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Here it says that the hydrocarbon tail is non-polar. I understand that the $\ce{H}$ on top of the $\ce{C}$ and on the bottom have dipoles that cancel, but at the very end, with the $\ce{CH3}$ group, there is no opposing vector to cancel with that dipole. Why then is the hydrocarbon tail still non-polar?

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    $\begingroup$ This is a 3-dimensional structure - so the dipoles do NOT cancel anywhere... Rather, the dipoles created by C and H are weak, as the electronegativity difference is low - which is considered unpolar. $\endgroup$ – Gerhard Apr 19 '15 at 4:02
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The hydrocarbon tail is considered nonpolar mainly due to

  1. The Pauling electronegativity of Carbon is 2.55 and Hydrogen is 2.2. Due to the small difference, .35, and the definition of a polar bond, C-H bonds are considered nonpolar.

Indeed, the molecule methane, $\ce{CH4}$ has a dipole moment of 0 D (debyes). I think part of your confusion arises from the picture you provided. Skeletal drawings are 2-d in nature and do not convey information about 3-d. For instance, each carbon has it's hydrogens arranged in a tetrahedral structure, with bond angles 109.5 degrees. The symmetry of this cancels all the vectors contributing to polarity.

enter image description here

If you look at the picture of methane above, and consider the top most hydrogen as the next carbon in the hydrocarbon tail, you can see that in reality, the bottom 3 hydrogens do experience a net dipole moment towards the carbon, and this increased by having another carbon further up in the tail. Relatively speaking, this distance is rather large from carbon 1 to carbon 2. We can say that the vector that arises from this is negligible, and indeed, there is a net dipole moment anyways towards the oxygen at the polar head.

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    $\begingroup$ methane is CH4. Did you mean methyl? $\endgroup$ – pikachu Apr 19 '15 at 5:59
  • $\begingroup$ @pikachu Oh, thanks for pointing that out. Edited. $\endgroup$ – Jun-Goo Kwak Apr 19 '15 at 15:03
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The hydrocarbon that you have depicted (decanoic acid) does indeed have a polar head and a non-polar head, though it is not apparent in the form it is presented to you in. When viewing decanoic acid as a 3-dimensional, ball-and-stick model, it becomes more obvious:

decanoic acid

The hydrogen on C-10 of this chain that sticks out in the plane of the rest of the carbon chain is balanced by C-9. Most importantly, it should be noted that there are no unbonded electron pairs in this region. Because the electron density along the chain remains consistent, the carbon chain is non-polar.

Each of the two oxygens in the carboxylic acid groups have two electron clouds that give these regions around the molecule a negative charge. The space around the hydrogen bonded to oxygen, and the space around C-1 that is oriented away from the oxygens are both more positive. These opposing charges result in the polarity of the carboxylic acid group.

Source: http://upload.wikimedia.org/wikipedia/commons/9/98/Decanoic-acid-3D-balls.png

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