I;VDUSTRIAL A N D ENGINEERING CHEMISTRY
June, 1929
nickel sulfate is the material involved rather than the simple salt. The gas-intake section of the purifying washer always consisted of a mixture of sulfur and nickel sulfide, while the gas-exit section consisted of the ammoniacal nickel sulfate and remained a clear blue solution. The tests were not made t o determine the exact life of the nickel salt. However, the action is distinctly catalytic, yet owing to the sulfur precipitation it is necessary to draw off the purifier washer liquors from time to time in order to separate the sulfur, which accumulates as a heavy sludge. The sulfur is so finely divided that it is easily separated from the nickel sulfide and accompanying liquor by a simple flotation process
567
in an auxiliary column, and hence there is very little loss of nickel sulfide. The actual loss of ammonia in these liquors is also very small. If Reaction 8 is taking place it i s noted that the ammonia lost as fixed nitrogen is related to the sulfur removed in the gas washer and hence must be relatively very small. A small amount of thiosulfate may also be formed. I n all the large-scale tests there was a tendency for the purifying washers to develop frothing, and accordingly the design of this unit must take the frothing factor into account. All the tests were very convincing as to the efficiency of this method for the utilization of crude coke-oven liquors for any form of platinum-catalyst oxidation units.
Capillary Phenomena in Non-Circular Cylindrical Tubes’ W. 0. Smith and Paul D. Foote MELLONI N S T I T UOF ~ INDUSTRIA& RESEARCH,UNIVERSITYOB PITTSBURGH, PITTSBUROH,PA.
I
PI’ SPITE of the volume of literature dealing with capil-
larity, little attention has been given to the consideration of phenomena occurring in non-circular cylindrical tubes, a problem of some practical importance. From the fundamental principles of capillarity the force exerted on any element in the meniscus-wall contour is directed perpendicular to the contour in a plane tangent to the meniscus a t that point. Let cp be the angle between the vertical z axis and the direction of this force on an element ds of the contour. The total force in the z direction is therefore
For a tube of rectangular cross section with the sides a and b we have zu = 2
U(CZ
+ b ) / p gab
(4)
For an elliptical tube having the semi-axes a and b z o = 4 u E ( k ) / n bpg
(5)
where E ( k ) is the complete elliptic integral of the second kind and k = (1 - b2/az)1/z. Equation 3 is obviously applicable to much more complicated forms of cylindrical capillariesfor example, the space enclosed by a bundle of circular rods, o b o s cp ds taken around the contour, where u is the surface etc. Frequently non-circular capillaries have been treated as tension. For a cylindrical capillary this is equal to u P cos b, circular capillaries of equivalent cross section. This in genwhere P is the perimeter of the cross section of the tube and eral, however, leads to erroneous results. As an illustration, 8 is the angle of contact-that is, the angle between the tan- data are given in Table I for the rise of carbon tetrachloride gent to the liquid surface and the wall. and pure water, respectively, in ordinary thermometer tubing of elliptical cross section. p gz cos a dS This total force sustains a weight of liquid
js,
where p is the density, g the acceleration of gravity, and dX is an element of meniscus surface a t a height z above the free liquid and inclined a t an angle a to the horizontal, the integral being taken over the entire meniscus S. Hence cos
‘p
ds
=:
u
P
cos
o
=
+
Js
p gz cos a d.S
(1)
We may put z = t o A?, where zo is the height of the lowest point of the meniscus above the free liquid and A? that of any element of the surface S above the plane 2 = zo. Then n
UP COS tp
= p gzo
COS Q
dS
J S
The integral
Jj
+ pg
AZ
COS CY
dS
(2)
J S
of the tube. The first term on the right of Equation 2 represents the supported weight of liquid below the plane z = zo, while the second term is the weight of liquid above this plane. The latter quantity may be neglected for capillaries of small sectional dimensions so that as an approximation we obtain
P
COS
1 Received January 24, 1929. Pipe Line Companies’ fellowship.
CAPILLARY RISE 80
2b
2a
Mm.
Mm.
0.133 0.305
0.101 0.192 0.062 0.142 c = 26.5
0.128 0.223
Obs.
Eq. ( 5 )
Cm.
Cm.
O / p gA
(3)
Work done under Gulf Producing and
6.00 2.94 8.50 4.00 p =
1.58
5.98 2.94 8.45
3.9s
g = 981
7
=
da r =
(a
+ b)/2
Cm.
Cm.
5.90 2.82 7.66 3.84 9 = 0
5.84 2.75 7.21 3.74
c.
PURE WATER AT 24‘ C.
0.142 0.192
0.223 0.305 u =
”
cos a dS is simply the cross-sectional area A
zo = u
of Liquids in Elliptical Tubes
CARBON TET~ACHLORIDEAT 19‘
P
/-
uJs
Table I-Rise
72.2
17.2 12.6
17.2 12.6
16.6 12.2
16.1
11.5
This agreement between the observed data and those computed by Equation 5 is within the error of the measurements. The fifth column shows the values computed on the assumption of a circular tube of equivalent cross section, and the sixth column values computed for a circular tube having a radius equal to the arithmetical mean of the semi-axes of the ellipse. Both of the last two methods are in current use but do not seem to be so satisfactory. There are references2 in the literature to the fact that the vapor pressure over a meniscus surface is different for circular and non-circular capillaries of the same cross-sectional area. This readily follows from a consideration of the above dis2
For example, Schultze, Kolloid-Z., 86, 65 (1825).
I,VDI;STRIAL A,VD ESGIXEERING CHEMlSTRY
568
cussion. In a closed system let PO be the vapor pressure over the free liquid, p , that over the meniscus, and d the mean vapor density. Then p o - pl = dg?, and from Equation 3 $9 - pi = d u P COS O / p A (6) This equation is usually sufficient for practical purposes, but
T’ol. 21, Xo. 6
may be easily extended by replacing p with ( p - d ) and by considering the variation in density of the vapor column. The formula so obtained is as follows: log /pi = d,i u P COS 8/p ( p - d ) A (7) where do is the vapor density over the free liquid.
Free Energy Charts for Predicting Equilibrium Pressures and Concentrations’ Ralph F. Nielsen INTERNATIONAL COMBUSTION EXGIXEERING CORPORATION, NEW YORK,N. Y .
D E S I R E has often been felt for thermodynamic c h a r t s f r o m which physical and chemical equilibria could be predicted directly, with little or no calc u l a t i o n . I n this paper a form of chart is suggested which allows practically direct reading of equilibrium pressures or concentrations, if a chart be prepared for each pure substance in question. It is intended to prepare these charts for such substances as are met in the work of this organization. hI e a n while the idea is presented here in the hope that charts of this kind may find favor elsewhere and, through criticism and cooperation, be d e vel o pe d in the most convenient form.
A
A form of chart is suggested which allows practically direct reading of physical and chemical equilibrium concentrations, if a single chart be prepared for each pure substance in question. The chart involves lines of constant pressure or concentration, with temperature as abscissa and a function of the free energy as ordinate. Various suggestions are given as to methods of preparation of the charts, and their extension to ions and solutions of electrolytes. Sample charts are given for oxygen. It is believed that the c’onstruction of these charts, with suitable modifications, from available thermodynamic data or free energy equations will result in a considerable saving of time to those making frequent calculations of chemical equilibrium concentrations. If free energy charts for a number of common compounds could be standardized and published, they would probably come into general use, even by those unfamiliar with thermodynamics, and serve a purpose in chemistry similar to that served by the heat-entropy charts in engineering.
Use of Free Energy Equations
The most common method of applying thermodynamics to the prediction of equilibria consists in expressing the change in free energy involved when a given reaction occurs with all components of the reaction (both resultants and reactants) present a t unit [“effective” concentration (activity). z This “standard change in free energy,’’ AF”, is usually given for a standard temperature or as a function of the absolute temperature, and is determined by making use of heats of reaction, specific heats, measured equilibrium concentrations, the third law, and electromotive force measurements, in various combinations. For the sake of condensation, the standard free-energy changes involved in the formation of a number of compounds from their elements may be tabulated, and the standard free-energy change for any reaction involving several of these compounds found by addition. Since all spontaneous reactions must occur with a decrease of free energy, the sign of AF” tells in what direction the given reaction will proceed when both reactants and resultants are mixed a t unit activity. If the concentrations change during the course of the reaction, the magnitude of AF” determines the concentrations finally reached a t equilibrium -that is, the point a t which a further proceeding of the reaction would involve an increase in free energy. I n other words, a t equilibrium A F (not A F ” ) is zero. Such a con1
Received September 26, 1928.
2
For definitions and theories involved in this paper see Lewis and
Randall, “Thermodynamics and the Free Energy of Chemical Substances,” McGraw-Hill Book Co.. New York, 1923.
dition can be reached because a given weight of a substance contains less free energy a t a low concentration than a t a high concentration. As far as thermodynamics is concerned, every reaction involving the formation of a dissolved substance will occur to a t least a very slight extent when only the reactants are mixed, unless AF” is infinite. While we cannot easily overestimate the value of these “free e n e r g y e q u a t i o n s , ” there are a number of practical d i f f i c u l t i e s attending their use. In the first place, it is not the numerical value of the standard change in free energy in which we are primarily interested, The driving force or the direction of a reaction could just as well be considered in other terms related to the free energy. In the majority of cases the quantity desired is the equilibrium pressure or concentration of a substance under certain conditions. This requires the calculation of the equilibrium constant from the free energy equation, which is a time-consuming operation, and finally, the calculation of the desired quantity from the equilibrium constant, which often necessitates the conversion of activities to concentrations. Again, the free energy equation for the formation of a compound from its elements must hold for any temperature a t which we desire to use it for some other reaction involving this compound, if the equations are t o be of general use. This requires an adequate equation for the specific heat, not only of the compound in which me are interested, but of its elements, in which we may not be interested. The difficulties attending the derivation of a simple but accurate specific heat equation for a large temperature range are well known. These difficulties may be overcome to a certain extent by the use of charts, as will be shown subsequently. The use either of charts or of free energy equations is subject to the assumption that the thermodynamic properties of any substance are not affected by the presence of the other substances involved in the given reaction. This assumption, however, can sometimes be removed by the use of special charts or equations for a given reaction. Description and Use of Free Energy Charts
The charts presented here are based upon the principles given above, employing the idea of constant pressure lines
