(283K) Sexsmith, D. R., Frazza, E. G., “Haloalkvl styrene-phosphine copolymers for coatings, paper sizing, and textile treatment,” ( t o American Cyanamid Co.), Ibid., 3,168,502 (Feh. 2, 1965). (284K) Shaoiro P. Collings L. V Counts T. 0 “Corrosion protection,” (to Sinclair Rbse&ch,’Inc.), Ibth.,3,1Q6,455 (Feb. 2, 19i’S). (285K) Sheldahl, D. €I“Disulfonatc ., fatty diamine salts of dicarboxylic acids as corrosion inhibitors in mineral acids,” (to Sinclair Research Inc.), Ibid., 3,153,171 (Oct. 13, 1964). (286K) Shepard, J. W., Shely, B. L., “High-contrast films for radiation photography,” (to Minnesota Mining and Manufacturing Co.), Ibid., 3,172,828 (March 9 , 1965). (287K,) Smith E. J. Vucich M . G. Austin L. W. “Aluminum-manganese alloy .Diatrnp.,” - (tdNatidna1 Steei Corp.),’Ibid., 33167,408 (Jan. 26, 1965). (288K) Spivack J . P., “Primary amines containing tertiary amino groups,” (to Geigy Chemich Corp.), Ibid., 3,201,472 (Aug. 17, 1965). (289K) Sreinberg, H., Hunter, D. L.,, Pickard, M. H., Petterson L. L. “Glvcoi monoborate salts as corrosion inhibitors for brake fluids,” (to S . Bbrax and Chemical Co.), Ibid., 3,163,506 (Dec. 29, 1964). (290K) Storcheim S. “Corrosion resistant strip from powdered iron ” (to Alloy Research 8; Ma4ufa)cturing Go.), Continuation-in-part of U. S. P a t e i t 3,163,527. (291Kj StromberR, W. I,., “C,orrosion inhibitor for oil wells,” (to Petrolite Corp,), U. S . Patent 3,200,071 ( h u g . 10, 1965). (292K) Strombcrg, V. L I‘Ester amide acid compounds as corrosion inhibitors,” (to Petrolite Corp.), I&;., 3,172,853 (March 9 , 1965). (293K) Tomono R. “Chromate processes,” (to Okuno Chemical Industry Go.), I b i d . , 3,259,506 (D&. I , 1964). (294K) Tousi-nant W. F “Oxazoles and Thiazoks,” (to Dow Chemical Co.), Ibtd.,3,1.52,?41 (Oct. 6, i b 6 4 ) . (295K) Udelhofen J. H. “Corrosion inhibitor oils,” (to Stand3rd Oil Co., Ind.), Ibid., 3,123,634 ( M a d 3, 1964). (296K) Udelhofen J. H. “Corrosion inhibitors for gasolinrs,” (to Standard Oil Co. of Ind.), Ibih., 3,189,069 (May 11, 1965). (297K) Van Poolen, H . K . “Corrosion inhibition l o petroleum production,” (to Marathon Oil Co.), Ibid.,’3,194,314 (July 13, 1965).
e.
(298K) White, J. C., Schuldiner, S . , “Fuel cell anode,” (to U. S. Dept. oItheNavy), Ibid., 3,183,122 (May 11, 1965). (299K) Wick, W. C.. “Hard nickel-base alloys for valve seat liners,’’ (to Wells Manufacturing Co.), Ibid.,3,167,424 (Jan. 26, 1965). (300K) Williams D “Design of fuel elements or nuclear reactors ” (to United Kingdom AtoAic h r g y Auihority), Itrid., 3,157,580 (Nov. 17, 1924). (301K) Wright, C. S . , “Boron phosphate esters as gasoline adaitivcs,” (to Pure Oil Co.), Ibid., 3,158,452 (Kov. 24, 1964). (302K) Yager, A., “Phosphating process and composition,” (to Purex Corp. Ltd.), Ibid., 3,181,976 (May 4, 1965).
U.S.S.R. (303K) Efimova, A . K., Shatunova, A. M., Sapoznikova E. A . “Preparation of corrosion inhibitor for metals,” (to Scientific-Research’ Institdte for Petroleum Kefining), L.S.S.R. Patent 166,428 (19 K o v . 1964). (304K) Golyanitshii, 0. I., “Protection of metals from atmospheric corrosion with the aid of quaternary ammonium bases,’’ Ibid., 168,577 (18 Feb. 1965). (305K) Lipin, A. I., Golovkina N. P “Increaqing the anticorrosion protection of steel -parts.” Ibti.. 169.’969 (17 Iharch 1965). --,. .phosphatized . , (306K) A‘egreev, y. F., Kydzimov A . hl. “Protrction of aluminum and its alloys from corrosion in alkaline media,” Ibid.: 167,115 (12 Dec. 1964). (307K) Segreev, V. F., Mamedov, I. A., Kotel’nikov, B. P., Divenko, A. P., “Corrosion inhibitors,“ Ibid., 168,827 (26 Feb. 1965). (3??K) Shtern M . A . , Danyushevskaya X. E . , Alekseeva, 0.V. Bogatyrev P. M Preparationi of calcium chromate-& anticorrosion pigment‘” (io stat6 ScieAl tific-Research and Design Institute of the Paint and Varnish Industry), Ibid., 167,592 (18 Jan. 1965). (309K) Smirnova, T. N.:,Zuhakhin, B. T., D’yakova, L. P., “Preserving articles made of ferrous metals, Ibid.,165,958 (26 Oct. 1964). (310K) Tkachepko, S. D., Rovinskii, E. A , , ‘‘Stirrer for mixing a hot, predominantly corrosive liquid,” (to Scientific-Research and Project-Technological Institute for the Automization and Mechanization of Machine Building, South Ural Council of h-ational Economy), Ibid., 169,497 (17 March 1965). I
,
.
~~
COR R ECTl ON Due to a publisher’s error, the following corrected derivation was not included in the paper, “Reaction Mechanisms for Engineering Design,” appearing in Vol. 58 (9), 21 (1966). The following substitution should be made between Equations 11 and 21, inclusive: If no products are initially present, the first case gives the Laplace transforms for [ B ]and [ C] as follows :
Moreover, if k 3 >> kz’, it is reasonable to suppose that F is present in undetectably small amount, and that the quasisteady-state approximation can be applied. We thus find for the intermediate F:
d[Fl = kn’[B] - k3[F] = dt
0
or
where s is the Laplace transform variable and A. is the initial concentration of A .
Then
and the concentration of the final product [C] is given by
which leads to the Laplace transform
I n the second case C(s) = S(S
+
A okikz ’k3 kd(s 4-kz’)(s
+
(1 4) k3)
Equation 14 is of different form from Equation 12, and [C] includes three exponential terms: [C] = A0
We note that Equation 1 9 is identical with Equation 12 in form, and thus the introduction of a n extra intermediate step along with the use of the quasisteady-state approximation leaves the form of [C] unaffected. The expression for [ B ]will not be affected either. I n the first case, we find
+ I n the second case,
However, if k 3 is much greater than k i and kz’, the solution for [C] reduces to Equation 13, where we take kz = kz‘. 48
INDUSTRIAL AND ENGINEERING CHEMISTRY
When kz‘ = kz, this is identical with Equation 20. Thus, only if F is directly observable, will it be possible to be sure of its kinetic significance.
