Understanding the chemical structure for saturated and unsaturated (cis and trans) fatty acids. A "fat molecule" is also called a "triglyceride" or "triacylglyceride." Fatty acids have a polar carboxylic acid "head" and a non-polar hydrocarbon "tail." Overall, a molecule with a large hydrocarbon chain is more soluble in fatsoilshydrocarbons (ie. nonpolar solvents). In general, we use the phrase "like dissolves like" to predict the solubility of a compound in a polar or non-polar solvent. A molecule with a very short hydrocarbon chain (vinegaracetic acid) is more soluble in water; the polar carboxylic acid functional group "wins". The hypothetical fat molecule that I showed is called a "triglyceride" because the glycerol is esterified with 3 fatty acids.
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