1076
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLEXI.
COhfPARISON O F CALCULATED AND MEASURED VALUES FOR IDEAL GASES(IN KILOGRAM-C.4LORIES/GRAM MOLE)
Cniud. AH/” a t 298O K. Allyl alcohol Pyrocatechol Glycerol Ethslamine Gluoxal“ AF; a t 298O K. Pyrocatechol
-31.8
-69.5 -139.6 -12.2
Lit. Value
Source
-33.7 -68.7 -140.9
I.C.T. ( 6 ) I.C.T. (6)
“B:d“d. B.&R. ( 3 )
-
-70.8
13 -75
-44.4
-42.5
(8)
0 5
T h e value of C = 0 was calculated from t h a t for -C
1 ‘% AH: for glyoxal was then taken as the sum of 2 O=
P.&€I. (8) H
\
/-
and 2
and,
/c
Vol. 41, No. 5
of estimating heat and free energies of gaseous organic compounds, Tables IX and X give heats of formation for a number of such groups. With additional work the data on all of the groups could be extended t o cover a range of temperatures by using the Dobratz heat capacity approximations (4). Table XI shows a limited number of comparisons of heat and free energy values calculated by this method with data reported in the literature. I n general, agreement is satisfactory, although there are not enough comparative data to permit a conclusion that the method of group equivalents is generally applicable to organic compounds other than hydrocarbons.
=
ACKNOWLEDGMENT
%l
The writer wishes t o express his appreciation to Humble Oil and Refining Company for permission to publish this work, to F. A. Matsen for advice in the conduct of this study, and t o I(. S. Pitzer for reviewing the paper.
CH.
s
data are less accurate than the data on heats of formation. Thus relatively few group cquiva1ent.s for free cnergy of formation at’ room temperature can be calculated, and the accuracy of these values leaves something to be desired. Further, reliable heat capacity data are available on very few organic compounds; consequently it has been possible to calculate values for the heat’ and free energy of formation of nonhydrocarbon groups over a range of t’empernt,ures in only a few instances. In the absence of heat capacity data it is possible to estimate the heat capacity of a gaseous organiccompound by the method developed by Dobratz ( d ) , and the resulting heat capacity equation, together with thc heat or free energy of formation a t a given temperature, may be used to calculat,e heats and free energies of formation of the compound a t other temperatures. This procedure was employed for calculating heat and free energies of several nonhydrocarbon groups over a range of temperatures. The resulting values must, of course, be recognized as highly tentative and subject t o revision when accurate data become available; however, in the absence of d a t e this procedure provides a means
LITEKATURE CITED
(1) Am. Petroleum Inst., “Collection, Analysis and Calculation of Data on the Properties of Hydrocarbons” (Research Project 44), 1947. (2) Aston, “Thermodynamic Data on Hydrocarbons,” Standard Oil Development Co., 1944. (3) Bichowsky and Rossini, “Thermochemistry of Chemical Substances,” S e w York, Reinhold Publishing Corp., 1936. (4) Dobratz, C. J., IND. ENG.CHEM.,33, 759 (1941). (5) International Critical Tables, Vol. 5 , 164 (1928). ( 6 ) Lawrie, “Glycerol and Glycols,’’ New York, Chemical Catalog Co., 1928. (7) ,Mulliken, Rieke, and Brown, J . Am. Chem. SOC.,63, 41 (1941). (8) Parks and Huffman, “Free Energies of Some Organic Compounds,” A.C.S. Monograph GO, New York, Chemical Catalog Co., 1933. (9) Pitzer, J . Chem. PhyY., 8, 711 (1940). (10) Spencer, J. Am. Chem. Soc., 67, 1859 (1945). RECEIVED March
22, 1948. Presented before t h e Division of Physical and Inorganic Chemistry at the 113th Meeting of the AXERTCAK CHXMICAL SoCIETY, Chicago, Ill.
d
om
a
EDWARD G. SCHEIBEL IIoffmann-LaRoche, Inc., AhrutIey, N. J .
A nomograph is presented which combinas i n a single chart all the empirical equations for correcting the calculated activity coefficient for the deviations from the gas laws and for the liquid pressure. The use of the chart is based on the reduced temperature and critical pressure of the pure component and eliminates the use of all other empirical charts and calculations required to determine this correction factor. The critical constants can be calculated reliably from previous correlations when they have not been determined actually and a simple nomograph for using one of these correlations is included on the original chart.
F
OR precise correlation and interpretation of vapor liquid equilibria data, it is necessary t o take into account the deviations of the vapor from the perfect gas laws and the liquid pressure effects. These corrections become more important a t the higher pressures, but are also significant when differences (6)
between the boiling points of the components of the mixture are large so that one or more of the components will be present in the liquid at a temperature considerably above its own boiling point. The determination of this correction factor requires a n involved calculation of the second virial coefficient for the gas law deviation, according to generalized charts or a n empirical equation, and a calculation of the density of the pure liquid a t the temperature of the mixture. This is rarely availabie and usually must be determined from general correlations. The values then are combined in the proper equation to calculate the activity coefficient correction factor. All of these operations are timeconsuming. However, by an analysis of a liquid density correlation, it has been possible to represent it in a convenient form for combination with the empirical equation of the second coefficient in the virial equation of state. Thus the final equation for the activity coefficient correction factor has been reduced to an equation in terms of critical pressure, reduced temperature, and the difference between the vapor pressure of the pure component and the total pressure on the system. This equation has been
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
1.'" I 0
I
0
.
'
'
CRITICAL VOLUME cc/gm. mol l""1'"' I" I ' ' l ' " q l " '' I " ' ' 1 "
0
S S I S
0
"
0
8
' '
2
CRITICAL TEMPERATURE
' I'
0
0
9
'
1077
' I
0
"
K
a
L
n
2E
DIFFERENCEBETWEEN VAPOR PRESSUREOF PURE COMPONENTAND TOTAL PRESSURE ON SYSTEM IN ATMOSPHERES
--
P
m
v)
constructed on a set square type of nomograph in which the correction factor is obtained by a single setting of the other three variables. A double nomograph is also possible, but the first type is considered preferable because i t eliminates one setting and the use of the reference line.
I n the case where deviations from the perfect gas laws are relatively small so t h a t only the second coefficient in the virial equation of state need be considered and all the higher coefficients neglected, Benedict et al. ( I ) has expressed the true activity coefficient as follows:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1078
where the fraction on the right hand side of the equation is the usual method for calculating the activity coefficient and the term Z , is the correction factor for gas lam deviations and liquid pressure and is givcn by the equation:
is the molal volume of the liquid and L 3 1 is the second where virial coefficient. An enipirical equation for this coefficient has been developed by ITohl ( 7 ) . 0.197 - 0.012 T , -
e rr -
0400
0.146
The molal volume of the liquid frequently is not known a t the boiling point of the solution being studied but can be determined from a general correlation of Meissner and Redding ( 2 ) in which they give values of PUL for different reduced temperatures and pressures. The saturated liquid densitv can be calculated from the equation:
on Figure 1, and the answer from the nomograph js 1.155. The value calculated by Mertes and Colburn (3) is 1.193. Similar agreement is found with the other values of 2 calculated by these authors. The use of this nomograph requires a knoiqledge of the critical constants and, if these are not known, it is necessary to rcfer to yenerd correlations for their values. hIeissner and Redding (9) have proposed several useful empirical equations for predicting these values. They found that the critical molal volume could be accurately calculated by the use of the parachor:
vc
=
and the values of
i-1L ~-determined
P,
froni the correlation were
plotted against T , to obtain numerical values for this function a t diflerent values of T,. The deviations from a constant, value of this function a t a given reduced temperature w x e numerically small because, in the region where the slope of the original correlation was significantly greater than unity, the length of the curve was so short that the constant did not vary appreciably n i t h P, and the values of the constant chosen for f ( T 7 ) were a t the midpoint of the range of P, values given in the correlation. Combining Equations 4 and 5 t,o solve for the molal volume:
and then substituting this equation and Equation 3 in Equation 2 after taking the logarithm of both sides of this equation, it finallv reduces to
This equation is represented on the nomograph in Figure 1 and requires only a knodedge of the critical temperature and pressure of thp pure component. Then the reduced temperature of this component at the temperature of the solution can be calculated, and by placing one leg of a right triangle so it passes through the critical pressure and reduced temperature scales in the loiver right hand corner and moving it so the other leg passes through the value of PI - P on the other vertical scale as determined from the data, the value of 2, is read by the intersection of this leg with the horizontal scale. As an illustration of the use of this chart, the value of Z was determined for n-butane a t 125" F. and zero total pressure. The critical pressure for n-butane is 37.5 a t m , and under these conditions, the reduced temperature is 0.769 and the value of PI - P i s 5.07. The method for determining 2 is shown in the small insert
+ ll,0)1.z5
(0.377 [PI
( 8)
where the values of the parachors are given by Sudgen (6). AIeissner and Redding ( 2 ) also proposed several useful equations for predicting the critical temperature of various compounds. The most useful equations are those for compounds boiling above 235" IC. and are given as follows: 1. Compounds cont,aining sulfur or halogens
Tc
=
1.41 T B
+ 66 - 11 F
where F is the number of fluorine atoms in the molecule. 2 . Aromatic and naphthenes
T c = 1.41 T B Inspection of their correlation of pr, indicated that the lines of constant ieduced temperature were nearly st.raight and had slopes not very different from unity as given on their plot of the logarithm of {LLagainst the logarithm of P , . Thus it wa? observed that
Vol. 41, No. 5
+ 66 -
T
(0.3831'8
- 93)
(10)
where T is the fraction of noncyclic carbon atoms of the total carbon atoms in the molecule. 3. Alllother compounds
Both of these critical properties can be determined reliably by the previous equations, and the maximum deviation of the critical temperature is 5oi,. However, the determination of critical pressure is not so reliable. The recommended equation is:
and the nomograph for this equation is shoivn in th? upper right hand corner of Figure 1. Thus by connecting the values of 2, and T C on the appropriate scales with a straight line, this line intersects the critical pressure scale a t the desired value of Pc. However, deviations as great as llyGor more are possible with this equatjon and, if other data ale available, it is advisable t o obtain an independent check on this value. One method for accomplkhing thi.: is by the use of vapor pressure data which can be plotted against the Fapor pressure of a reference substance a t the same temperature on a logarithmic scale as proposed by Othmer (4). This method is not entirely reliable up to the critical point, and a better method would be t o plot the vapor pressure of the compound against the vapor pressure of the reference substance a t the same reduced temperature. This will give the same result as the reduced pressure plot proposed by Othiner ( 5 ) because dividing the ordinate and abscissa of a logarithmic plot by constant values merely displaces the line, but does not change its shape or slope. Then by extrapolating this line to the critical pressure of the rcference substance the critical pressure of the other compound can be determined and this can be compared to the value from the nomograph. Also, if latent heat data are available for the compound, it is possible to construct the vapor pressure line fiom the relation of the latent heat t o the slope of the line on this type of plot and the atmospheric boiling point. From the comparison of these methods, the critical pressure can be estimated with sufficient accuracy to be used in the nomograph for the determination of the activity coefficient correction factor. The nomograph presented in this work allows a rapid method for correcting the activity coefficient for liquid pressure and for
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1949
deviations from the perfect gas law. The reliability of nomograph is poorest in the region of the critical temperature because the empirical relations on which the nomograph is based are least reliable in this region. However, vapor pressure data are rarely ever taken in this region. I n the usual range of temperatures and pressures, the value obtained from the nomograph agrees with the calculated value almost within the accuracy of reading the scales and also within the reliability of the empirical equations on which it is based.
2’ = temperature of system, ’ K. T B = atmospheric boiling point of pure com ound, K. T c = critical temperature of pure compoun$ K. yl = molal volume of pure component at temperatureT , cc, O
vc
= critical volume of pure component
concentration of component in liquid, m d e fraction concentration Of component in fraction Zl = correction factor for liquid pressure and perfect gas law deviations y1 = corrected activity coefficient p~ = universal constant for calculating liquid density 21
=
NOMENCLATURE
B, = first coefficient in virial equation of state
D1 e
F MI P P1
PC PR [PI R r
= = = = =
= = = = = =
saturated liquid density of pure compound, g./cc. base of natural logarithms number of fluorine atoms in molecule molecular weigh’t of pure compound total pressure on system, atm. vapor pressure of pure component of mixture, atm. critical pressure, atm. reduced pressure value of the parachor gas-law constant ratio of number of noncyclic carbon atoms to total carbon atoms in molecule
1079
LITERATURE CITED
( I ) Benedict, M., Johnson, C. A., Solomon, E., and Rubin, L. C., Trans. Am. I n s t . Chem. Engrs., 41, 371 (1945). (2) Meissner, H. P., and Redding, E. M . , IND. ENG.CHEM.,34, 521 (1942).
(3) Mertes, T. S . , and Colburn, A. P., I b i d . , 39,787 (1947). (4) Othmer, D. F., Ibid., 32, 841 (1940). (5) Ibid., 34, 1072 (1942). (6)
Sugden, “The Parachor and Valency,” London, Routledge & Sons
(7)
Wohl, K., 2. p h y s i k . Chem., B2, 77-114 (1929).
(1930).
RECEIVED January 23, 1848.
Development of Available Magnesia RESULTS OF REACTIVITY OF CONCENTRATED SUPERPHOSPHATE IN MIXTURES WITH OLIVINE, SERPENTINE, MAGNESITE, AND THEIR CALCINES W. H. II/I4cINTIRE, L. J . HARDIN, AND H . S. JOHNSON, JR. Agricultural Experiment Station, The University of Tennessee, Knoxville 16, Tenn.
MAG“
L ESIUM is essential to plant growth. I t functions in the synthesis of the chlorophyll molecule and serves to mobilize phosphorus in the seeds of crops. A deficiency of the element is evidenced by “sanddrown,” the interveinal chlorosis of the leaves ( 6 , 7’, 10, 16, 24-26).’ For many years magnesium compounds have been supplied t o crops, those grown on the soils of the South Atlantic states in particular, through direct incorporations of dolomite and through dolomited superphosphates (4, 6, 11). The inclusion of dolomite in fertilizers was pioneered by a Tennessee manufacturer upon suggestion from the Tennessee Experiment Station. From this station and other sources have come publications on the transitions that occur in mixtures of superphosphate and dolomitic materials (11-14). The problem of the inclusion of magnesium in fertilizers has been dealt with through different approaches (4, 5, 9, 10,17-19). More recently “manure salts,” calcined kieserite, magnesium oxide, hydrated dolomitic lime, selectively calcined dolomite, and domestic salts of magnesium-potassium have come into use for either direct application or admixture with fertilizers. Pulverized serpentine proved effective upon red clover ivhen incorporated at rates in excess of the saturation capacity of the soil in early pot cultures a t this station (16). However, virtually no plant response F a s induced by serpentine in recent pot culture comparisons, when the incorporations were restricted t o rational rates. In soils, added mineral magnesic silicates do not undergo dissolution with rapidity comparable to t h a t registered by their suspensions in carbonated water (16). Hence, it is unlikely t h a t ordinary incorporations of olivine and serpentine would provide an adequate immediate supply of magnesium for crops in general and for tobacco in particular.
Because of the scarcity of dolomite in ICew Zealand, dunite ( 1 ) and serpentine (2) were used to produce neutralized and magnesium-fortified superphosphates. The proposal for the inclusion of a mineral magnesium silicate in fertilizers had been patented by Reichelt, however, in 1909 and 1913 (19). The behavior of such inclusions was studied by Smith in this country (20, 25) and by Andrex ( 1 ) and Askew ( 2 ) in New Zealand. T h e late G. H. Holford, a New Zealand proponent of serpentine inclusion, stated in correspondence that he had been informed the practice was in vogue in Russia. The question of adequacy of magnesium inclusions in mixed fertilizers, without attendant inclusion of calcium, is of particular importance in the South Atlantic states where magnesium deficiency is widespread, and where fertilization is int,ensive. T h e demand for cheap magnesic materials of low calcium content for inclusion in mixed goods is accelerated by the trend t o highanalysis fertilizers. This situation prompted consideration of the possible utility of the extensive peridotite formations of the dunites, olivine, and serpentine that occur in the Blue Ridge Mountains of North Carolina and Georgia. These formations were described in a report upon the survey conducted by T h e North Carolina Department of Conservation and Development i n cooperation ~ i t the h Tennessee Valley Authority ( 8 ) . Many of these formations contain between 40 and 50% of magnesia and virtually no calcium. The present contribution deals with the development of available magnesia through reactions between concentrated superphosphate and various inclusions of olivine, serpentine, magnesite, and their calcines, with uniform moisture content.
