curring a t the double bond proceeds a t a much slower rate. Other reactions like hydrolysis of glycerides and formation of sulfonic acid, lactones, lactides, and estolides also occur ( 3 ) . For the wetting out action, the ester formation is important, as this brings the hydrophilic radical -0SOzOH in the middle of the fatty acid ester chain, giving the molecule a balanced structure. Taking the formation of sulfuric ester, there are two opposing reactions: (1) formation of ester and (2) hydrolysis of ester formed by the water in the presence of excess acid. Any catalyst added should favor the ester formation. A negative catalyst will favor the hydrolysis of ester and might also promote other side reactions which would use large amounts of sulfuric acid, thus reducing the concentration of acid available or ester formation. In any case, the total yield of combined sulfur trioxide will be less than that with no additive. Analysis of results in Table I shows that during the period of reaction chosen, mercury as catalyst gives the highest yield and also highest increase in the rate of reaction-5.5% of combined sulfur trioxide being formed, compared to 3.71% with no additive, in 345 minutes. Mercurous sulfate is slightly less active and gives 5.22% of combined sulfur trioxide. About 97% of the metallic mercury and about 43% of the mercury salt used as catalysts were recoverable. The 3% of mercury not recovered might have been converted into salt during the reaction. Recovery was effected during washing of the reaction mass with water, when the
catalyst settled to the aqueous layer. Vanadium pentoxide, although initially increasing the rate of reaction, does not give a higher yield compared to the use of no additive. When copper sulfate is added, there is only a slight increase in per cent combined sulfur trioxide formed. Pyridine is used as a sulfonation aid in aromatic sulfonation reactions (6). However, in sulfation of castor oil it acts as a negative catalyst, reducing the amount of ester formed. O n analyzing the rate of formation of combined sulfur trioxide with no additive, it may be seen that this is fairly high up to 3% combined sulfur trioxide; there is negligible further formation of combined sulfur trioxide when the reaction is continued. The periods required for formation of 3% combined sulfur trioxide are taken for comparison with catalysts against no additive. Mercury increases the rate of reaction by 200% and reduces the period of formation for 391, combined sulfur trioxide by 63%. Mercurous sulfate increases the rate by 194% and reduces the period by 59.7%. Vanadium pentoxide shows a slight increase in rateLe., 116%-and copper sulfate gives only a negligible rise in rate. Pyridine acts as a negative catalyst, reducing the rate by 11% and increasing the period of formation by 29%. Table I also shows that maximum yields of per cent combined sulfur trioxide during the period of reaction chosen are obtained only in runs where mercury and mercurous sulfate are used as catalysts. I t is possible to reach with no additive a sulfur trioxide content of
5.5 to 6% by use of stronger sulfuric acid in the place of the 92% acid used in this investigation. However, the use of catalyst considerably reduces the time of sulfation and about the same amount of ester is formed with acid of lower strength. M‘ith 25% addition of acid on weight of oil, the reaction has not reached equilibrium in 345 minutes, but can be continued to get slightly higher per cent combined sulfur trioxide. The catalysts mercury, mercurous sulfate, and vanadium pentoxide can be recovered during washing of the sulfated oil with salt solution. Copper sulfate, being soluble, is lost as solution in the aqueous layer. Pyridine is miscible with the highly viscous reaction mass and is not separable. literature Cited
Bailey, A. E., “Industrial Oil and Fat Products,” p. 392, Interscience, New York, 1952. Burton, D., Byrne, E. E.. J. Soc. Leather Trades’ Chemists 37, 243 (1953). Burton, D., Robertshaw, G. F., “Sulfated Oils and Allied Products.” p. 27, A . Harvey, London, 1939. Ibid.,p. 28. Ibid., p. 90. Groggins, P. H., “Unit Processes in Organic Synthesis,” p. 310, McGraw-Hill. New York, 1952. Grun, A. D.; Woldenberg, M., J. Am. Chem. Soc. 31.496 11909). Sislev, J. P., “kncyclopedia of SurfaceActive Agents,” p. 51, Chemical Publishing Co., New York, 1952. RECFJVED for review May 9, 1957 ACCEPTEDMarch 11. 1958
CORRESPONDENCE
least Squares SIR: In the article on “Least Squares” by Chou [IND. ENG. CHEM. 50, 779 (1958)] the heat transfer data of Sieder and Tate are used to illustrate the use of statistics. These data have been treated in a similar way by W. Volk (“Applied Statistics for Engineers,” McGraw-Hill, New York, 1958). I n addition, Mr. Volk points out that in the generally accepted form of the heat transfer equation Nu
=
0.402 (Re)1/3(Pr)l/3 (,)0.142
the exponents for R e and P r are not included in the 95y0 confidence ranges. In addition he shows that the equation
1788
accounts for 93.4% of the variation in log Nu, and eliminating the P r variable 83.1% of the variation is still explained. SEYMOUR B. ALPERT Hydrocarbon Research, Inc. Princeton. N. J.
SIR: Your letter with regard to Chow’s article has come to me. D r . Chou left the country about a year ago and we have never received a n address from him, so I a m taking care of the correspondence with regard to his article. Your letter refers to a book by W. Volk. A letter came a short time ago from Mr. Volk to Dr. Chou, giving some of the same information:
INDUSTRIAL AND ENGINEERING CHEMISTRY
You might be interested to know that in my book on statistics for engineers I used the same Leverspiel et al. data to show what more could be done with confidence ranges; and, I’m glad to say, came out with numerical answers practically identical with yours. I also calculated the fraction of the variation that could be attributed to each variable. and showed the high correlation between Re and Pr for these data, which makes the P r term somewhat superfluous. From the data of your paper, it is evident that we were doing this work a t the same time.
H. C. VANNESS Rensselaer Polytechnic Institute Troy, hT.Y .
