Solubility of Oxygen in Nitric Acid Mixtures G. D. ROBERTSON, JR., D. M. MASON, AND W. H. CORCORAN California Institute of Technology, Pasadena, Culif.
S
T U D l E S have been made of the kinetics of the thermal decomposition of nitric acid mixtures (7). The pressuretime histories of the systems considered provided means for treating the kinetics. I n the analysis of the pressure-time data t o give the desired information on rates of reaction, it was necessary t o obtain a material balance for the oxygen present in the system. The solubility data for oxygen were therefore obtained, and values of the coefficient in Henry's law were computed. EQUIPMERT AND METHODS
I n the determination of the solubility of oxygen in nitric acid mixtures, equipment was used t h a t has been described ( 7 ) A sample of acid and oxygen was confined in a precision-bore glass capillary tube with an internal diameter of 3 mm. The confining liquid was a fluorinated hydrocarbon designated as Fluorolube S (manufactured by Hooker Electrochemical Co.). The desired temperature was maintained b y means of a vacuumjacketed oil bath which could be controlled within &0.05" C. of any temperature between 35' and 90' C. Pressure was measured by means of an oil-filled pressure balance having an accuracy of &0.005 atmosphere up t o a total pressure of 22 atmospheres. T h e balance was checked against a standard laboratory balance which was periodically calibrated against the vapor pressure of solid carbon dioxide a t the ice point. The pressure balance was connected t o the Fluorolube S used as the confining liquid through a mercury-filled trap. After the sample of acid and oxygen had been introduced into the capillary tube, the volume was adjusted so as t o raise the pressure t o about 40 atmospheres. The liquid phase was well agitated in order t o allow an approach t o physical equilibrium. Next, while t h e agitation was maintained, the pressure was lowered t o about 22 atmospheres. As t h e pressure was reduced, bubbles were evolved, indicating t h a t the liquid phase was a t least saturated with oxygen. T h e pressure of the system was measured with the balance, and the volumes of the gas and liquid phases were obtained by direct observation with a cathetometer. Determination of liquid levels with the cathetometer was possible with an error less than +0.005 em.
Table I.
Nitric acid was prepared by procedures described (6). It was distilled from a mixture of potassium nitrate and pure sulfuric acid and condensed a t a pressure of less than 0.01 inch of mercury at dry ice-acetone temperature. I n a titration with sodium hydroxide the acid was found t o contain less than 0.001 weight fraction of water. Previous experience with optical absorbance ( 3 ) showed t h a t if the sample were colorless t o the eye, no nitrogen dioxide was present. Commercial oxygen t h a t was not further purified was used in the tests. After the measurements a t 22 atmospheres, the pressure was lowered t o about 8 atmospheres with continued agitation. T h e new values for pressure and volume were obtained after gas bubbles ceased t o appear in the liquid phase. I n each instance the liquid phase remained constant in volume within t h e limits of measurement. The time between measurements was minimized in order t o make the correction for oxygen formed in the thermal decomposition of acid as small as possible ( 7 ) . T h e agitation of the liquid phase and the gas-liquid interface was achieved by means of a magnetically driven iron pellet t h a t was encased in glass. Since the pellet moved back and forth through t h e entire length of the liquid phase once during each second, equilibrium conditions with respect t o the solution of oxygen were assumed t o be obtained. RESULTS
Calculations were made t o determine the coefficient 01 in Henry's law and the experimental results are given in Table I. Henry's law may be written as =
(02)
(1)
+
Data at two different pressures for each sample of acid were employed in computing C Y , Using the perfect gas and Dalton's laws, Equation 2 may be written a t constant temperature for the two pressures as follom:
Experimental Data on Solubility of Oxygen in Nitric Acid and Mixtures with Nitrogen Dioxide or Water
Composition, Wt. Frao.
Test
No.
Elapsed 108, Timea, Ed X 106, Liters Sec. Mole 0.816 600 0.017C 0.830 600 0 185 0.778 540 0 0.778 540 0 0.791 540 0.071 0.791 540 0.071 0.797 1500 0 0.797 1500 0 0.786 0 600 0.788 0 900 0,800 0 600 0.030 0.817 900 0.158 0.835 420 oxygen, z d , formed from decomposition
ZL X
PI PA, I G i X 108, xu%X 108, PI, Atm. At& Atm. Liters Liters 1 37 7 21.73 7 . 9 1 0.160b 0.302 1.048 1.00 HNOa 2 54.4 21.73 7.91 0.335 0.311 1.122 0.85 3 21.73 7.91 0.350 0.309 1.007 37.7 0.304 0,999 7.91 0.350 21.73 4 37.7 "Oa NO? 0.15 1.083 0.748 0.315 5 54.4 21.73 7.91 1.074 0.748 0.311 6 54.4 21.73 7.91 0.94 7 37.7 14.80 12.73 0.090 0.466 0.557 HNOa 8 37.7 12.73 10.66 0.090 0.557 0.683 0.06 Hz0 9 37.7 7.91 0.090 0.257 0.860 21,73 10 37.7 7.91 0,090 0.246 0.825 21.73 11 54.4 21.73 7.91 0.224 0.232 0.814 0.936 0.410 0.254 7.91 12 71.1 21.73 0.244 0.994 13 87.8 21.73 7.91 0.783 a Time elapsed between measurements which define conditions 1 and 2. This time is used in determining amount of of sample. b Cf. (9-6). Computed from decomposition d a t a (1). System
O1pB
I n the calculations use was made of a material balance for oxygen. The total moles of oxygen as such in the system a t any given time are expressed as q = 3.1-j q, (2)
t,
C.
1470
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
July 1955
1471
5 .oo
1.00 U W
r
P
6I
0.50
a W
a v) 3
w
0.Ib
0.05
0.0 I
TKCP ERATU R E oc Figure 1. Effect of temperature on bubble point pressure a t physical equilibrium for nitric acid and mixtures with nitrogen dioxide or water
TEMPERATURE
OC
Figure 2. Effect of temperature on coefficient i n Henry's law coefficient for solutions of oxygen in nitric acid and mixtures with nitrogen dioxide or water
(3).
(4) Equations 3 and 4 are related by the following expression
where E d is the number of moles of oxygen formed by the decomposition of nitric acid in the time between the first and second sets of pressure and volume measurements. The effect of the term was small, its maximum contribution to the CY term being about 3%. The value of 3,m-as obtained using data for the rate of decomposition of nitric acid ( 7 ) . By combining Equations 3 and 4 with Equation 5 the following relationship is obtained
As the total pressure is the sum of the partial pressure of oxygen p ~ and , of the acid vapor, PA, Equation 6 may be rewritten in terms of the total pr;essureto give
CYl/L(Pl
Solution of Equation 7 for f f = [
(P2VC2 -
PlyGI)
CY
+
E d
(7)
results in the following expression
- P A ( y G 2 - ?GI)
RT
- PA)
- m,] -
!GI, ~ G Z YL, , and T are all experimentally measured quantities. Values of p d obtained from data in the literature (1, I, 4, 8) are shown in Figure 1 as a function of temperature and composition.
P I , P2,
Table 11. Henry's Law Coefficient, CY,for Solubility of Oxygen i n Nitric Acid and Mixtures with Nitrogen Dioxide or Water a t Various Temperatures Composition,
Test iV0.
System HNOa
W t . Frao. 1.00
1 2
HNOs Hz0
0.85 0.15
3 4
HNOa H20
0.94 0.06
5 6 7 8 9 10 11 12 13
t,
c.
37.7 54.4 37.7 37.7 54.4 54.4 37.7 37.7 37.7 37.7 54.4 71.1 87.8
a X 108, G . Moles/ Liter Atm. 5.55 5.80 3.60 3.78 3.84 3.86 4.44 4.16 4.17 4.05 4.26 4.98 5.63
Table I1 gives the results of the calculations for CY. Figure 2 shows graphically the variation of OL with temperature. When Table I1 recorded more than one value of 01 for a given temperature and composition of nitric acid mixture, an average was computed and plotted in Figure 2. It is evident from a comparison of tests 7 through 10 a t 37.7" C., that CY is essentially constant with respect to pressure, and thus Henry's law applies in the pressure range studied. CONCLUSIONS
For the nitric acid mixtures studied, Figure 2 shows that oxygen solubility increases with temperature. This typical behavior is also observed in the case of the solubility of oxygen in water a t temperatures above 90' C. (6). It is thus apparent t h a t the enthalpy change when oxygen is dissolved in water or nitric acid mixtures a t constant temperature and pressure is positive 07 er a limited temperature range.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1472
NOMENCLATURE = total number of moles of oxygen not chemically combined 3 (02) = concentration of oxygen in liquid phase, moles per liter
p P
= = = = = = =
R t T C Y
’
G
ACKNOWLEDGMENT
This paper presents results of a part of the research carried out for the J e t Propulsion Laboratory, California Institute of Technology, under Contract No. DA-04-495 ORD-18 sponsored b y the U. S. Army Ordnance Corps.
partial pressure, atmospheres total pressure, atmospheres universal gas constant, atmosphere liters per mole O K. temperature, O C. temperature, OK. total volume, liters coefficient in Henry’s law, gram-mole per liter atmosphere
Subscripts A = vapor above acid solution for physical equilibrium at bubble point in absence of decomposition products B = oxygen d = contribution of decomposition of acid between states 1 and 2 t o oxygen not chemically combined
1 2
Vol. 41, No. 7
= gas phase = liquid phase = state 1 of system = state 2 of system
LITERATURE CITED
(1) Egan, E. P., Jr., IND. ENG.CHEM,,37, 303-4 (1945). (2) Klemenc, A., and Rupp, J., 2. unorg. Chem., 194, 51-72 (1930). (3) Lynn, S., Mason, D. M., and Sage, B. H., IND. ENQ.CHEM.,46, 1953-5 (1954).
(4) Perry, J. H., and Davis, D. S., Chern. and Met. Eng., 41, 188-9
(1934). (5) Priy, H. A., Schweikert, C . E., and Minnich, B. H., IND.ENG. CHEM.,44, 1146-51 (1952). (6) Reamer, H. H., Corcoran, W. H.. and Sage, B. H., Ibid.,45,2699704 (19531. (7) Robertson, G. D., Jr., “Some Physicochemical Properties of the System Nitric Acid-Nitrogen Dioxide-Water. Kinetics of the Thermal Decomposition of Nitric Acid in the Liquid Phase,” thesis in chemical engineering, Part I, California Institute of
Technology, 1953. (8) Taylor, G. B., IND.ENQ.CHEM.,17, 633-4 (1925). RECEIVED for review July 23, 1954.
ACCEPTED November 4, 1954.
Paint Viscosity and Ultimate Pigment Volume Concentration U
d
W. IC. ASBECIQ, G. -4. SCHERER2, AND MAURICE VAN LOO The Sherwin- Williams Co., Chicago, Ill.
A
PREVIOUS paper (2)demonstrated the usefulness of the hypothetical term “viscosity a t infinite shear velocity” applied t o practical problems of viscometry involving paint systems. This theoretical point is obtained by extrapolating the plot of the logarithm of the apparent viscosity of the system at finite shear velocity, log )I, against the reciprocal of the square as ,measured on a high shear root of the shear velocity l/a velocity viscometer (3, 6, 11) t o the point where the shear velocity is infinitely great. It represents a specific rheological state of the paint system, It is that point at wrhich all rheological structure, be it shear volocity or time sensitive, is removed. At this point only the viscosity of the supernatantliquid and the pigment siee distribution, shape factor, and concentration play major roles in determining the viscosity of the system. A t infinite shear velocity the viscosity of the pigment/binder svstem is directlv DroDortional to the viscosity of the binder, ” T h e Vand (10) and Brailey ( 5 ) equations, relating the concentration of dispersed pigment to the viscosity of the system, are valid. This is true because both derivations were carried out on the assumption t h a t no rheological structure resided in the dispersion. This condition can be realized only at infinite shear velocities for any system containing rheological structure. Most paint systems fall into this category. The Vand equation states
constants of the system. K is the pigment shape factor and q is the immobilization constant which corresponds t o the amount of vehicle immobilized during the collision of pigment particles. T h e data presented in this paper deal only with rheological systems in which the vehicle is essentially Newtonian in nature. This is true for most oil paint systems but not all, The validity of actual data applied t o the Vand equation can be tested by 1 plotting log ?I- against log If the value of (I has (1 -c - (IC?. ?lo been chosen properly, the data will lie on a straight line with slope K . The choice of the Proper values of P and K requires considerable manipulation. The values can be established either roughly by solving a series of Vand equations simultaneously or by trial and error methods. Both are cumbersome and time consuming. Nomography does not seem t o reduce the difficulty materially because of the complexity of the diagrams involved.
where 7 is the viscosity of a pigment dispersion at infinite shear velocity, 70 is the viscosity of the binder, c is the volumetric percentage of pigment present in the dispersion, and K and q are
where 70, and c conform t o the notations in the Vand equation, and k is very nearly proportional t o K , the form factor, while U is a function of q, the immobilization constant. The ratio of K to k is constant t o within less than 10% for all useful values of p or U . This equation can be thrown into a number of forms that can be solved graphically quite readily.
1 Present address, Carbide and Carbon Chemicals Co., South Charleston, W. Va. * Present address, Earlham College, Richmond, Ind.
HYPERBOLIC EQUATION
Fortunately the Vand equation and the improved form suggested by Brailey can be converted semiempirically into a simple hyperbolic form which conforms very closely to the results obtained by these equations. The theoretical grounds for this hyperbolicequation are described by Mooney (9)and Maron ( 7 , 8 ) . It is of the type
