INDUSTRIAL AND ENGINEERING CHEMISTRY
934
TZBLE I. HIGH-TEMPER tTt7RE H E Z T C0NTE:Pi.P r--
T o K.
FeCr20r-HT -
-.
Hzss.1b.
oal./g. mol. w t . 2.940 7,090 11,820 16,300 22,000 26,200 29,860 33.920 38;880 43,7011 46,870 51,670 ~ , 3 2 n 57.250 63,040 63,990
386.2 498.7 616.6 725.4 861. o 959. z 1041. 1133.6 1242. D 1350,s 1418.8 1622.8 1622.1 1845. D 1769. o 1786.2 1786.9
--
sIgCr20i----
H T - Hzsn.16, eal./g. mol. w t .
T o Ii.
2,930 8,900 i3,mn 19,740 35,970 80,810 37,570 43.600 24,980 19,270 53,0511
387.1 546. o 658.9 816.1 961,s 1077,6 1232. n 1370.1 1400. i 1473.8 1581.6 1644.9 1782. s
55,900
tx.140
64,090
Vol. 36, No. 10
the smooth curves, and calculated entropy increments at even 100' intervals from 298.16' K. to temperature T are summarized in Table 11. No previous high-temperature heat content data of comparable accuracy appear in the literature. From the specific heats a t 298.16' K., Cp = 31.98 and 30.30 calories per degree per mole for ferrous and magnesium chromites, resprctively ( I ) , and the heat content data, the following algebraic rqnations were derived. Below 600' K. the heat content equation for ferrous chromite may be in error by as much as 150 calories; at higher temperatures it has an average deviation of 0.2% with a maximum deviation of 0.4% around 1200" K The heat content equation for magnesium chromite fits the data within 30 calories below 600" K.; above that temperature it has an average deviation of 0.15%, the maximum error being about 0.3%. The specific heat equations wcre obtained by differentia tion :
FcTr,O,:
7'62
T 400 500 600 700 8ao 900
1000 1100 1200 1300 1400 1500 1600 1700 1800
3,450 7,100 11,150 15,280 19,450 23,660 27,960 32,390 36,920
41,460
46,000 50,550 55,200 59,860 64,600
9.88 18 03 25 41 31 77 37 25 42 31 46 84 51 OR
55 0 0
58 64 6 2 . 00 H5.14 68.14 70.97 73.67
3,350 7,040 10,930 14,920 19,050 23,280 27,500 31,800 36,120 40,460 44,920 49,390 53,880 58,360 62,860
9.63 17.86 34.95 -31.10 36.62
C,
=
38.96
MgCrs04: H T -
'"6
+ 5.34 X
Hz98.16=
40.02T
'"*
41.60
--____
46,04 50.14 53,90 57.38 60,68 63.76 66,66 69,38 71 95
tiong were made to the values ill Table I for the silica ( 2 ) arid iron impurities. The silica of the ferrous chromite wah taken as 0.75% and the iron in the magnesium chromite was considered to be present as 0.5% ferrous chromite. All molecular weights accord with the 1941 Interriational Atomic Weights. No discontinuity is discernible in the heat rontent curve of eithrr substance. The heat contents, read from
+ 2.67 X
H T - H298.18 = 38.961'
CP = 40.02
T
10-32'2
+
-
14,410 (298-1800' K.)
T
X 106 - 7.62 T --
+ 1.78 X 10-3T2 -f - 15,310 (298-1800° K.)
+ 3.56 x 10-3 T
x - 9.58 --Fi
106 --
ACKNOWLEDGMENT
Both samples were prepared and chemically analyzed at this station by F. S. Boericke, assisted by W. M. Bangert. The x-ray examination of the chromites was kindly carried out under the direction of E. v. Potter at the Salt Lake City Station. LITERATURE CITED
C . H., IND.ENG.CHEM.,36,910 (1944). (2) Southard, J. C., J. Am. Chem. Soc., 63, 3142 (1941). (1) Shomate, PURLISRED
by permission of the Director, U. S. Bureau of Mines.
Nomogram to Convert Weight and Mole Percentages in Binary Systems ROBERT F. BENENATI AND JOHN G . HARRISON, JR. Polytechnic Institute, Brooklyn, N. Y.
A
NALYTICAL results are almost always expressed as weight percentage, but the physical chemist, the engineer, or the operator in synthesis usually works with mole fraction or mole percentage. The physical chemist best understands ideal solutions and deviations from them when dealing in mole fractions. The chemist in synthetic work considers his reactions in terms of moles of reactants and moles of products. The chemical engineer designs much of his equipment in unit operations by working with mole fractions. Since both additive and multiplicative operations are involved in this conversion, a mathematical solution is imposed to which no ready short cut is available even when a whole series of similar calculations is to be made. Several graphical calculators to effect
this conversion of weight per cent to mole per cent arid vice vtma have appeared in the literature'. Each of these, however, requires an arithmetic calculation, and in some cases the chart is complicated. The nomogram presented here involves no calculation and furnishes a direct solution for mole per cent when composition by weight and molecular weight of the two components are known. A solution is also possible for weight per cent when mole per cent is known.
* Baker, J. S.,Chem. & Met. E m . , 45,166 (1938); Bridger, G.L., Ibid., 44, 451 (1937); Nevitt. E. C., I b i d . , 39, 673 (1932); Patton, T. C.,Ibid., 41, 148 (1934); Winnioki, H. 9.. and Chellis, L. N.. Ibid., 47, 694 (1940); Underwood, A. J. V.,Trans. A n . I n s t , Chern. Enyrs., 10,145 (1932).
October, 1944
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
935
An expression of weight per cent is converted to mole per errit as follows: The point representing the weight composition of the system is located on the center vertical scale. Two lines are drawn from this point through the proper molecular weights and extended to extreme vertical scales representing number of mole8 of each constituent. The two points so obtained are connected with a straight line to give mole per cent on the long diagonal.
To solve for weight per cent from mole per cent, a short trial and error method is necessary. A point on the mole per cent line must lie on a straight line with points on the lines showing the number of moles. Therefore a point on weight per cent is guessed and tried until the above condition is fulfilled. Quick trials allow the point to be moved up and down until the correct answer is obtained.
An example is shown on the nomogram for converting an 80 weight per cent acetic acid-water solution to mole per cent. The point 80 per cent A-20 per cent B is located on the center vertical scale, and lines are drawn from it through 60 on molecular weight A and 18 on molecular weight B (representing the molecular weights of acetic acid and water, respectively). This shows 1.33 moles of acetic acid and 1.11 moles of water on the two extreme vertical scales. These two points are connected with a straight line to give an answer of 54.5 mole per cent acetic acid on the long diagonal. This compares favorably with the value of 54.5 obtained with a standard 10-inoh slide rule.
This chart is interesting from consideration of nomograms in general. The unusual consolidation of a large 2-type chart with two smaller and related 2-charts results from the complex formula involved. It should be noted that the greatest space on the molecular weight scales is allotted t o the lower molecular weight compounds, which places greatest accuracy where most desired. For compactness the chart is presented in approximately square form. I n 8 few cases the number of moles of A or B may be greater than 5. An extension of the outer lines is then required.
