INDUSTRIAL AND ENGINEERING CHEMISTRY
952
where TJB = partial molal volume of B W E = molecular weight of B. By reasoning similar to that above, the shrinkage factor for volume fractions is found to be
I n this case the units are liters per liter, gallons per gallon, etc. Figure 4, which shows \kAfor ethanol-water mixtures a t various temperatures, indicates that a t higher temperatures the amount of the contraction becomes reduced and the expansion a t low ethanol concentrations tends to disappear.
Vol. 34, No. 8
Figure 5 shows Q 4 for sulfuric acid-water solutions. When the initial solution that is to be diluted with water has a round weight fraction, it becomes unnecessary to take two readings of \kA and to form the difference. The chart is entered on the appropriate curve (that corresponding to the initial weight fraction), and the curve is followed to the weight fraction corresponding to the solution after dilution. This value of \EA is then multiplied by the weight of solution and the weight fraction as before.
Literature Cited (1) Baxter. G. P.. and others, J. Am. Chem. SOC.,33, 901, 922 (1911): 38, 70 (1916). (2) Lexis and Randall, "Thermodynamics and the Free Energy of
Chemical Substances", Chap. IV, New York, McGraw-Hill Book Co.. 1923.
Correlating Gas Solubilities and Partial Pressure Data DONALD F. OTHMER AND ROBERT E. WHITE' Polytechnic Institute, Brooklyn, N. Y.
F FUNDAMENTAL importance in the study of any gas-liquid absorption or desorption process are the gas-liquid equilibrium or solubility data. A survey of the literature for these data reveals that much is still to be desired in the quality, quantity, and form of data presentation. Since a t least four variables (temperature, concentration in the liquid phase, concentration in the gas phase, and total pressure) must always be evaluated, it is evident that many data are required to define a system. Although experimenters have worked many years with various types of apparatus to obtain such data, these data are incomplete for practically every system. However, a variety of methods does exist for expressing gas solubility. Bunsen coefficient 01 is defined as the volume of gas (reduced to 0" C. and 760 mm.) dissolved in a unit volume of solvent a t the temperature of the experiment when the partial pressure of the gas (excluding the vapor pressure of the solvent) is 760 mm. (Data are expressed as corrected "volume in volume,'). Experimental results often are recorded in terms of this coefficient without maintaining the specified conditions. I n some cases the partial pressure of the gas has not been maintained a t 760 mm., due either to neglect of the vapor pressure effect of the solvent or otherwise. The Ostwald solubility expression, I , represents the ratio of volume of gas dissolved a t any pressure and temperature to volume of absorbing liquid. This expression differs from the Bunsen absorption coefficient in that the volume of dissolved gas is not reduced to 0" C. and 760 mm. The solubility is therefore the volume of gas dissolved in unit volume of solvent under conditions of the experiment (volume in volume). Similar to the Bunsen coefficient is the Kuenen coefficient which gives the volume of gas, measured a t standard conditions, dissolved in one gram of the solvent a t the temperature of the experiment, when the partial pressure of the gas is 760 mm. (volume in weight).
0
1
P r e s e n t address, York Ice Machinery C o r p o r a t i o n , York, P e n n a .
The Raoult coefficient expresses the solubility as grams of gas dissolved in 100 cc. of solvent a t the temperature of the experiment, when the partial pressure of the gas is 760 mm. (weight in volume). There seems to be no commonly used name for the solubility expressions in terms of the other combination of measurements, such as weight of gas dissolved in weight of solvent, or moles of gas in a mole of solvent. These latter two ratios are by far the most useful in any engineering calculations. Furthermore, gas solubility is often expressed in terms of the Henry law constant, H , which relates the concentration of dissolved gas to the partial pressure or concentration of gas in the gaseous phase. (This has been used as a measure of the gas dissolved, even in those cases where the law is specifically indicated as inapplicable.) The Henry law constant varies with temperature and with the nature of gas and solvent; its numerical value depends on the units in which the pressure and concentration are expressed. Henry's law is applicable over a wide pressure range with reasonable accuracy for many systems. On the other hand, many systems deviate widely from this relation; in general, deviations increase with increase of partial pressure of the gas and with decrease of temperature. Gases of low solubility, such as inert gases, and gases that do not change molecular form in solution usually follow Henry's law closely. Gases that combine with or dissociate in the solvent show large deviations. A particular handicap has been the fact that the variation of the Henry law constant with temperature is not linear.. Markham and Kobe ( 5 ) ,in a review of gas solubility determinations and data, mention the shortcomings of the methods for expressing gas solubility but made no attempt to suggest more useful methods of expression or correlation. The International Critical Tables contain considerable gas solubility data expressed in terms of the Bunsen coefficient and also the Henry law constant. Here, in particular, there has been a confusion of several coefficients,due to variation of the pressures.
INDUSTRIAL AND ENGINEERING CHEMISTRY
August, 1942
A new method of representing gas solubility data has been developed and applied to a number of gasliquid systems. The representation is graphical and similar to the method applied to vapor pressures of liquids, and described in a previous article. The plot is based upon the equation:
log P =
(Q/Q‘)log P’
+C
By considering liquid water and water vapor as the reference system, the equation becomes: log p = ( Q / L ) log P
+C
A plot of this equation is made on logarithmic scales with vapor pressure of water as the abscissa, the gas partial pressure as the ordinate, and the concentration of the solution as the parameter. Data for systems obeying Henry’s law closely and for systems that deviate widely from it have been
For chemical engineering design calculations involving gas-liquid equilibrium or diffusion, none of the above methods expresses the solubility data in a form suitable for use. Because of the units employed in gas absorption calculations, it is desirable to have the gas solubility data on a weight or mole basis for the liquid phase. The equilibrium gas phase should be defined either by molar concentrations and total pressures or by the gas partial pressure. The total pressure is not usually essential if the gas partial pressure is determined. Perry’s handbook (9) has avoided the use of the Bunsen coefficient by recalculating the data, usually to a weight basis, and including the gas partial pressure when available. Values for the Henry law constant are also given where this could be indicated as having reasonable accuracy.
Physical Basis for Correlation Inspection of the methods of expressing gas solubility indicates that most studies of gas solubility have been directed toward measuring the actual quantity of gas that dissolved in a unit quantity of solvent under the conditions of the experiment. Use of such data in the design of engineering equipment, however, may hinimize consideration of the physical volumes of gas going into solution and focus attention on equilibrium conditions such as the pressure exerted by some given concentration of gas dissolved in a liquid a t a specified temperature. “The solubility of the gas can be considered from two points of view. x may be regarded as the solubility of a gas in mole fractions under the (partial) pressure p , or alternately p may be regarded as the vapor pressure of a volatile solute when it is present to the extent of mole fraction z in the solution” (1). Several equations relating gas solubility and temperature have been developed on the basis of the Clausius-Clapeyron equation and the van’t Hoff isochor. These involve the incorrect assumption that the heat of solution of the gas is independent of temperature. This assumption usually invalidates the derived equations or limits their use to narrow ranges. The solubility of a gas in a liquid depends upon the temperature and the partial pressure or concentration of the gas in the gas phase. Since neither the temperature nor the gas concentration (nor gas partial pressure) remains constant in a gas absorption process, a complete knowledge of the solubility variation with temperature and gas partial pressure is
953
plotted in this manner with equal success. In every case the data give lines which may be considered straight within experimental accuracy or lines made up of straight sections of different slopes. An abrupt change in the slope of a line indicates a change in the chemical form in which the gas exists in solution. The straight lines or straight-line sections support the applicability of the plot and also indicate the constancy of the ratio Q / L over ranges involving no chemical change in the gas. From the basic equation the variation of the Henry law constant with temperature may be developed and represented graphically in the same manner. Heats of solution of gases in liquids may be evaluated readily from the slopes of the lines. This is particularly useful because of the few experimental data available for this important thermal quantity.
needed. Obviously, a graphical representation of the data best fulfills this requirement. A minimum of interpolation becomes necessary if the temperature and partial pressure can be used as the coordinates and the gas concentration in the solution is made the parameter. A plot on ordinary paper, however, does not give the straight lines which are desirable for interpolation, and are preferable in any new representation of data for engineering uses. The usual plot, based on Henry’s law, is of partial pressure us. concentration with temperature as the other parameter. On this plot, lines of constant temperature are sometimes nearly straight. Sherwood (11)made such a plot of ammonia in water and of sulfur dioxide in water on logarithmic coordinates-i. e., a Henry’s law plot on log-log paper. The curvature, however, was still pronounced. He also tried to straighten these curves by a method suggested (3) for gases giving ions of compounds in aqueous solutions. This depends on an attempt to evaluate and subtract the amount of dissolved gas which dissociates into ions and then to apply Henry’s law to the amount which does not dissociate. A solution of a gaseous solute is not far different from a solution of a volatile liquid solute; and it was considered likely, therefore, that a suitable representation of vapor pressure data of liquid-liquid solutions should be applicable to gas-liquid solutions. This point was suggested in previous articles (7, 8) on the correlation of vapor pressure and latent heat data. This correlation is derived from the ClausiusClapeyron equation and is based on the equation: log P
=
(L/L’) log P’
f
c
where P and P’ are vapor pressures and L and L’are molal latent heats of two liquids, all a t the same temperature; and C is a constant. Graphically this equation represents a straight line on a logarithmic plot of the vapor pressure of one material against the vapor pressure of another material a t the same temperature. A reference substance, the vapor pressure of which is known accurately over the desired temperature range, is taken as one of the materials; the material to be considered may be either a solution or a pure compound. Temperature ordinates corresponding to the various vapor pressures of the reference material may be located on the reference material axis; and thus the previously mentioned plot of vapor preeaure 08, temperature results.
INDUSTRIAL AND ENGINEERING CHEMISTRY
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Vol. 34, No. 8
vapor pressure of the reference liquid, water, a t the same temperatures for gas-liquid systems in the manner described in a previous article (8); these are shown in the figures. Although it is not necessary to use the solvent as the reference liquid, this iy often the most convenient material. Because of the form in which the original solubility data were given, in some cases it was necessary first t o plot gas partial pressure against solution composition a t various temperatures. By cross plotting, then, the partial pressures of solutions of constant composition a t various temperatures were graphed. The method may be exemplified, using water as the reference material, by the following steps for a gas dissolved in water or other solvent: (1) A sheet of logarithmic graph paper is selected (although, if desired, the logarithms of the values to be plotted may be obtained from a table and plotted on a sheet of ordinary graph paper). ( 2 ) Corresponding temperatures and vapor pressures of water are taken from a table, and temperatures are indicated on the X axis a t the appropriate values of pressures. (3) Ordinates are erected a t these temperatures. (4)A scale of pressure is laid off on the Y axis for the values of partial pressures of gas. (The same pressure unit for this scale as for the X scale is not required, since there is a constant ratio between units; and changing units would merely have the effect of moving the line up or down on the scale without changing its slope or form.) (5) These values of partial pressures are plotted on the respective temperature ordinates. (6) Points representing constant liquid composition are connected by a line usually straight. Perry and Smith ( I O ) used the Ddhring relation for plotting partial pressures of dissolved gases. The relation of the Duhring plot t o the above method of plotting and the fact that the reciprocal of the temperatures a t constant pressures, rather than the real values of the temperatures themselves, should be used in a plot if a straight line is desired, were discussed in a previous article (8); and this discussion is equally valid for the partial pressures of dissolved gases.
Gases Giving Highly Ionized Solutions in Water
VAPORPRESSURE OF WATER
(MM.)
FIGURBI 1. PARTIAL PRESSURES OF HYDROCHLORIC ACID GAS FROM AQnEouaSOLUTIONS OF INDICATED K r PERCENT ~ HCl ~
Systems that would be expected t o deviate widely from Henry’s law because of chemical combination with the solvent were first considered, because these are the ones for which a simple method of correlation would be most useful. ~
~
~
The applicability of this correlation t o solutions of gases in liquids follows directly. For gases dissolved in a liquid and having measurable partial pressures a t the same temperatures, it might be expected that
+
(&/Q’) log P‘ C where p and p’ are the partial pressures at the same temperature of the respective gases; Q and &’ are the respective differential heats of solution of one mole of each gas in its saturated solution, always a t the same temperature. If liquid water and water vapor make up the reference system, &’ becomes the molal latent heat of water and p’ the vapor pressure of water, always a t the same temperature. Or, in general, log P = ( Q / L )log p c log P
=
+
where a t corresponding temperatures L is the latent heat of the reference liquid and P is its vapor pressure.
Method of Plotting Data The logarithms of the partial pressures of a gas out of a liquid solution were plotted against the logarithms of the
‘FIGURE2. PARTIAL PRESSURES OF SULFUR DIOXIDEFROM ITS SOLUTIONS IN SULFURIC ACID (CONCENTRATIONS EXPRESSED AS TOTAL HnSOa)
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INDUSTRIAL AND ENGINEERING CHEMISTRY
955
the range 40-250" F. and solution concentrations of 5 to 90 per cent ammonia is shown in Figure 3 . The same general characteristics are indicated as in the previous two systems. The data for the system sulfur dioxide in water (9), mentioned above, have been plotted by this method in Figure 4. Solutions of 0.5 to 15 grams sulfur dioxide per 100 grams water and temperatures of 10" to 100" C. are included. Again, the data give parallel lines which, without exception, may be regarded as straight within experimental error. The parallelism shown on this plot by the given data indicates a constant molal differential heat of solution a t any given temperature, independent of the sohtion concentration; i. e., the heat effect of dissolving a given amount of sulfur dioxide is the same regardless of the amount of solution or the initial concentration. This is not the usual behavior of a gas; and the peculiarity of this plot may have been caused in this case by previous smoothing of the original experimental data. Data for the system chlorine in water (9) over a temperature range of 0" to 100" C. and concentrations up to 8 grams chlorine per 1000 grams water are plotted in Figure 5. Only the line for the lowest concentration is straight without a break throughout its PRESSURES OF AMMONIAFROM AQUEOUSSOLUTIONS OF FIGURE 3. PARTIAL length. The data for the other concentraINDICATED MOLEPERCENTNHa tions do not give continuous straight lines but lines made up of straight sections with different slopes. One such change of slope for all concentrations except the lowest occurs between 0' The data for hydrochloric acid gas (9) in water are plotted and 10" C., due possibly to inaccurate measurements a t in Figure 1 by the method described. (Individual points are 0" C. The lines representing concentrations of 2 and 3 not indicated, although in every case they were practically grams chlorine per 1000 grams water also show another break within the thickness of the line and are as close as those of a t a higher temperature, about 70" C. This break, while Figure 3, for example. The plot may be used somewhat more sharply defined, gives a-much smaller chlange of slope and readily with the points omitted.) The solution concentrations might be caused by a small experimental error in the data; are expressed as weight per cent of hydrochloric acid and the although in each case the several points form a new straight vapor pressures in millimeters of mercury. The data give line starting a t 70" C. It is believed that the breaks occurring straight plots throughout the entire temperature and cona t the lower points and a t approximately the same temperacentration ranges. The positive slopes of the lines indicate that heat is always required to release the hydrochloric acid gas from solution; that is, this heat is always directly comparable to the usual latent heats of evaporation. For any fixed concentration, the gas partial pressure increases with temperature, as would be expected. I n other words, the solubility of the gas decreases with increase of temperature at constant partial pressure. The slopes of the concentration lines decrease as the concentrations increase. The slope of a concentration line is the ratio of the molal differential heat of solution of the hydrochloric acid gas in an aqueous solution of the indicated concentration to the molal latent heat of water at the same temperature. Therefore, the diminishing slopes indicate a decrease of molal differential heat of solution of hydrochloric acid gas as the solution concentration increases. Following the same general trends as hydrochloric acid gas i n water is the system sulfur trioxide in fuming sulfuric acid (9) shown in Figure 2. The data for this system cover the temperature range 20" to 90" C., and the concentration range sERUGSlFLb+-, -+REP 4 4 ] j 100 to 115 per cent total sulfuric acid. The data fall closely 100 Gus. WATER SO, IN WATER I I I I I 1 1 1 1 1 I I I I I I H on straight lines, all of which have positive slopes. Again, 20 30 4 0 50 60 80 100 ZOO 400 600 ? 8 IO VAPOR PRESSURE WATER MM. HG t h e slopes of the lines decrease with increased concentration, b u t not so noticeably for hydrochloric acid gas. FIGURE4. PARTIAL PRESSURES OF SULFUR DIOXIDEFROM The plot for the solubility of ammonia in water (7, 9) over AQUEOUSSOLUTIONS OF INDICATED CONCENTRATIONB
956
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 TEMPERATURE
-
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slightly steeper than those of Figures 6 and 6A; this indicates that the tenacity of holding of the carbon dioxide (using the heat involved as a criterion) is only slightly greater for the solution of sodium bicarbonate than for the water alone.
%.
1000
800 600
500
$! 400
3 300
Gases in Inert Solvents
N
d 200
As examples of cases in which the solute gas is believed not to combine with the solvent, systems of nitrogen and carbon dioxide in benzene as a reprew E 100 sentative nonaqueous solvent were considered. The solubility data for carbon dioxide in benzene 2b- 80 (12) appear to follow the normal trends. These data 5 50 60 are plotted in Figure 8; over the temperature range 40 involved, 30" to 60" C., and the solution concentration range, up to 70 mole per cent carbon dioxide, 30 they give straight lines. These lines fan out slightly, 20 indicating a slightly increasing amount of heat reVAPOR PRESSURE WATER MM. HG quired for gas evolution with higher gas concentraFIGCRE5. PARTIAL PRESSURES OF CHLORINEFROM AQCEOUS tions~which is the usual case* SOLUTIONS OF INDICATED CONCENTRATIONS The data for nitrogen in benzene (6) plotted in Figure 9, are given for 75", loo", and 125" C.; and nitrogen concentrations in solution up to 16 mole per ture for all concentrations, indicate a change in the form in cent are included. These data give straight, practically which the chlorine exists in solution. It is known that chloparallel lines over the temperature range; but unlike the rine forms a number of hydrates, containing from one to eight molecules of water. It is likely that these breaks occur a t Temperature ("C.) temperatures at which some change in the degree of hydration 300, 2o 30 40 50 60 70 80 90 100 takes place. The resulting change in the heat of hydration causes a corresponding change in &, the total heat involved in 200 the evolution of the gas; thus an abrupt change in slope would be expected a t the temperature where the chemical form changes. -E 100 Numerous examples of the change of partial pressures due 4 80 to a change of state, such as liquid to solid, or of hydration 0" were discussed in the previous paper ( 8 ) . 0 60 ? 50 Also, the slopes of the main sections of these lines for chlo40 rine increase with increasing concentration, indicating corre? a spondingly larger amounts of heat required to disengage a - 30 mole of gas as the solution becomes pore concentrated. a m
-
2 20
Carbon Dioxide in Water and Water Solutions Two sets of data on the solubility of carbon dioxide in water were available. One set (9) is plotted in Figure 6 and results in straight parallel lines throughout. The other set (IS), plotted in Figure 6A, gives straight lines with breaks occurring in the range 60" to 70" C. If the second set is assumed to be correct, i t is again necessary to assume that a chemical change of the carbon dioxide in solution occurs at this temperature. Such a change can easily be the decomposition of carbonic acid to carbon dioxide and water or perhaps to some other hydrated form of carbon dioxide. Figure 7 represents the system carbon dioxide in sodium carbonate solution, in which a chemical combination is known to occur. The data are reported in a n empirical equation by Harte, Baker, and Purcell (2). I n the commercial application of this system, the carbon dioxide reacts with the sodium carbonate in solution to form the bicarbonate, which on heating to a higher temperature decomposes into the constituents again. Only the data for solutions of 1 N sodium concentration are plotted. Each line represents a fixed fraction of the sodium as bicarbonate-namely, 0.1, 0.25, 0.5, and 0.75-and corresponds to a fixed amount of carbon dioxide dissolved. The temperature range is from 10" to 70" C. The slope of the lines is evidently a measure both of the heat of solution of the carbon dioxide in the water and of the chemical heat of formation of the bicarbonate. The lines are, however, only
IO
I
0
Vapor Pressure Water (Mm.Hq)
FIGURE 6. P A R T I A L PRESSURES O F C A R B O N DIOXIDEFROM AQUEOUSSOLUTIONS OF INDICATBD CONCENTRATIONS (DATA FROM PERRY, 9) FIGURE 6A. PARTIAL PRESSURES OF CARBONDIOXIDEFROM AQUEOUSSOLVTIONS OF INDICATED CONCENTRATIONS (DATA FROM WIEBE AND GADDY, 19)
.
August, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
usual gas-liquid system, the slopes of these lines are negative. The solubility of nitrogen in benzene increases with temperature, as shown by the fact that a horizontal, or constantpressure line, cuts higher valued concentration lines in going toward the right (higher temperature). The heat of evolution of nitrogen from benzene is negative; i. e., unlike any latent heat of vaporization, heat is given up and the liquid is heated by evolution of the gas.
957
of water a t the same temperature. The straight-line plots of the partial pressures of solute gases for the various systems considered indicate the constancy of the ratio Q/L.
Relation of Plot to Henry’s Law The Henry law constant is recognized t o be a function of the temperature and of the nature of the gas and solvent. At a fixed concentration, however, Henry’s law states that p = HX
where x is the mole fraction of gas in the solution and H is the Henry law constant for the given concentration a t the temperature where the partial pressure of the gas is p .
0
FIGURE 8. PARTIAL PRESSURES OF CARBON DIOXIDE BENZENE SOLUTIONS OF INDICATED MOLEPER CENTCO,
PROM
VAPOR PRESSURE WATER MM.HG
FIGURE 7. PARTIAL PRESSURES OF CARBON DIOXIDEFROM AQUEOUSSOLUTIONS 1 N SODIUM CARBONATE AND CONTAINING INDICATED CONCENTRATIONS OF CO,
The constancy of Q/Q‘over a fairly wide temperature range has been discussed previously (8) with reference to liquids where Q and Q’ are directly comparable to the molal latent heats of the liquids. I n the present case where dissolved gases are concerned, as with liquids, this plot gives lines more nearly straight than any method heretofore described. The variation of log H with temperature has thus been shown to be identical with the variation of log P with temperature; in other words, the slopes of the lines plotted for values of H a t different temperatures on the log plot will be the same as the slopes of the partial pressure lines. These lines for the “constant” of Henry’s law should be parallel to the partial pressure lines (the locations on the plot depending on the relative values of the constants C and C’).
Taking logarithms, log p = log H
+ log x
Or since 2 is constant, log p = log
H f C’
where C‘ is a constant. The basic equation for the solubility plot is: log P = (Q/Q’)log P’
+C
Eliminating log p from the last two equations, there results: log H = (&/&’) log p’
FIGURE 9. PARTIAL PRESSURES OF NITROGENFROM BENZENE SOLUTIONS OF INDICATED MOLEPERCENTNz
+ C”
where C” is a new constant (the difference of C and C’) and H and p’ are always taken a t the same temperature. If the reference substance is a liquid, as above: log H = ( & / L )log P
0
+ C”
If water is again taken as the reference liquid, the last equation indicates that a plot on logarithmic paper of H us. partial pressure of water a t corresponding temperatures would give a line with a slope of Q/L,the ratio of the molar differential heat of solution of the gas to the molar latent heat
Figure 10 is a plot of all of the values of H,tabulated by Perry (9) and taken mainly from International Critical Tables (4),for commercially important gases in water solutions. The proximity to straight lines of the points representing the tabulated values in Figure 10 indicates the general applicability of the relation proposed. Systems obeying Henry’s law and also those deviating widely from it are considered in this plot. I n a number of cases two intersecting straight lines must be used; and this calls attention to the phenomenon mentioned above of association, hydration, or other chemical combination which is effective above or below some
958
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Vol. 34, No. 8
equally satisfactory plots by this method, as shown by the vapor pressure plots of such systems in Figures 1 and 3. Of course, the spacing of the concentration lines in relation to each other is no longer regular; but interpolation between the lines is not difficult.
Heats of Solutions of Gases The straight lines obtained in this logarithmic plot relate, as above indicated, to the partial heat of solution of a gas and afford a simple means for evaluating this quantity. B s shown by the basic equation, the slope of any concentration line is the ratio of the partial molar heat of solution of the gas in the solution, &, to the molar latent heat of the reference substance, L. Since the lines of partial pressures may be regarded as straight in the usual case, the slope for each is constant over the temperature range. This constancy indicates that the partial molar heat of solution of a gas in a solution of fixed temperature varies with temperature in the same proportion as does the molar latent heat of water, the reference material in the cases illustrated. The partial heat of solution of a gas in a solution of fixed concentration can be calculated from the heat content and total heat of solution, when these values are known. However, thermal data of this type are not available for most gases; in fact, the International Critical Tables give data for only two systems-ammonia in water and hydrochloric acid gas in water. The slope of a partial pressure line relates the partial heat of solution of a mole of gas in a solution of the corresponding concentration to the molar latent heat of the reference substance. Therefore, if solubility data of the gas sufficient to make the logarithmic plot (two points for a given concentration) are available, the partial heat of solution of the gas can be determined.
30
FIGURE 10. PLOT OF HENRY'S LAWCONSTANT FOR DIFFERENT GABES
definite temperature. Such changes alter both &, the heat quantity involved in the release of the gas, and the rate of change of the partial pressure with temperature. In Figure 10 only the data for oxygen and air would seem to be represented best by more than two straight lines or possibly by a curve. If a curve must be used, then oxygen and air would be exceptions to the rule; if three or more straight lines are used, then oxygen and air ivould seem to have three or more different states while in solution in water. It is possible that neither is the case, and that the data (already correlated from several sources) should be regarded as inaccurate. It should be noted that the data for air are weighted means of data for nitrogen and oxygen. Hence it would be expected that discrepancies in the values for oxygen would show up in the values for air. In general, the widest deviations (usually abnormally low values) seem to be those for data at 0 ' C.; this is a difficult temperature for accurate determination, owing to the possible presence of ice or to other reasons resulting in incomplete solution of the gas or insufficient indication of the true pressure. On the log plot of partial pressures, systems obeying Henry's law giveooncentration lines that, a t any one temperature, are spaaed in logarithmic order. This is obvious, since Henry's law gives a linear relation between concentration and gas partial pressure, and on this plot the gas partial pressure is on a logarithmic scale. Data for cases where Henry's law is known to fail give
0.78
m
30.74 L
I
Y
I
1
2 0.70 m P
a 0.66
zd-
a 4 0.62
z
y.
0.58
P
9
"0.54
0.54
,b
do
do
do do $0 o; MOL % N H 3 IN WATER
do
do
Id0
P L O T O F S L O P E O F LINES O F P A R T I A L P R E S S U R E S OF AMMONIA GASFROM FIGURE 3 VS. &TOLE PER CENT 8" (INDICATIVE O F P A R T I 4 L &lOLAR HEATS OF SOLUTION OF SOLUTIONS OF DIFFERENT
FIGURE 11.
CONCENTRATIONS)
The simplicity and accuracy of this method are readily shown by the following typical examples, for the two systems for which data are available, and a comparison of results from the vapor pressure plots made with those obtained using thermal data. For a 10 mole per cent solution of ammonia in water a t 18" C., the partial molar heat of solution of ammonia gas is
August, 1942
INDUSTRIAL AND ENGINEERING CHEMISTRY
calculated from the tabulated data to be 7640 calories. From the plot in Figure 3, the slope of the 10 mole per cent ammonia line is 0.733. This slope is obtained as the tangent of the measured angle between the 10 per cent line and the horizontal, or from the measured lengths of the legs of the right triangle formed by the 10 per cent line, the abscissa, and the ordinate. The molar latent heat of the reference substance, water, at 18’ C. is 10,555 calories. The partial heat of solution of ammonia gas in a 10 mole per cent ammonia solution is the product of the slope and the molar latent heat of water 0.733 X 10,555 or 7720 calories. This value checks that obtained from the tabular data within 1 per cent. While this value is called the “partial heat of solution” of ammonia gas, it is redly the latent heat of ammonia gas on condensation, plus the heat of solution. The latent heat of ammonia a t 18” C. is 5120 calories per gram mole. Thus, the actual chemical partial heat of solution without the physical heat of condensation is only 7720 - 5120, or 2600 calories per gram mole. The partial molar heat of solution of hydrochloric acid gas in a 10 mole per cent solution of the gas in water is calculated from thermal data to be 14,750 calories. The corresponding value determined from the slope of the 10 mole per cent (18.2 weight per cent) hydrochloric acid gas line in Figure 1 is 15,800 calories. The difference in values obtained by the two methods is about 7 per cent, and probably within the limits of accuracy of the various data involved. Figure 11 is a plot of the slopes.of the lines of partial pressures of ammonia out of aqueous solutions. It must be noted that this plot permits direct calculation of the partial molar heats of solution at any concentration (i. e., the heat involved
959
in dissolving a mole of ammonia gas in such a large amount of solution of the given concentration that the concentration of the solution is not affected). The integral heats of solution may, of course, also be related to this plot. They would refer t o the heats involved in going from one concentration to another by removing or adding ammonia gas or a solution of different strength (as would be done, for example, in a rectifying column fed with a given strength of solution), taking off an overhead product of higher strength of ammonia, and discharging water from the base. Normally, distilling-column calculations neglect these heats; but suitable corrections may be incorporated, if desired, from values found in this manner.
Literature Cited (1) Glasstone, Samuel, “Textbook of Physical Chemistry”, p. 691, New York, D. Van Nostrand Co., 1940. ENG.CHEM.,25, 528 (1933). (2) Harte, Baker, and Purcell, IND. (3) Haslam, R. T., Hershey, R. L., and Keen, R. H., Ibid., 16, 1224 (1924).
(4) International Critical Tables, Vol. 111, New York, McGrawHill Book Go., 1929. (5) Markham, A. E., and Kobe, K. A., Chem. Rev., 28, 519 (1941). (6) Miller, P., and Dodge, B. F., IND. ENQ.CHEM.,3 2 , 4 3 4 (1940). (7) Othmer, D. F., Chem. & Met. Eng., 47, 551 (1940). (8) Othmer, D. F., IND.ENQ.CHEM.,32, 841 (1940). (9) Perry, J. H., Chemical Engineers’ Handbook, 2nd ed., New York, McGraw-Hill Book Co., 1941. (10) Perry, J. H., and Smith, E. R., IND.ENQ. CHEM.,25, 195 (1933). (11) Sherwood, T. K., Ibid., 17, 745 (1925). (12) Wan, S., and Dodge, B. F., Ibid., 32, 95 (1940). (13) Wiebe and Gaddy, J. Am. Chem. SOC.,61, 315 (1939); 62, 815 (1940). PRES~NTED before the Division of Industrial and Engineering Chemistry CHEMICAL SOCIETY, Memphis, Tenn. at the 103rd Meeting of the AMERICAN
Waxy Starch of Maize and Other Cereals J
R. M. HIXON Iowa Agricultural Experiment Station, Am=, Iowa
G. F. SPRAGUE
A POSSIBLE COMPETITOR FOR TAPIOCA
Bureau of Plant Industry, U. S. Department of Agriculture, Washington, D. C .
The properties of starch from waxy corn are discussed. This starch has high viscosity, low gelling characteristics, and slight tendency to retrograde. These qualities suggest the utilization of this starch as a replacement for tapioca in many commercial products. Indicated uses are as a remoistening glue, in paper sizes, and as a minute-tapioca substitute. Starch has been milled from waxy rice, waxy sorghum, and waxy barley. That from waxy barley differs from the others in having both red- and blue-staining granules.
OR the past six years duty-free imported starches, consisting chiefly of tapioca, have made up about one fourth the total United States supply of starches as shown in Figure 1 (14). The annual consumption of 350 million pounds of tapioca in the world’s largest cornstarchproducing country may be attributed to two factors, price differential and the properties of the starch itself. Most tapioca has been imported from the Netherlands Indies, where labor is cheap and cassava produces large yields. Since 1930 the price of tapioca has been consistently about 0.5 cent less per pound than that of cornstarch ( I S , 29). The present emergency, however, has made tapioca difficult to obtain. The estimates of the quantities of tapioca required for purposes which cannot be readily replaced by other starches vary greatly. Some place the figure as low as 15 million pounds, if tapioca is considered indispensable only in the production of remoistening glues and certain food products.
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