Gas Solubility and Partial Pressure NOMOGRAPH FOR CORRELATION OF DATA DONALD F. OTHMER AND ROBERT F. BENENATI Polytechnic Institute, Brooklyn, N. Y.
PREVIOUS report (4) showed that gas solubility data may be readily correlated and expressed as str l i e plots on logarithmic paper where each concentration of gas in the liquid is the parameter for a single line when the gas partial pressures are plotted vertically, always at the
is calibrated both in centigrade and Fahrenheit degrees (corresponding to vapor pressures of water on the original or temporary logarithmic calibration which is not shown), To use the nomogram, therefore, it is necessary merely to connect the temperature value on the right-hand scale with the concentration on the intermediate or concentration line, same temperatures as the vapor pressures of the reference and then continue the straight line so drawn to the left-hand substance (usually water, the liquid solvent) which are plotted horizontally. This was an extension of the general plot (3,S) or pressure scale. This gives the partial pressure of the gas for vapor pressures which were shown always to be capable of in equilibrium with a solution of the given concentration a t representation on the logarithmic plot simply and accurately. the given temperature; and this pressure represents either The fact that the data for gas solubility have been reduced that which must be impressed or that which will be given. If to a representation as straight lines suggested that one of the the concentration is known and it is desired to find the temmost easily constructed forms of nomograms could be drawn peratuke which will give a desired pressure, or if the temperato enable the ready use of the values. This involves the use ture and pressure are known and it is desired to find the of the Y-axis representing pressure, exactly as normally caliequilibrium concentration, any one of the three variables brated, as one of two parallel scales. The other parallel scale may be found if the other two are known. at a convenient distance is the X-axis which has been caliIn the nomogram of Figure 1, reduced from a much larger brated directly in temperatures according to the vapor presoriginal, it is possible to add pivot points or lines of concensure relation of the reference substance and with the calibratration for any additional data by the above method. Also tions going in the reverse direction. The pivot poinLs for difit was found that all of the values for the Henry law constant ferent gases are located graphically from the experimental plotted in the previous article could be expressed on this nomogram as individual points for each system. They are data. To make such a nomogram, water may be utilized for the not shown, however, on Figure 1. reference substance as in the accompanying figure (page 876): In the case of carbon dioxide dissolved in water, there was a decided break in the lines of the original plot (4)which was at1. A lo arithmic scale of pressures is calibrated downward on a tributed to the formation of a hydrate. An entirely different line near %e left-hand edge of a sheet of paper, using either a relation might therefore be expected; and the concentration suitable log scale such as a slide rule slider or log paper. parameter was expressed by two different functions, one for 2. Parallel to this point at the right-hand side of the paper a the upper set of lines above these break points and one for second lo scale is temporarily calibrated, also in pressure units. This can %e of any convenient size, either larger or smaller than those below. As drawn, it is assumed that the break point the first, and increasing in the opposite direction-i.e., u ward, comes for each Concentration a t the same temperature 3. Temperaturesare then indicated on the scale on t t e right(65' C.); the one curve is therefore used above that temperahand side corresponding to the vapor pressures of water at each ture and the other is used below. This assumption is slightly temperature value. 4. An intermediary point between the two scales must be in error (according to the plot), and a more complicated found as the pivot for lines connecting the two, for reading parmethod could be devised to express the relations exactly if tial pressures of any given concentration of a dissolved gas at difit was felt that the experimental data warranted any great ferent temperatures. This point is found at the intersection of precision in this range around 65" 0. where the breaks come. any two lines connecting two different temperatures on the scale on the right-hand side, respectively, with the two correspondin In the case of solutions of gases in a liquid of more than one gas partial pressures for the same concentration on the left-han8 component, it is obvious that still another parameter, comscale. position of the liquid, must be involved. Thus a four-variable 5. Other points for other values are located similarly. or four-dimensionalsystem mu& be satisfied for temperature, pressure, concentration of gas, and composition of liquid. Each point represents some particular concentration; and The example shown is that for the solubility of carbon dioxide any l i e through it represents a solution of that concentration in water solutions of sodium carbonate taken from Harte, which, when extended to the two scales, gives directly the parBaker, and Purcell (1). They expressed the composition, C, tial pressure on the left-hand scale corresponding to the temof the liquid solvent as the normality of total sodium in the perature indicated on the right-hand scale. Since the relation water in the range 0.5 to 2.0 normal. The concentration of o f the parameter, concentration, to the temperature and parcarbon dioxide was expressed as X,the fraction of the sodium tial pressure is a continuous and usually single valued funcin the form of bicarbonate. (This limits the range of the extion for any one system, it follows that the locuk of the pivot pression to values of X not greater than unity and disregards points so found for different concentrations will be a line of the possibility of solution of carbon dioxide in an aqueous anpredictable shape. These Lines have been plotted from the solution of bicarbonate alone.) The temperature range of 'data previously discussed (4) for the various concentrations the data was from 20-70" C. of each of the several solute gases. In some cases these lines To use the chart with the four males necessary for these .are straight or nearly straight. four variables, a fifth or reference line must also be used. In the accompanying chart the left-hand or pressure scale These several scales are in the upper left-hand part of the is calibrated in millimeters of mercury and in pounds per nomogram. (In some cases it may be necessary to extend the square inch; the right-hand and parallel temperature scale 375
A
c
,
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
376
USE
Vol. 36, No. 4
THESE SCALES FOR C 0 2 N o 2 C 0 3 - NaHCO,
I
MIXTURES
2.0 260$i30 120
3.0
E 5.0
cn
2 IO Ir,
0
'O-f-30
40 3&0 Figure 1. Nomogram for Gas Partial Pressures on Left-Hand Scale for Given Temperatures on Right-Hand Scale Obtained by the Intersection of a Straight Line through a Given Concentration of Gas on the Intermediate Scale for the Particular System
CONCN.UNITS, GAS SOLVENT GASIN SOLVENT 803 HzSO4 Total % ' His04 HCl NHa SO2
CL
Water Water Water Water
M't. HC1 Mole % NHa G. SOz/lOO g . He0 G. C12/1OOO g. HzO
GAS
SOLVENT
COZ Benzene CO2 Water
coz
AqueousNazCOs NaHCOa
+
CONCN. LNITS, GASIN SOLVENT Mole fraction COe G. COn/100 g. water Na on Scale C NaHCOa on Scale X The fraction NaHCOa Nn2C03 Normality -total
+
INDUSTRIAL A N D ENGINEERING CHEMISTRY
April, 1944
reference line downward; this was not done in the figure because of confusion with the other lines.) To use the nomogram, the temperature and X scales are connected with a straight line. The point at which this line crosses the reference line is then connected with the C scale; and the extension of this second construction line to the left gives, on the pressure scale, the value of the partial pressure of carbon dioxide exerted by such solutions. The combination of scales
311
may be used to obtain the value for any one of the other four variables provided three are known, LITERATURE CITED
(1) Harte, C. R., Jr., Baker, E. M., and Purcell, H. H., IND. ENQ. (2) Othmer, CREM., D. 25,F., 528 I ~(1933). ~32,~841 . ,(1940). (3) Ibid., 34, 1072 (1942). (4) Othmer, D.F.,and White, R. E., Ibid., 34, 952 (1942).
Specific Heat of Zirconium Dioxide at Low Temperatures ENTROPY AT 298.16O K.
K. K. KELLEY Pacific Experiment Station, U. S. Bureau of Mines, Berkeley, Calif. The specific heat of crystalline zirconium dioxide was measured throughout the temperature range 52' to 298' K., and the entropy was computed as S O 2 9 8 . 1 8 = 12.03 * 0.08. The entropy and free energy of formation from the elements are, respectively, A S o 2 9 a . 1 6 = -46.5 and A F O 2 s s . 1 6 = -244,200.
T
.
HE determination and correlation of fundamental thermal data of substances of metallurgical interest have been activities of the Bureau of Mines for several years. Some time ago, a t the request of the industry, an investigation of the low-temperature specific heat of zirconium dioxide was undertaken, The zirconium dioxide was furnished by J. C. Southard of the Titanium Alloys Manufacturing Company. It was a crystalline product that had been crushed to about 40-mesh size after electrical fusion. Analyses furnished by the company indicated a purity of 99.14%. The principal impurities were 0.30% SiOz, 0.20% TiOz, and 0.07% CaO. The remaining 0.29% was divided among several other oxides; none was present in an amount greater than 0.05 yo,according to the spectrographic analysis. The specific-heat measurements were made by methods and apparatus described previously ($2). The defined calorie is used (1 calorie = 4.1833 international joules), and the molecular weight of zirconium dioxideis taken as 123.22 grams in accordance with the 1941 International Atomic Weights, The measured results, in calories per mole per degree, are listed in Table I and shown in Figure 1. They have been corrected for the effects of the principal impurities, assuming that the specific heats are additive. The correction varied from 0.54% in the lowest to 0.05% in the highest recorded specific-heat value. The specific heat a t room temperature is about 0.5 calorie per mole higher than given by the equation derived previously (3) by the author on the basis of less reliable data at higher temperatures. The present results are considered to be accurate within 0.3%; the precision error is much less than this.
TABLE I. SP~CIFIC H ~ A OF T ZIRCONIUM DIOXIDE T, K.
CP
T,OK.
CP
T,O K.
54.3 57.9 62.2 66.8 71.4 75.7 81.0 85.3 94.6 103,6
1.473 1.692 1.958 2.260 2.573 2 858 3.211 3.504 4 151 4 770
114.0 124.3 134.3 144.9 155.4 165.0 175.3 185.1 195.4 "205.1
5.471 6.154 6.761 7.399 8.016 8.542 9.057 9.537 10.03 10.44
215.0 225.2 235.7 245.5 255.6 265.9 276.1 285.8 295.0
C, 10.86 11.22 11.59 11.93 12.24 12.55 12.84 13.07 13.25
The entropy increment between 50.12' and 298.16' K., obtained by graphical integration under a plot of C, against log T, is 11,587 units. The entropy below 50.12' K. was obtained by 345 extrapolation. It was found that the function sum, D (7)
E
( y )+ (y), E
.- + I
adequately represents the measured spe-
cific-heat results over the entire experimentally determined range, where D and E denote, respectively, Debye and Einstein functions. This function sum was used in extrapolating to obtain 0.445 unit as the entropy increment between 0" and 50.12" K. In this instance the specific heat has decreased to such a low value at the lowest temperatures 12 i n v e s t i g a t e d that any method of extrapolation would yield virtually the 10 same result. The en3 tropy at 298.16' is the 8 sum of the two portions = 12.03 * or Soz~s.la 0.08 calories per mole per degree.
L8 .I
j 6
u"
FREE ENERGY OF FORMATION AT 298.16'' K.
4
Bichowsky and R o s s i n i (1) a d o p t e d -258,100 calories per mole as the heat of formation of zirconium 50 150 250 T,OK. dioxide. The entropy of Figure 1. Specific Heat of formation, from the enZirconium Dioxide tropy value given above and those of the elements (4), is A S " 2 ~ 8 . 1 8 = -46.5. From the relation, AFO = AH" - TAS', A F " 2 ~ 8 . 1 ~= -244,200 calories per mole is computed as the free energy of formation of zirconium dioxide from the elements. 2
LlTERATURE CITED
(1) Biahowsky and Rossini, "Thermochemistry of Chemiaal Substances", New York, Reinhold Pub. Gorp., 1936. (2) Kelley, J. Am. Chern. Soo., 63,1137 (1941). (3) Kelley, U. 8.Bur. Mines, Bull. 371 (1934). (4) Ibid., 434 (1941). PUBLIEREID by permission of the Director, U. 5. Bureau of Mines.
