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A fatty acid is a long hydrocarbon tail that is capped with a carboxyl group (COOH). 

The hydrocarbon tail of a fatty acid can be saturated or unsaturated. A saturated hydrocarbon tail has hydrogens that fully surround every carbon atom. Thus, there are only single bonds. Every carbon atom within an unsaturated fatty acid is not fully surrounded with hydrogens. Thus, in order to fulfill the octet rule, there are double bonds between some of the carbons. 

When fatty acids combine with a glycerol, a triglyceride is formed. Triglycerides make lipids (fats). The single bonds within the saturated fatty acids cause the fatty acid to be straight. Thus, saturated fats are often solids, such as butter or lard. The double bonds within unsaturated fatty acids cause kinks. These kinks so not allow the triglycerides to reside nicely on top of one another. Thus, triglycerides containing unsaturated fatty acids are often liquids, such as oils.