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How does the carbon chain length affect the polarity of an alcohol? What effect does this have on the solubility of the alcohol in a polar vs. a nonpolar solvent?

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Alchols are slightly polar molecules due to their hydroxyl group. If you increase the length of the carbon chain, you are actually increasing the nonpolar domain of the molecule. the C-H bonds that make up the carbon chain are nonpolar. Therefore, as you add more, you essentially "dilute" the polarity of the hydroxyl group and are left with a more and more nonpolar molecule, which becomes less soluble.
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