T h e results indicate that the magnitude of the effects of the structure of the isomers is small, a t least insofar as this group of alcohols is concerned. Assuming, as before, that surface equilibrium has not been reached a t the plate surface, the effectiveness of the isomers would depend on the rate of their transfer to the interface. Investigation showed (Addison, 1945, p. 98) that, while there is a considerable difference in migrational velocities of normal and isooctyl alcohols, this difference decreases with the molecular size of the alcohol and becomes very small for normal and isoamyl alcohols. It may be assumed that it is negligible for the butyl alcohol isomers. T h e similar migrational velocities of the isomers are one of the possible reasons for their similar behavior.
Conclusions
T h e mono- and dicarboxylic acids as well as aliphatic alcohols decrease considerably the size of the air bubbles, thus increasing the interfacial surface area of air-water dispersions. T h e magnitude of this effect is similar in the case of monocarboxylic acids and alcohols but much smaller for dicarboxylic acids. I n all cases this effect increases progressively with the length of the carbon chain of the compound. T h e magnitude of this action can be illustrated by the effect of the octanoic acid, which a t a concentration of 10 p.p.m. increased the surface area by over 700% of that in pure water. The possible explanation of this effect is discussed. T h e effects of these substances on mass transfer coefficient also show a consistent pattern. Except for the decanoic and octanoic acids, the values of KJ, first increase with concentration and then drop well below that for distilled water. T h e position of the maxima (low concentration range) and the subsequent drops of the K L values in the region of higher concentrations were found to be functions of the length of the carbon chain in each of the investigated groups of compounds. T h e total transfer rate, K L A may be profoundly affected by some of the investigated substances-e.g., heptanoic acid a t a concentration of 10 p.p.m. increased the rate of oxygen transfer by 180%. I n the range of low solute concentration this improvement in the rate is more pronounced the higher the molecular weight of the substance in each of the investigated groups of compounds. T h e effects discussed in this report depend on the air dispersing system. Since the principal action of the substances appears to be in preventing the coalescence of the bubbles, their effectiveness will improve in systems where the possibility of coalescence is greater. T h e practical importance of the results is discussed.
Correction
PREDICTION OF DISSOCIATION PRESSURES OF M I X E D GAS HYDRATES FROM DATA FOR HYDRATES OF PURE GASES WITH WATER I n this article by Isamu Nagata and Riki Kobayashi [IND. ENG.CHEM.FUSDAMENTALS 5,466 (1966)], several errors have been found. O n page 466, in Equation 6, the first term on the right-hand side should be AH/RT2 in place of (AHIRT). Graphs in Figures 1 and 4 have been interchanged, but the captions are located correctly. O n page 467, in Table I, column 1, the value 277.5 should be 277.6. Also in Table I, under “Parameters used,” C,A should be c,A. 242
I&EC FUNDAMENTALS
Tests conducted with normal, iso-, and tert-butyl alcohols did not show any pronounced difference in their effects on size of the air bubbles and the rate of oxygen transfer. Nomenclature
a
b A C Ci Ct C, d,
= major semiaxis of a spheroid, cm. = minor semiaxis of a spheroid, cm.
= total surface area, sq. cm. = D.O. concentration, p.p.m. = equilibrium concentration of oxygen, p.p.m. = D.O. concentration a t any time, p.p.m.
= initial D.O. concentration, p.p.m.
surface-volume mean diameter of bubble, cm. total air holdup, cc. oxygen transfer coefficient, g./(hr.) (sq cm.) (p.p.m.) number of bubbles time of absorption, hr. weight of water in column, g. a = eccentricity, [I - ( b / ~ ) ~ ] ” ~ ut = dynamic surface tension a t time t , dynes/cm. uC = equilibrium surface tension, dynes/cm. AU = - U* = = KL = n = t = W =
H
literature Cited
Addison, C. C., J . Chem. SOC. 1943, p. 535. Zbid., 1944, p. 252. Zbid., p. 477. Ibid., 1945, p. 98. Zbid., p. 354: Baird, M. H. I., Davidson, J. F., Chem. Eng. Sci. 17, 87 (1962). Bikerman, T. T., “Surface Chemistry,” Academic Press, New York, 1958. Braasch, H., Braasch, A., German Patent 605,912 (1934). Carver, C. E., “Absorption of Oxygen in Bubble Aeration” in “Biological Treatment of Sewage and Industrial Wastes” J. McCabe, W. W. Eckenfelder, Eds., Reinhold, New York, 1956. Cullen, E. J., Davidson, J. R., Chem. Eng. Sci. 6 , 49 (1956). Drost-Hansen, W., Znd. Eng. Chem. 57, No. 4, 18 (1965). Foulk, C. W., Miller, J. N., Zbid., 23,1283 (1931). Garner, F. H., Hammerton, b.,Chem. Eng. Sci.3, 1 (1954). Garner, F. H., Haycock, P. J., Prod. Roy. Sod. 252, 457 (1959). Harkins, D. W., “Physical Chemistry of Surface Films,” Reinhold, New York. 1957. Holroyd, A.,’Parker, H. B., Water Sanit. Engr. 3, 301 (1952). Jackson, Roy, Chem. Engr. No. 178, 107 (1964). Sawyer, N. C., J . Water Pollution Control Federation Lynch, 0. W., ’32,25 (1960). . Mancv. K. H., McKeown. T. T.. Okun, D. A., “Oxvgen in Waste Treatment,’; Dept. San’itary Engineering, Univerztv of North Carolina. Propress ReDort. Februarv 1959. Verschoor, H., Trans. Znst. Chem. Eners. 28, Zieminski, S. A., . .- , (1960). Zieminski, S. A., Hill, R. L., J . Chem. Eng. Data 7, 51 (1962). RECEIVED for review February 7, 1966 ACCEPTED December 29, 1966 Investigation supported by Public Health Service Research Grant WP-00562-01A1 from Division of Water Supply.
Correction
NECESSARY AND SUFFICIENT CONDITIONS FOR INEQUALITY CONSTRAINED EXTREME VALUES In this article by R. P. King [IND.ENG.CHEM.FUNDAMENTALS 5,484 (1966)], two errors have been discovered. O n page 485, column 1, fifth line from the bottom, “for each gi in g*” should be replaced by “for some gi in g*.” O n page 485, column 2, tenth line from the top, the strict inequality should be replaced by “(x - x”)’G* 2 0.”
