PHYSICAL PKOPEKTIES? OF FATTY ACIDS 91 



though the product of these measurements muUiphed by the sine /3 (angle 

 of incHnation) does give a constant. The relationship of these vahies in 

 laurie and stearic acids, as well as in unsaturated and substituted fatty 

 acids and in a hydrocarbon, ^^^ is sho\vn in Table 30. 



The chains of stearic acid molecules are so oriented that the carboxyl 

 groups are in juxtaposition. This causes each layer or sheet to consist of 

 two layers of molecules. The thickness of the sheets is correspondingly 

 increased over that of the aliphatic hydrocarbons, which are packed regu- 

 larly with the chain axes parallel in flat sheets a single molecule in thick- 

 ness. The methyl estei's of the fatty acids behave in a manner similar to 

 that of the fatty acids; however, in the case of the ethyl esters, the layer 

 is only a single molecule in thickness. 



The values measured by the x-ray photograph are the perpendicular 

 distances between the planes. In the case of the fatt,y acids, this space ap- 

 proximates that of two fatty acid molecules, although it is somewhat less 

 than this value. ^^'* The plane length in the case of the stearic acid mole- 

 cule is readih^ calculated from the expression 2/ sin /S, where / is the length 

 of one stearic acid molecule and j8 is the angle between the c axis and the ac 

 axis (Fig. 18). 



Another interesting fact on the arrangement of the carbon atoms in a 

 single fatty acid molecule can be gleaned from the x-ray measurements. 

 If one assumes that the distance between adjacent carbon atoms is 1.54 A., 

 as will occur when the carbon atoms ai'e arranged in a zigzag chain, and also 

 that the corresponding tetrahedral angles on the carbon valences are 

 109°28', then the distance between the alternate carbon atoms is cal- 

 culated as 2.52 A. This is in excellent agreement with the figure arrived 

 at from the measurement of the c axis of n-nonacosane ; the latter has been 

 shown to be at 2.54 A. These relationships are illustrated in Figure 19. 



Fig. 19. A diagrammatic representation of the zigzag arrange- 

 ment of the carbon atoms of aliphatic acids. ^ 



Malkin^^^ has suggested that this zigzag arrangement of the carbon 

 atoms accounts for the phenomenon of alternation of properties in long- 

 chain aliphatic compounds which possess odd- and even-numbered carbon 

 atoms. In the even-numbered carbon molecules, the end groups are 



3" S. B. Hendricks, Cheyn. Revs., 7, 431-477 (1930). 

 "^ S. H. Piper, J. Soc. Chem. Ind., 56, 61-66T (1937). 

 ^^ T. Malkin, 'Nature, 127, 126-127 (1931). 



