INDUSTRIAL AND ENGINEERING CHEMISTRY
82
PHYTIN CONTEXTOF EXDOSPERM Although the investigation on the distribution of phos.
phorus-containing compounds liere reported jvas confined chiefly to the bran and embryo, the phytin phosphorus content of the endosperm received Some attention. I n their studies on the phytin content of foodstuffs, A4veri11 and ~i~~ ( I ) included several wheat flours. In some instances they report phytin phosphorus contents as high as 0.36 and 0.346 per cent. Approximately 25 per cent of the ash of commercial patent flours can be considered as phosphorus. Assuming that all the phosphorus is originally combined as phytin, the ash content of these two flours should be approxi'mately 1.4 per cent. This value is several times higher than that (0.40 per cent *) reported by the manufacturers of the flour in question. A sample of second middlings, representative of a pure commercial endosperm, examined in this laboratory, .contained 0.35 per cent of ash. By titrating an extract, following the method as modified by Averill and King, the amount
Vol. 24, No. 1
of phytin present is too small to be detected. Assuming that all the-phosphorus present is combined as phytin, nearly 0.32 Per cent of phytin should have been found. As the titration method shows the presence of such quantities, it becomes evident that only a very smxll proportion, if any, of the phosphorus in the endosperm occurs in the form of phytin. LITERATURE CITED (1) Averill. H. P., and King, C. G . , J . .4m. Chem. SOC.,48, 721 (1926). (2) Collison, R. C., J . Biol. Chem., 12, 61 (1912). (3) Guerrant, N. B., J . Am. Chem. SOC.,48, 2185 (1926). (4) Heubner, W., and Stadler, H., Biochem. Z., 64, 422 (1914). (5) Osborne, T. B., and Harris, I. F., Conn. Agr. Expt. Sta., Repl. 25, 365 (1901). (6) Osborne, T . B., and Mendel, L. B., J. Biol. Chem., 37,557 (1919). (7) Rather, J. B., Ark. Expt. Sta., BUZZ. 135 (1917). (8) Sullivan, B., and Near, C., Cereal Chem., 5, 166 (1928).
RECEIVED September 9, 1931 Presented before the Division of Aqricultural and Food Chemistry at the 82nd Meeting of the Amerioan Chemical Society, Buffalo, N. Y., August 31 to September 4, 1931.
Dew Points of Paraffin Hydrocarbons KARLHACHMUTH, Phillips Petroleum Company, Bartlesville, Okla.
T
HE dew points were de-
termined by either measuring the contraction in volume of the vapor as the temperature was lowered and the p r e s s u r e held constant, or by measuring the c o n t r a c t i o n in volume when the pressure was increased and the temperature held constant. In either case, the dew point was indicated by a sudden increase in the rate of the contraction a t the dew-point temperature or pressure.
DETERMINATION OF DEW
T H E W I D E S P R E A D domestic and industrial use of the liquejied petroleum gases has made necessary a n accurate knowledge of their dew points. The theoretical dew points of such mixtures are easily calculated by use of Raoult's law and other well-known rules. However, until verijied experimentally, it is unwise to assign very great accuracy to such theoretical data. This article describes a method for experimentally determining dew points, indicates the accuracy of Raoult's law, and describes a method f o r representing and calculating dew points of complex mixtures.
POINTS
The apparatus consisted of a glass bulb containing the sample and surrounded by a constant-temperature bath. This glass bulb communicated with a buret so that volume changes could be detected and the pressure changed a t will by a transfer of more or less of the sample from the buret to the bulb. The bottom of the buret was closed by mercury which served as a seal to the buret and dew-point bulb system, and also as a piston for transferring the vapor from the buret to the bulb. The pressure in the bulb was measured by balancing against a known external pressure on the mercury seal. Figure 1 is a diagrammatic sketch of the dew-point apparatus and auxiliaries. The water or alcohol bath was of about 1 gallon (3.8 liter) capacity and filled with one or the other of these liquids as the temperature required. The temperature of the bath was lowered and maintained b expanding a refrigerant (liquid propane or butane) througi the cooling coil contained just within the wall of the bath. The temperature of the vapor within the dew-point bulb was determined by a thermometer placed as shown. This thermometer was either a -40 to +120" F. mercury thermometer, graduated to 1' F., or a -110 to +50" C . toluene thermometer graduated to 1' C. for the first part of the work. During recent work a +30 to +120° F. mercury thermometer graduated to 0.1" F. has been used. The dew-point bulb was a small Pyrex glass bulb of ap-
roldmately 10 cc. capacity. The uret was of 3 mm. internal diameter and about 750 mm. in length. The volume of its contents was read on an ordinary meter stick fixed behind the buret. The bottom of the buret was sealed to a rather large U-tube which served as a mercury reservoir and a seal for the buret. Two s t o p c o c k s sealed into the side of the U permitted evacuation of the bulb and buret through one, and introduction of the s a m p l e t h r o u g h the other. During a test the mercury was always raised above the level of these stopcocks, thereby effectually sealing the srtmple within the bulb and buret. The right-hand side of the U-tube communicated with a source of constant oressure through a system of valves which were used to vary the pressure as desired. A 2000-mm. mercury manometer and a pressure gage were used to measure the pressure. A high-vacuum connection was made to both right and left sides of the U-tube so that the apparatus could be evacuated preparatory to introducing a fresh sample. The 100-cc. measuring buret and storage bulb shown at the left of the figure were used in synthesizing samples of known composition from pure com ounds. The stopcocks and connecting tubing were so arrangei that SLtm les could be introduced to the apparatus without passing throug: the buret or storage bulb. All the apparatus and tubing coming in contact with the samples were of Pyrex glass. Rubber tubing was not used because it is very pervious to paraffin hydrocarbons. A non-grease stopcock lubricant should be used when working with the less volatile hydrocarbons, such as isopentane. The dew-point determinations were easily made after a little practice. Determinations during the first part of the work were made by holding the pressure of the sample at some constant value while the temperature was lowered by steps. Conditions were held constant a short time during each step before a reading was taken. This method is the more difficult since it requires t h e adjustment of the pressure as well as the temperature after each step. This pressure adjustment is made necessary by the rise of the mercury in the buret during each lowering of the temperature. During recent work, the
January, 1932
I N D U S T R I A L .AND E N G I N E E R I N G C H E M I S T R Y
temperature was held constant and the pressure increased by steps. This procedure is considerably easier than the first, since the temperature can be held constant with very little attention, and all readings concerning the pressure may be recorded without any calculations a t the time. The corrections for height of mercury in the buret may be made a t any tiine after the completion of the test. Another advantage of this second method is the fact t h a t readings may be taken immediately after a change in pressure, since pressure equilibrium is obtained almost instantaneously. It is necessary t o wait some time for temperature conditions to come to equilibrium when using the first method.
83
was graduated to 1.0" F., and consequently the fractional parts of a degree had to be estimated. The theoretical dewpoints are calculated by use of Raoult's law as demonstrated later in this paper. The accuracy of such calculated values, assuming Raoult's law to be correct, depends on the accuracy of the vapor-pressure tables. The tables used in these calculations are a compilation of what are supposed to be the best data obtainable. The vapor pressures are expressed to three significant figures and are probably about that accurate for normal temperatures. If this is the accuracy of the tables. then the calculated dew points are accurate within about 0.1" F. (0.06' C.) in some ranges and within somewhat less than 0.5" F. (0.3" C.) in others. The reason for this variation in accuracy is the use of three significant figures in the tables, regardless of the size of the number. Table I gives the dew points found for the first three types of samples. Sample 1 is the only example of the first type. Samples 2, 3, 4, 5 , and 6 are of the second type. The remainder of the samples are of the third type. h'umbers 7 , 8, 9, 10, 11, and 12 were synthesized from samples 2 and 5. Samples 13, 14, and 15 were made from samples 2, 3, and 5. TABLE I. DEW POINTSOF PARAFFIN HYDROCARBONS AND COMMERCIAL PARAFFIN HYDROCARBON PRODUCTS COMPOSITION
SAMPLE Gas
Moles
R Propane Isobutane n-Butane Isopentane
-
0.5
LOO. 0
762
100.0
14.73
-43.5a
762
14.73
f12.75
$12.4 (-10.9)
1986 1666 1384 1288 1190
38.40 32.22 26.76 24.91 23.01
C60.0 +40.0 +36.0 4-32.1
+59.7 (+15.4) +50.0 (flO.0) +39.9( +4.4) + 3 6 . 2 ( +2.3) +32.0( 0.0)
762
14.73
+31.5a
+ 3 1 . 2 ( -0.5)
624 392 265
12.07 7.58 5.12
+71.8 +32.4
+50.0
4-72.2 ( + 2 2 . 3 ) $50.4 (+10.2) + 3 3 . 1 ( +0.6)
17.2 1 2.1 80.7 \
762
14.73
+24.5a
+24.1 ( -
4.4)
Isobutane n-Butane
33.6 1.7 64.7
762
14.73
+li
+16.6 ( -
8.6)
Propane Isobutane n-Butane
45.5 1.41 53.1\
762
14.73
+10.7"
+10.1 (-12.2)
Propane Isobutane n-Butane Isobutane
FIGERE 1. DEW-POINT APPARATUS ( ~ H A R A C T E ROF ~ A N P L E S TESTED-The samples used in these dew-point determinations were of four types:
i'l) Natural samples, such as the commercial grades of liquefied petroleum gases, the composition of such samples being determined by analysis. ((2) Pure or very nearly pure paraffin hydrocarbons, the composition of which was checked by analysis. (3) Synthetic samples of known composition made by mixing known weights of pure compounds (4) Synthetic mixtures of air and hydrocarbons made by mixing a known volume of air with one of the samples contained in the three previous types.
Isobutane n-Butane Isopentane
Propane Isobutane n-Butane
\ Propane
g j
D E WPOINT ABSOLETE ExperiPRESSURE mental Theoretical M m . Lbq/ liy si. In. F. F. ( " C.) 1185 2 2 . 9 1 + 4 5 . 5 + 4 6 . 2 ( +7.9) 895 17.31 +32 + 3 2 . 5 ( +0.3) 571 1 1 . 0 4 +11 +11.2 (-11.6) 383 7.41 6 - 5.7i-21.oj 2 . 9 8 -40.7' -39.8 (-39.9) 154 89 1 . 7 2 -57.5' -57.5 (-49.7)
9:
I!
LOO. 0
I
1
$50.0
-43.6 (-42.0)
The compositions of the several samples tested are noted in 56.8 Propane the tables. .4nalysis of the samples was by low-temperature 762 1 4 . 7 3 + 3 . 7 n + 3 4 ( - 1 5 . 9 ) 1.11 Isobutane 42.1 n-Butane fractionation, which is accurate to about *0.3 per cent. The compositions of the synthetic samples are approximately of 71.2 Propane 762 14.7:1 - 6 . j a - 7 . 1 ( - 2 1 . 7 ) 0.7 11 Isobutane the same degree of accuracy. 28 1 n-Butane COhfPA4RISOY OF EXPERIMEKTAL AND CALCULATED DEW 88.9 \ Propane POIYTS.The values tabulated below are those (determined by 762 1 4 . 7 3 - 2 4 . 7 " -25.3 ( - 3 1 . 8 ) 0.3 l 2 i 1s3butane ,?-Butane 10.81 the writer over a period of about three and one-half years a t various times when certain specific data were required. The Propane ll.O/ 13 ,Isobutane 15.5. 762 14.7.3 +24 +24.2 ( - 4.3) apparatus used for all the determinations was essentially 73.5 \ n-Butane that described previously, the only real differences in the Propane 73.5) various apparatus used being in dimensions and arrangement. 7 6 2 14.73 - 1 1 , 5 = -11.3(-24.1) 6.0 b Isobutane 20.5 \ n-Butane The accuracy with which the compositions (of the several Propane 3.1) samples are expressed has been covered. The temperature 56.9, 762 1 4 . 7 3 + l 9 . S a + 1 9 . 5 ( - 6 . 9 ) Isobutane values are probably accurate to 1 1 " F. (+0.6' C.) in most 40.01 n-Butane a See paragraph on Comparison of Experimental and Calculated Dew cases except when below - 30" F. ( - 34" C.). Experimental Points. deJv-point values expressed to 0.1 " F., which are not followed by footnote reference, indicate that the thermometer used in The samples of the fourth type are presented in Table 11. these instances was read that closely and was probably The composition is given in terms of the percentage of air and correct to within +0.2" F. (0.1" C.), Values designated by the of one of the previous samples. Reference must be made to footnote indieate that t h r thermometer used in such instances Table I for romposition of the hydrocarbon mixed with the
1
INDUSTRIAL AKD ENGINEERING CHEMISTRY
84
air. The theoretical dew points are calculated in the same way as those for the previous table, except that the partial pressure of the hydrocarbons is used as their total pressure in the calculations. This partial pressure is found by multiplying the given pressure by the percentage of hydrocarbon sample, and dividing by 100. The air is treated merely as a diluent of the vapor and is supposed to have no effect on the dew. OF PARAFFIK HYDROCARBONS AND AIR TABLE 11. DEWPOINTS
COMPOSITION SAMPLE Gas Volume
ABSOLUTE Experi-
DEWPOINT
PREBSUREmental
Mm. LbsJ H Q ag. tn.
% '
+26 +12 -10 -29
F. ( 0 C.) 2 5 . 5 ( - 3.6) 11.7 (-11.3) -12.5 (-24.7) -30.5 (-34.7)
26.47 10.91
-17 -47
-19.2 ( - 2 8 . 4 ) -49.2 (-45.1)
1369 564
'A] %] 90
lo]
5:)
Theoretical
3100 5 9 . 4 4 2314 4 4 . 7 5 1308 2 5 . 2 9 801 1 5 . 4 9
F.
6 -23
-
-
1525
29.49
+40.0
+40.0(+ 4.4)
1498
28.97
$32.3
+32.4(+
0.2)
1712
33.10
+32.5
+32.4(+
0.2)
294
5.69
$32.4
+33.1(+
0.6)
335
6.48
+32.6
+33.5(+ 0.8)
379
7.33
+32.6
+33.2(+
0.7)
532
10.29
f32.6
+33.3(+
0.7)
888
17.17
+32.4
+ 3 3 . 5 ( + 0.8)
5.0(-20.6) -25.2 ( - 3 1 . 8 )
The results of the experimental work may be summarized by the statement that the calculations made with Raoult's law check the determined values to within the limits of experimental accuracy. The values not checking the theoretical dew points either did not depend on Raoult's law (those for pure isopentane) or else were more dependent on other physical laws or assumptions (mixtures of sample 1 and air a t lower temperatures).
DERIVATION OF DEW-POINT EQUATIONS The nomenclature used in the equations appearing in this .ection is summarized in the following table: = partial pressure M = mole fraction P = vapor pressure PT = total pressure
For three component mixtures, (5)
Similar equations may be written for any number of components. These equations refer to liquid mixtures and are considered to represent the conditions obtained in the very first dew formed. The next step is to substitute vapor composition for liquid composition: Dalton's lav gives the equation: PAV
M A L P A= PAL =
X B refers to n-butane Z P refers to isopentane N P refers to n-pentane L refers to liquid phase V refers to vapor phase
Raoult's law gives for perfect solutions the equations: PAL =
=
MALPA
(1)
MBLPB, etc.
(2)
The total pressure of the mixture equals the sum of the partial pressures : P T L = M A L P A MBLPB . .. (3)
+
Solving this equation for MAL:
+
(6)
PAT, =
i M ~ ~ P ~
(7)
From Equations 4 and 8, for two component mixtures,
For three component mixtures,
For each additional component the equation practically doubles in complexity. It is obvious that this type of equation becomes unmanageable for more than three components. In any event, it is of the indirect type, giving the desired result in vapor pressures rather than temperatures. Moreover, the one equation contains four or more variables, depending on the number of components in the mixture. This means that three of these variables must be assigned values before the equation is solved. The vapor pressures are always assumed since they are interdependent. This leaves either the composition or the total pressure to be fixed. The complexity of the theoretical dewpoint equations makes it desirable to determine some other method for calculating dew points. There is, of course, the cut-and-try method, more often termed the "approximation" method. This method works very well when the dew point is known to within two or three degrees. I n this method the temperature is found at which: MAV
Subscripts:
- MAVPTV
Equilibrium between vapor and liquid give:
__
p
PBL
For two component mixtures,
0
3950 7 6 . 3 8 2324 4 4 . 9 4
A refers to component A B refers to component B C refers to component C P refers to propane ZB refers to isobutane
Vol. 24, No. 1
+ pg + pc + .... PT-1 JMBV
1MCV
(11)
This equation is derived from Equation 8 and its analogs. Another method of determining dew points would be by some general empirical equation in which the constants depended on some known property. A dew-point curve (Figure 3) for a two-component mixture gives no hint as to what form a general equation should take. An empirical equation covering such a curve becomes rather complex if any accuracy is desired. The graph (Figure a), representing dew points of a threecomponent mixture, a t once suggests an empirical method of representing the dew points of such mixtures. I n Figure 2 the isothermal dem-point lines all originate on one side of the chart, are all straight lines, and are practically parallel. An equation indicating the point of origin of these lines and their slope should represent all conditions in the chart. This equation, X = Mpv 0.456 .Tfr~v (12)
+
I N D U S T R I A L A N D E N G I N E E R I N G C H E If I S T K Y
January, 1932
gives the point, X , a t which a dew-point line passing through the composition determined by MPV and M I B V intersects the n-butane to propane side of the chart. This X is in terms of percentage of propane. The constant factor 0.456 is found by determining the composition of a propane and n-butane mixture, which has a dew point equal to the dew
DEW-POINT TEMP. O F .
+go $60
+3:
-30
COMPOSITIOX
83 MAX. DEVIATIOS
F.
+ MIBI. MYPV + M i s v + MPL' M.?isv + MIPI' +
-0.3 -1.5 +2.0
.M.MPV
MIPV
+4.5 -2.3
MPV MPL.
.
At first glance these errors seem rather berious, but further consideration shows that the mixtures having these large errors are unnatural. For instance, there is no possibility of obtaining mixtures of propane and isopentane directly from natural sources. Such a mixture must be synthesized from the pure compounds, and the writer can conceive of no occasion when this would be of any practical use. The largest error occurring in natural two-component mixtures is about 2" F., which is not too large for practical application of the equation. As the number of components in the mixture increases, the error decreases. For instance, a mixture of the following composition. % Propane Isobutane n-Butane Isopentane n-Pentane
40
10
20 15 15
has a dew point of 46.3" F. by the empirical method while the theoretical dew point is 46.2' F. (The above composition was chosen at random and not because i t had almost the same dew point by both methods.)
FIGURE 2. DEWPOINTS OF THREE-COMPONENT MIXTURE point of pure isobutane. The 0.456 is the mole fraction of propane in such a mixture. Thus, the dew points of threecomponent mixtures may be exprebsed in ternis of the dew points of a two-component mixture and one additional factor which is determined in turn from the same two-component mixture. Since the dew-point lines in Figure 2 are not exactly parallel i t is desirable to determine the amount the empirical equation deviates from the theoretical values. The following table gives the maximum deviations found for several selected temperatures: DEW-POINT TEVP. F.
MAXIMUM DEVIATION OF EMPIRICAL V A L U E S F R O V T H E O R E T I C 4 L
z+:
O
F.
+o 1 +o 1 -0.1 +o 3
10 0 -10 -20 -30
+0.3 +O 6 +o 3 +O.l
-40
The average deviation for the entire chart is approximately 0.1" F. The empirical equation is nearly as accurate as the original data and is considerably more accurate than necessary for practical purposes. It is neither easy nor practical to draw a chart representing dew points for more than three-component mixtures, but reasoning by analogy would indicate that the same scheme used for three components could be applied to any number of components. This was done for a five-component mixture containing propane, isobutane, n-butane, isopentane, and n-pentane. The two component system used as a reference is that of propane and n-pentane (see Figure 3). The equation is:
It must be remembered that the above empirical equations apply a t one total pressure only. A corresponding curve and equation must he determined for each different pressure.
CONCLUSIOS
Raoult's law gives a surprisingly accurate method for determining dew points of paraffin hydrocarbon mixtures. It can probably be assumed that Raoult's law will be sufficiently accurate for use in calculating all vaporization and condensation phenomena pertaining to paraffin hydrocarbons of any molecular weight, as long as no attempt is made to cover too great a range in volatility. The empirical method of calculating dew points derived in this report suggests t h a t relatively simple equations and curves could be found to represent any bind of vaporization or X = M P V 0.905 M I B =~ 0.805 M N B V 0.262 M I P B (13) condensation phenomena with sufficient degree of accuracy for wherein X is the composition (expressed as percentage of all practical uses. Such equations and curves would be propane) of a mixture of propane and n-pentane having a dew valuable in that they could be based on a theoretical foundapoint equal to t h a t of the five-component mixture whose tion which is more accurate than usual for theoretical assump composition is expressed by M P V ,M I B V M , N ~ vand , M I P I T . tions, and that they could be safely used to predict results with This empirical representation introduces the following maxi- very little experimental support. mum deviations: RECEIVEDAugust 17, 1931.
+
+
