressure. Since the slope is not very sensitive to a relatively large error in the freezing point, this offers a very exact method for checking the slope of a known Duhring line. Checks on Data in the Literature
Since all the above discussion is made on the assumption that Duhring's rule holds for low pressures, it is necessary to check this from data in the literature. A large number of systems were studied and all of them found to check very well In a few cases the freezing points were accurately known and these systems checked exactly.
141
Table 11-Data
SOLN.
from Literature BOILINGPOINT K K 760mm. 92.3 mm. ACTUAL CALCD.
FREEZINQ
STRENGTHPOINT
-
2
c.
C.
G./lOO 8 . Ha0 5 10 20 30 40 50 60 70
1.6 3.5 6.5 9.0 11.6 14.2 16.8 19.4
0.22 0.45 0.82 1.12 1.40 1.67 1.94 2.18
5 10 20
4.0 9.1 21.8
0.50 1.12 2.41
5 20 lo 30 40
2.0 5.1 18.0 31.6 45.0
0.26 0.65 2.05 3.20 3.98
10 20 30 40
4.90 13.40 24.2 37.3
0.63 1.60 2.62 3.56
O
c.
SODIUM NITRATE
100.52 101.08 102.16 103.18 104.19 105.24 106.32 107.29
50.30 50.75 51.41 52.13 53.08 53.60 54.22 55.00
1.004 1.006 1.015 1.021 1.022 1.033 1.042 1.046
1.003 1.006 1.012 1.019 1,024 1.031 1.040 1.045
1.007 1.015 1.026
1.006 1.012 1.026
1.006 1.013 1.027 1.045 1.065
1.007 1.014 1.026 1.042 1.062
1.008 1.016 1.023 1.030
1.007 1.015 1.025 1.03S5
1.004 1.005 1.012 1.018 1.026 1.035 1.053
1.004 1.005 1.010 1.016 1.024 1.034 1.052
SODIUM HYDROXIDE
POTASSIUM HYDROXIDE
CALCIUM CKLORIDE
7 ." _Salt 2.5 5.0 10.0 15.0 20.0 25.0
101.30 103.20 105.83 109.25
50.90 52.40 54.68 57.75
SODIUM CHLORIDE
1.40 0.20 2.90 0.38 6.60 0.84 10.90 1.33 16.30 1.88 23.50 2.56 Satd.b 21.10 2.34 a Data very uncertain. b Diihring line is practically
100.44 100.90 101.93 103.16 104.72 106.78 108.73
50.26 50.62 51.35 52.22 53.40 55.01 56.08
straight.
Table I1 shows the results obtained on some of the systems studied. The slopes calculated are very accurate indeed, when one considers that a change of one in the third decimal place corresponds to 0.05" C. a t a temperature of 50" C. Very few data in the literature may be relied on to this extent, especially a t high concentrations. Certainly, for all industrial purposes the accuracy is quite sufficient. Thus, it is possible to determine the vapor pressure of any aqueous salt solution with an accuracy of about 0.1" C. a t any pressure, if the freezing-point curve and the boilingpoint curve are known for various concentrations. Many such data are available for salt solutions whose vapor-pressure curves are unknown. I n many other cases this furnishes a valuable check on existing data. The only limitations are that the concentration must not exceed that a t the cryohydric point, and the salt or other solute must exert no appreciable vapor pressure of its own. Application to Concentrations above Cryohydric Point
Figure 3-General
Duhring System
Freezing-point data were taken from Landolt-Bornstein tables and Seidell's "Solubility of Organic and Inorganic Substances." Original papers were used in some cases and the best available data chosen. Vapor pressures were taken
One obvious limitation to this method is that in many cases the concentration of the solution in question is much higher than that a t the cryohydric point. In evaporation and crystallization the solutions become saturated, or very nearly so. It would be of great use in these fields, therefore, if this method could be applied to these concentrations. This is possible only when the vapor pressures of the saturated solutions and the solubility a t the boiling point are known. Phase-diagram study has resulted in many data of this type up to very high concentrations. If the vapor pressure of the solution is known a t any other temperature the Duhring line may be drawn. In this way a complete system may be drawn as shown in Figure 3. For high concentrations this
142
INDUSTRIAL AND ENGINEERING CHEMISTRY
method for determination of the vapor-pressure curves is probably the easiest. Figure 3 shows the Diihring system of a solution that has two possible solid phases with one transition point as shown. For a one-phase system the saturated-solution line would be a smooth curve from the cryohydric point. In other words, this curve is the vapor-pressure curve of the saturated solution plotted as a Diihring line, that is, of course, not generally straight. At each transition point there is usually a break in the vapor-pressure curve and hence in the Diihring line. The line from 0 ' C., called the F vs. F x curve, is really the freezing point-composition curve plotted as the freezing point us. the temperature of water at the same pressure. The Diihring lines of solutions up to the cryohydric com-
+
Vol. 21, No. 2
position run from their respective freezing points on this curve. For compositions above the cryohydric the Diihring lines run from the saturated solution curve at points that correspond to the respective concentrations of the solutions. The use of Diihring's rule for the calculation of activity coefficients does not seem to be generelly known. If the lines are plotted for the system a t different concentrations, it is easy to determine the activity of the water at any temperature and concentration by reading the temperature of the water at the same vapor pressures as the solution. The ratio of the vapor pressure of water at this temperature to that at the temperature of the solution is the activity of the water in the solution. This should be of great use a t very high concentrations.
Viscosity Relationships in the System Sulfuric AcidNitric Acid-Water1 F. H. Rhodes and H. B. Hodge, Jr. CORNBLL UNIVBRSITY, ITHACA.N. Y.
N SPITE of the very great
The viscosities of a large number of binary and terthese rough measurements, nary mixtures of these components have been deterhowever, indicated that the technical importance of mined at temperatures of O", 25", 50°, and 75" C. viscosity relationships in the "mixed acid," we have The results indicate the existence, in liquid form at portion of the system relabut little information as to the ordinary temperatures, of a hydrate of sulfuric acid tively rich in sulfuric acid identity of the compounds of the formula HzSOI.HZOand of a ternary compound presented some very interestwhich may actually exist in which contains SO8 and N2Os in the ratio of lOSO::N2Os. ing features which had been ternary mixtures of sulfuric There is no definite evidence of the existence of a previously overlooked. acid, nitric acid, and water hydrate of nitric acid in liquid form. These measurements have a t o r d i n a r y temperatures. Various investigators have been repeated, using an acstudied the relationships betweem the composition of mixed curate viscometer. The results are described in this report. acid and certain of its ihemical and physicd properties, but Experimental Procedure in general the data thus obtained have not served to identify the compounds which may actually be present. Much of this VISCOMETER-The viscometer used in this work was of the work has been done a t temperatures considerably above or type described by Bingham.a Two such instruments were below those at which the acid is used in nitration, so that the employed, the one with the smaller capillary being used with information that is available may not apply to the constitu- the mixtures which showed viscosities of less than about 10 cention of mixed acid under the normal conditions of use. The tipoises a t 0" C. Connections between the viscometer tube and results of these various investigations will be considered later, the rest of the apparatus were made by ground-glass joints, in connection with the discussion of the data obtained by since rubber connections might have been attacked by some viscometric methods. of the solutions used. The viscometer tube was set in a Since any change in the nature or the relative amounts of thermostat. A 10-liter bottle served as a pressure reservoir. the molecular species present in a liquid should affect the This bottle was provided with a rubber stopper through which viscosity, and since viscosities, may be measured a t the tem- extended three glass tubes-an inlet tube for water, an outlet peratures a t which mixed acid is ordinarily used, the measure- tube for air, and an outlet tube for water (extending to near ment of the viscosities of mixed acid should afford some in- the bottom of the bottle). The outlet tube for water was formation as to the nature of the compounds actually present connected by rubber tubing to a glass overflow outlet. By and might, perhaps, throw some light on the mechanism of admitting water slowly through the inlet tube, the air in the the nitration reactions, Viscosity relationships in this system bottle was compressed until sufficient pressure was developed have been studied by Bingham and Stone1#*but the number to lift the water to the overflow outlet, a t which point the of individual mixtures of which the viscosities were determined pressure remained constant. By adjusting the height of was rather small and only a few of those containing large this overflow outlet the pressure within the system could be amounts of sulfuric acid and relatively small amounts of water regulated. An empty bottle was connected into the air were investigated. At the time of the publication of these pre- outflow line to provide additional capacity and to minimize vious results B. B. Paul, working in this laboratory, was engaged any fluctuations in pressure. With this system it was possible in themeasurement of the viscosities of mixed acid. Since the to eliminate any detectable variations in pressure within the measurements were being made principally for the purpose of apparatus during a determination. The pressure reservoir obtaining information for use in the design of pumps and was so connected with the viscometer tube that the pressure agitators for handling nitrating acids and nitration mixtures, could be applied to either arm of the tube while the other arm the viscometer used was a rather crude one and no special was vented to the air. To prevent the absorption of moisture pains had been taken to insure extreme accuracy. Even by the acids while a measurement was being made, bulbs containing glass wool moistened with concentrated sulfuric 1 Received June 26, 1928. acid were inserted in the lines between the pressure bottle * Numbers in text refer to bibliography at end of article.
I
