Based on the analysis given in U.S. Patent No. 3,933,780 , the composition of Ivory Soap was determined to be 12.8% Lauric Acid, 7.5% Myristic Acid, 0.6% Myristoleic Acid, 21.8% Palmitic Acid, 3.7% Palmitoleic Acid, 13.6 % Stearic Acid, 31.6% Oleic Acid, 3.1% Linoleic Acid, and 5.2% Other (includes C6-C10). All these acids are as their sodium salts. The numbers are probably plus or minus 3% and vary with the species of animal rendered for tallow, and the time of year that either the tallow, or coconut oil was obtained. The mixture is optimized for cleaning. The coconut oil (cocoate) has C12-C14 sodium salts that give a good lather, but are not very good for cleaning. The tallowate is not good for lather, but is very good for soil removal. The acids are shown in their cis form. There can be some isomerization to trans, during processing. The ivory soap bar may also contain some glycerin, sodium chloride, and water. Taken as a whole, the average molecular weight of the sodium salts is 281 grams/mole. A wikipedia article discusses fatty acids. http://en.wikipedia.org/wiki/Fatty_acids . A table of the GLC analysis and chemical structures of the fatty acids found in Ivory Soap (reg. trademark) are illustrated below:
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