Correlating Solubility a istribution Coe

DONALD F. OTHhlER AND MAHESH S. THAKAR Polytechnic Inst i tute of Brooklyn, Brooklyn 2 , -1'. Y .

REVIOUSLY, many physical properties of systems contain- ing solids, liquids, and gases have been correlated by a simple

method of logarithmic plotting and correspondingly simple alge- braic equations.

For vapor pressures and latent heate the tollowing equation applies (S) ,

(1) log I' = A log P' + c L'

where at the %me tempei ature P and P' are vapor pressures and L and L' are molal latent heats, respectively, of two compounds and C is a constant Log P' actually serves as a temperature scale which can be obtained directly from vapor pressure data of standard substances. LIL' 16 nearly independent of temperature and a logarithmic plot of P versus P' gives substantially a straight line whose slope L/L ' provides latent heat data a t any tempera- ture for the compound in question from that of the reference sub- stance. This method of plotting has been applied to correlate as straight linea othei properties, such as gas solubilities and partial pressures, adsorption pressure, vapor compositions, equilibrium constants, activity coefficients, relative volatility, electromotive force, and viscosities (4-8). The slopes of these lines have been identified in each case with the heat effects accompanying the chemical or physical change.

In most cases an alge- braic equation is not needed .and the property can be p l o t t e d d i r e c t l y on a logarithmic paper by the following steps:

1. Plot vapor pressure of t,he reference substance on the X axis and cali- brate it by indicating ('orre- sponding temperatures from a standard table a t respec- t,ive vapor pressures.

Plot the values of the property in question on the appropriate t e m e r a t u r e lines against t i e corre- sponding Y axis scale.

3. Connect t,he points so obtained by a, straight line.

2.

APPLICATION TO SOLU- BILITY DATA

Solubility data of solidh in Liquids can be plotted by the method indicated. Fig- ure 1 indicates such a plot for s e v e r a l s u b s t a n c e e , w h e r e s o l u b i l i t i e s ex- pressed in mole fraction (or per cent) of different solids in water are plotted versus temperature, indi-

cated in the regular way from the corresponding vapor pres- sure of water as the reference substance. All data were taken from ( 2 ) .

In most cases correlation is good and straight lines are obtainod over wide temperature ranges. In gome cases the straight line shows a sharp break with a consequent change in slope. This break is obviously due to the change of a physical or a chemical nature of the subst.ance at, that particular temperature. Thus, in the case of sodium sulfate, a sharp break in the straight line occurs a t 36" C. where the sodium sulfate decahydrate, NazSOc.- lOHzO, changes to its anhydrous form, SaeSOr. One advantage of this method of plotting is that it helps to locate the transition point wherc such a physical or chemical change occurs more pre- cisely than is possible by intersection of curved lines of empirical shape.

The equat,ion may be expressed for these lines representing solubilities, x, expressed as mole per cents.

(2) log z = Lf 7 log P' + c I,

If z,/L', where tf is equal to (6, - h,) and L' is the molal latent heat of vaporization of the wfercnce liquid, is assumed to remain

TEMPE R A T U RE,OC.

VAPOR P R E S S U R E OF WATER mm. H g

Figure 1. Logarithmic Plot of Solubility in Water against Vapor Pressure of Water

1. Urea fi. Sodium sulfate (anhydrous) 2. Sucrose 7. Sodium sulfate (decahy- 3. Ammonium sulfate drate) 4. Copper sulfate (a) 8. Potassium permanganate L Copper sulfate (PI 9. Calcium hydrodde

46.34

nearly constant, it is ob- vious that a plot of solubili- ties versus the vapor pres- sures of the reference liquid at the same temperatures M-ill give a straight line on standard logarithmic paper.

For some solutes, such as sucrose in water, the plot gives a slight curve because of the very major deviations from Raoult's or Henry's l a w s . T h e s e irregular cases are proba- bly due to high solubility, high molecular weight, and possible varying hydration of the solute molecules.

APPLICATION TO DISTRI- BUTION COEFFICIENTS

Distribution coefficients of a solute between two solvent layers are closely related to the solubility of the solute in either of the solvents. T h e r e f o r e , i t should be possible to corre- late the variation of dis- tribution coefficients with t e m p e r a t u r e as straight l ines b y fo l lowing t h e method of plotting indi- cated previously.

July 1952 INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY 1655;

TEMPERATURE. O C . cases of the van’t Hoff equation and can be found in standard

VAPOR PRESSURE OF WATER mm. Hg

Figure 2. Legarithmic Plot of Distribution Coefficients of Various SubBtances between Various Solvents and

Water Data multiplied by 10 1. 2. 3. 4. 5. 6.

Succinic acid between ether and water Dimethylamine between ether and water Bromine between carbon tetrachloride and water Trimethylamine between ether and water Trimethylamine between toluene and water 2.3.4-Trimethylpyridine between toluene and water

In Figure 2, such a plot of distribution coefficients of various distributed solutes in two solvent layers is given, where the dis- tribution coefficients are plotted versus the vapor pressures of water at the same temperature. Straight-line correlation again is obtained. All data were taken from ( 2 ) .

The equation of this line representing KD, the distribution co- efficient, is

(3) AL, L log KO = log P‘ + C

The slope of the line A L , / L ’ represents the ratio of the molal heat of transfer for the solute from one solvent layer to the other to the molal latent heat of vaporization of the reference sub- stance. This slope, ALJL‘, is nearly constant over the usual tem- perature ranges for many systems and therefore a straight line is obtained when the distribution coefficient is plotted versus the vapor pressure of a reference substance on a logarithmic paper.

The distribution law is rigorously applicable only to dilute solu- tions where Henry’s law applies and a straight line plot will be obtained in such cases. Where the concentration of the solute in solvent becomes so appreciable as to affect the distribution co- efficient, a better correlation will be obtained if the distribution coefficients at various temperatures are selected in the concentra- tion range of the same order of magnitude.

THERMODYNAMIC DERIVATIONS

Thermodynamic derivations are given here to indicate briefly the basis for the correlations.

SOLUBILITY. For the solubility of a pure solid in a solvent, when the solution obeys Raoult’s law or Henry’s law, an equation has been derived previously by numerous authors as special

textbooks on physical chemistry and chemical thermodynamics.

- (4)) d l o g x = - Lf dT

RT2

or integrating

A logx = + B

If Equation 4 is divided by the Clausius-Clapeyron equation, always a t bhe same temperature

L‘ - d7’ RT2 d log P’ =

there follou7s -

d log2 L ___ =r d log P’ L’

This, on integrating, assuming zf/L‘ to remain constant, yields approximately

(8) El log 5 = 7 log P‘ + C L

which is the equation used in the correlation above. i p defined a5 ( E l - h,) or the difference between the partial molal enthalpy of the solute in saturated solution and the molal enthalpy of solute in pure solid state. For solutions obeying Raoult’s ideal law, this quantity becomes equal to the latent heat of fusion of the solid from the pure liquid state t o the solid state. However, for real solutions which obey Henry’s law, this quantity depends on the differential heat of solution of the solute in saturated Holution and can be plus values as well as minus values.

DISTRIBUTION COEFFICIENTS. Following similar procedure of derivation, it can be shown that for distributed sys tem in which the solute obeys Raoult’s law or Henry’s law, Equation 9 can be derived

Dividing this relation by the Clausius-Clapeyron equation, and integrating as before, there is obtained the relation used for correlating distribution coefficients

log KO = $log P‘ + C (10)

RELATION OF REFERENCE SUBSTANCE PLOT (LOG P) TO RECIPROCAL TEMPERATURE PLOT ( 1 / T )

In other papers of this series, particularly those relating to vapor pressure, reference has been made to the corresponding integration of the simple Clausius-Clapeyron equation (or re- lated equations for other functions). Thus, there is the common expression log P = A / T + B. This equation is sometimes plotted directly on specid graph paper, ruled with logarithmic scale on the Y axis and a reciprocal temperature scale (or negative reciprocal temperature scale) on the X axis.

Attention has been called to the greater eaae of using standard logarithmic paper on which the X axis is then calibrated directly in temperature values from the corresponding points of vapor pressure of a reference substance, usually water. Because of the ease of using different range of both temperatures and pressures which can be done readily with logarithmic paper of different numbers of cycles, and the several inherent advantages of logarith- mic paper and its ready availability, the present plot has muck practical advantage.

Furthermore, it has ~ f t e n keen noted that the liaes SQ ob-

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1656 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 44, No. 7

tained are more nearly straight on the logarithmic plot than on the reciprocal temperature plot for reasons which have been de- veloped.

In the present case, working with solubility and distribution co- efficients, this is also noted in numerous cases. It follows directly that L//L‘ and particularly AL,/L’ are more nearly constant with a variation of temperature than are z j and AL, alone, since the numerator and the denominator of the fractions are both decreas- ing with increase in temperature. As the straightnesa of the line depends on the approach to constancy of its slope, the better correlation is obtained using the method of this paper. This is more particularly true for distribution coefficients since, in all cases tested, the decrease of AL, with temperature is notable.

The breaks in the lines caused by transition points in the chemi- cal compositions has been noted with the reciprocal temperature plot by Davidson (1 ) who relates the changes in slopes to the heats of transition. Obviously in the case of the logarithmic plot, the heats of transition may be developed even more readily by reference to the latent heats of the reference substance and the different slopes of the lines in question.

NOBIENCLATUR E

A, B , C = constants hr = partial molal heat content of the solute in its saturated

h, = molal heat content of pure solid phase K D = distribution coefficient of solute between two solvent

solution

layers

L L’ 1,

= molal latent heat of Vaporization of liquid = molal latent heat of vaporization of reference liquid = difference between partial molal heat content of the

solute in its saturated elut ion and the molal heat con- tent of pure solid, or (hi - h,) [heat of solution for 1 mole in dissolving in (01 negative of 1 mole crystal- lizing from) its saturated solution],

A L = molal heat of transfer of solute between two solvent layers

P = vapor pressure of liqid P’ = vapor pressure of reference liquid R = gas constant T = temperature, OK.

x = solubility in mole fraction of solid in solution

LITERATURE CITED

(1) Davidson, J . Chem. Education, 10, 234 (1933). (2) “International Critical Tables,” Vol. 4, New York, RIcGraw-Hill

(3) Othmer, D. F., IND. ENG. CmaI., 32, 841 (1940). (4) Ibid., 36, 669 (1944). (5) Othmer, D. F., and Conwell, J. W., Ibid., 37, 1112 (1945). (6) Othmer, D. F., and Gilmont, R., Ibid., 36, 858 (1944). (7) Othmer, D. F., and Sawyer, F. G., Ibid., 35, 1269 (1943). (8) Othmer, D. F., and White, R. E., Ibid., 34, 952 (1942).

Book Co., 1928.

RECEIVED for review September 26, 1951. ACCEPTED March 13, 1952. Previous articles in this series have appeared in IKDUSTRIAL AKD ENGINEDR- I N G CHEMISTRY during 1940, 1942, 1943, 1944, 1945, 1946, 1948, 1949, and 1950: Chem. & Met. Eno., 1940; Chimze et IndzLstrze (Parzs), 1948; Euclzdes ( M a d i a d ) , 1948; Sugar, 1948; Petroleum Refiner, 1951 and 1952

Alkali Lignin to Stabilize Slow- Break Asphalt Emulsions

W. A. McINTOSH Development Department, West Virginia Pulp & Paper Co., Charleston, S. C .

HE recent development of commercial grades of alhali T lignin could hardly come a t a more appropriate time for the good of streets and highways. This abundant raw material is very useful as a stabilizer for soap emulsified slow-break asphalt emulsion. Shortages, caused by the national emergency, of the light petroleum fractions required for application of asphalt as cut-back need not interfere with proper maintenance of roadway systems. Lignin even can extend the emulsifying soap, even though it is not itself an emulsifier.

LIGNIN

Pine wood alkali lignin is available in three forms under the general trade name Indulin. It is isolated from the waste liquors resulting from pulping pine wood by the kraft or sulfate process. One of the three commercial grades, designated Indulin A, is lignin in its acidic or phenolic form. As such, it is insoluble in water or acids, but can be easily dissolved in aqueous alkalies such aa caustic soda, which forms a water-soluble sodium salt. In Indulin C, the sodium salt is already present, and this product dis- solves readily in water without the addition of other chemicals. Indulin B is a very recent addition to commercially available pine wood lignins. Like Indulin C i t is a sodium salt of lignin and is water soluble. Because of its very recent development, Indulin B has not yet been investigated for asphalt emulsion stabilization.

All three of these materials are free-flowing brown to black powders of spherical particles. Shipped in dry form, no freight is paid for water of solution. The dry powders are virtually nonhy- groscopic. They may be stored indefinitely without deterioration

or creation of a nuisance. Solutions up t o 18 weight ’% have low viscosity and are easily handled. Increases in concentration above this figure cause disproportionate increases in viscosity, which can be controlled within limits, however, by using addi- tional alkali.

Alkali lignin should be distinguished from the so-called sulfite lignin derived from the acid, or sulfite, process for pulping Rood. The latter is comprised chiefly of lignin sulfonates formed by the action of sulfite liquor, which adds sulfonate groups to the lignin occurring in the wood. iilkali lignin, on the other hand, resembles more closely the lignin as it is present in the wood.

The sodium compounds of alkali lignin are used in the stabiliza- tion of slow-break asphalt emulsions. Because of solubility in water and insolubility in hydrocarbons, they are applied with the sodium soaps in the aqueous phase. These sodium compounds of pine wood lignin are compatible with all of the widely used soap emulsifier solutions in all normal proportions. Concentrated solutions of the lignins should be maintained a t pH 9.5 or higher to prevent precipitation, but at the low concentrations used for mixing with asphalt, considerably lower pH values could he tolerated if desired.

V 4 T E R I A L S

The purpose of the present study was to verify the application of pine wood alkali lignin as a stabilizer for a wide variety of asphalts from different crude sources. It was also hoped that some conclusions could be drawn from the effect of source on the quantities of chemicals required. Unfortunately for the latter