May, 1942
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
3. The average molecular weights of the volatile intermediate products constantly decrease as the temperature of carbonization rises. This decrease is marked by the evolution of water, carbon monoxide, hydrogen, methane, and other hydrocarbons. 4. The initial decom osition of coal, giving semicoke and low-temperature tar, is irought about by (a) splitting off of radicals containing heterocyclic and homocyclic rings, (b) opening of some heterocycles to intermediate aldehydes which give rise to phenols, amines, and naphtiienic compounds, (c) progressive dehydrogenation and splitting off of side chains by the action of the develo ing hydrogen. 5 . Final &compositions are a t a maximum between 600’ and 800” C. and are marked by (a)loss of hydrogen and other simple gases from semicoke and hydroaromatic volatile compounds, (b) hydrogenation of phenols to aromatic hydrocarbons with the formation of methane, ethane, and water, and ( c ) formation of higher aromatics from semicoke proper and by secondary pyrogenetic syntheses.
Literature Cited (1) Blayden, H. E.,Riley, H. L., and Taylor, A., J. Am. Chem. Soc., 62, 180 (1940). (2) Brooks, B. T., IND.ENQ.CHEM.,18,621 (1926). (3) Bruins, P. F., and Czarnecki, J. D., Ibid., 33, 201 (1941). (4) Burgess, M. J., and Wheeler, R. V., Fuel, 4,208 (1925). ( 5 ) Daniels, F., “Chemical Kinetics”, pp. 14 and passim, 49, Ithaca, Cornell Univ. Press, 1938.
571
(6) Fowler, R. H., and Guggenheim, E. A., “Statistical Thermodynamics”, p. 528, Cambridge Univ. Press, 1939. (7) Fuchs, W., Am. Inst. Mining Met. Engrs., Tech. Publ. 1333 (1941). (8) Hackh, I. W. D., with Grant, J., Chemical Dictionary, 2nd ed., p. 770 (1937). (9) Hammett, L. P., “Physical Organic Chemistry”, p. 69 (1940). (10) Hurd, C. D., “Pyrolysis of Carbon Compounds”, A. C. S. Monograph 60, pp. 11, 16,New York, Chemical Catalog Co., 1929. (11) Marson, C. B., J. Armstrong College Min. Soc., 6,7 (1930). (12) Moore, E.S., “Coal”, 2nd ed., p. 188 (1940). (13) Morgan, J. J., and Soule, R. P., Chem. & Met. Eng., 26, 1025 I , Ann\
(lYL.6).
(14) Noyes, A. A.,and Sherrill, M. S., “Course of Study in Chemical Principles”, p. 426 (1938). (16) Parks, G. S., and Huffman, H. M., “Free Energies of Some Organic Compounds,” pp. 93-4, New York, Chemical Catalog Co., 1932. (16) Pictet, A., in Fuchs’ “Die Chemie der Kohle”, pp. 310 & ff. (1931). (17) Porter, H. C.,and Ovitz, F. K., U.S. Bur. Mines, Bull. L (1913). (18) Randall, Merle, in International Critical Tables, Vol. VII,pp. 224 & ff ., New York, McGraw-Hill Book Co., 1930. (19) Schrader, H., in Fuchs’ “Die Chemie der Kohle”, p. 364 (1931). (20) Stadnikoff, G. L., “Die Enstehung von Kohle und Erdol”, p 144 (1930). (21) Whitmore, F. C., “Advanced Organic Chemistry”, p. 841,New York. D. Van Nostrand Co., 1937.
of Solution of the System Trioxide-Water &.&!p& A table of partial molal heats can be used to calculate the heat involved in forming, mixing, and diluting solutions. Values are given for partial molal heats for the system sulfur trioxide-water which include all concentrations for sulfuric acid in water and oleums up to 100 per cent free sulfur trioxide. Similar data for systems in which crystallization occurs can be used to calculate the heat of crystallization.
P
ARTIAL molal quantities (3) have not received the widespread attention in engineering calculations that their value deserves. Any extensive propeey of a solution, G, has ita corresponding partial molal value Gl for the solvent and G, for the solute. The discussion is valid for any number of components b u t will be confined to the case of a two-component system. At any given temperature and pressure GI and G2are defined b y the equations:
One of the fundamental equations of calculus (4) gives the relations between partial and total derivatives as follows:
/$fv,
University of Florida, Gainesville, Fld.
(3)
whence i t follows that dG = Bldnl
+ &dnl
(4)
The use of these equations implies that all variables other than concentration remain constant. Since G1and G2 are always the same for a given concentration of a given solution and are independent of the quantity or past history of the solution, the partial molal values are intensive properties of the solution. A table of partial molal values can be used to calculate the corresponding extensive property of the solution. Partial M o l a l Heats of Solution The partial molal heats of solution of the system sulfur trioxide-water are used to illustrate the usefulness of partial molal quantities. Thermodynamically the heat of formation of a solution can be handled in the same manner as the heat of any chemical reaction. If the standard states are defined as the pure materials in their most stable form a t the given temperature and pressure, then the heat of reaction for the formation of the solution is the sum of the partial molal heats of each constituent multiplied by the number of moles of each constituent involved. For example, if one mole of liquid sulfur trioxide is added to one mole of liquid water, the resulting product can be considered a solution of sulfur trioxide in water in which the mole fraction of sulfur trioxide, 22, is 0.5. As Table I shows, this value is the same as the heat of forma-
I N D U S T R I A L A N D E N G I ~ E E R I N GC H E M I S T R Y
572
TABLB I. PARTIAL MOLALHEATSOF SOLUTION OF SULFUR TRIOXIDE (LIQWID) IN WATER(LIQUID)
-
Mole tion
Frac-
so:, I 1
0.02 0.04 0.05 0.07
8.33 15.6 19.0 25.1
0.0 10.2 19.1 23.2 30.8
0.10 0.15 0.20 0.25 0.30
33.6 44.0 52.6 59.7 65.6
40.5 53.8 64.4 73.1 80.6
0.36 0.40 0.45 0.60
70.5 74.8 78.4 81.6
0.52 0.65 0.60 0.65) 0.70 0.75
82.5 84.5 87.0 89.2 91.2 93.0
0.80 0.85 0.90 0.95 1.ooc
94.7 96.2 97.6 98.3 100.0
0.00
a
b C
d
-
-
(Temperature 18" C.; for Hs0 (I.), Hi 0 ; for 90s ( l . ) , H % 0 ) B.T. U. /Lb. Mole Per Cent by Weight Kg.-Cal./Gram Mole Free so: AH HI wer Zsper HI per Ha per (based per m6le mile mole mile on mole Hg0 in Sosin Hz0 in SOain 501 HzSOd HISOL) soln. soh. soln. soh. soin. 0.0
.
86.4 91.6 96.1 100.0
...
...
...
...
...
...
.. ... ...
-0.78 -1.51 -1.89 -2.62
-0.01 -0.02 -0.08 -0.21
...
-43.25 -38.5 -37.5 -37.3 -36.8
...
-18 -36 -144 -378
-77,850 -69,300 -67,500 -67,140 -66,240
...
...
-3.65 -5.15 -6.63 -7.80 -8.79
-0.50 -0.85 -1.21 -2.59 -3.98
-32.11 -30.09 -28.11 -23.57 -19.90
-900 -1,530 -2,178 -4,662 -7,164
-57.800 -54,160 -50,600 -42,430 -35,820
... ... ... ...
-9.47 -10.00 -10.41 -10.69
-5.16 -6.33 -7.80 -10.59
-17.50 -15.48 -13.60 -10.59d
-9,288 -11,390 -14,040 -19,060
-31,500 -27,860 -24,480 -19,060
6.4 15.4 29.0 41.2 n2.1 62.0
-10.45 -10.10 -9.37 -8.52 -7.68 -6.61
-15.92 -17.17 -19.50 -19.50 - 20.28 -23.35
-5.40 -4.35 -2.60 -2.60 -2.22 -1.01
-28,660 -30,910 -35,100 -35,100 -36,500 -42,030
71.0 79.2 86.7 93.6 100.0
-5.48 -4.25 -3.03
-23.56 -23.95 -27.21 -31.0 -37.0
-0.95 -0.80 -0.39 -0.10
-42,410 -43,110 -48,980 -55,800
... , . .
... ...
...
-1.60
...
...
Heat of solution of 1 mole of SO8 in an infinite amount of H2O. Curve corrected t o supercooled liquid HzSzO, a t 2 1 = 0.67. Heat of solution of 1 mole H20 in an infinite amount of SOs. Pure HsSOd liquid.
-66,600
--7,830 9,720
-4,680 -4,680 -4,000 1,818
-
-1,710 -1,440 -700
- 180
...
Vol. 34, No. 5
(H/ = -104.2 kg.-cal.) f (HI = -68.37) + (Ht = -193.75) AH (-193.75) - (-104.2) (-68.37) = -21.18 kg.-cal. (6)
Using similar calculations, the heats of solution, mixing, and dilution of any desired solution, from mole fraction sulfur trioxide = 1 t o mole fraction water = 1, can be calculated as soon as the data for the partial molal heats of solution are available. Table I waa obtained by recalculating the data from the literature. Up to mole fraction sulfur trioxide = 0.5, which corresponds to pure sulfuric acid, the data were obtained from Bichowski and Rossini (1). From mole fraction z2 = 0.5 to mole fraction zz = 1, the data were recalculated from Herrmann ( 2 ) . Column 1 is the mole fraction of sulfur trioxide and column 5 is the heat evolved when one mole of solution is made from liquid water and liquid sulfur trioxide. One mole of solution is that weight of solution obtained by adding the products of mole fraction times molecular weight-i. e., 80 for sulfur trioxide and 18 for water: 1 mole of solution = $1
tion of liquid sulfuric acid made from one mole of sulfur trioxide and one mole of water. The calculations follow:
+ HzO(l.)
+ solution SO8 in HzO (zg = 0.5) E, OFIS = O d H 2 = -10.59 kg.-cal.; H I = -10.59 kg.-cal. (pure) (pure) (xz = 0.5) (21 = 0.5)
SO,(l.)
-
Products A H = nJT1
+
nZH2
= 1.0 (-10.59) =
-
+
nlfT, (pure) 1.0 (-10.59)
-
Reactants
n2Ez(pure)
-21.18 kg.-cal.
or SO8 (1.)
+ HnO(1.)
--+
[&SO,(l.) 1
(5)
(18)
+ 2d80)
(7)
By using column 1 as abscissa and column 5 as ordinate, Figure 1 is obtained, It can be shown (3) that the tangent to this curve a t any m@e fraction x pwill intersect the = 0 axis $ a value equal to HI, and the x2 = 1 axis a t a value equal to Hz. Columns 6 and 7 of Table I were obtained in this manner. A slight discrepancy in the data apparently occurs a t zz = about 0.67. This corresponds to the compound 2SOs.lH20 = HzSz07. The stable form of this compound a t room temperature is crystalline. The table and curve are based on pure liquid sulfur trioxide and pure liquid water reacting t o form a liquid solution. When the estimated heat of fusion (1) of oleum (-2.64 a t 30" C.) is added, the point comes on the curve.
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1942
573
Since all the sulfur trioxide enters in solution 1, 1.056 pound moles of sulfur trioxide is 0.07 times the total moles in the final solution, Water in final solution = (1.056/0,07) 0.93 = 14.030 Dound moles. Water added is 14.030 - 0.917 = 13.113 pound moles. The reaction now may be written and the appropriate partial molal heats read from Table I, as follows:
Illustrative Examples
To d m - " h t e the utility of this type of table for calculating properties of solutions, four illustrative examples are given. EXAMPLE One hundred pounds of an oleum containing 15.4 per cent free sulfur trioxide is to be diluted with pure water to make a 30.8 per cent solution of sulfuric acid
