Fat and oil are names for the same class of compounds, called triglycerides, which contain three ester groups where $\mathrm{R}, \mathrm{R}^{\prime},$ and $\mathrm{R}^{\prime \prime}$ represent long hydrocarbon chains. (a) Suggest a reaction that leads to the formation of a triglyceride molecule, starting with glycerol and carboxylic acids (see Section 11.3 for structure of glycerol). (b) In the old days, soaps were made by hydrolyzing animal fat with lye (a sodium hydroxide solution). Write an equation for this reaction. (c) The difference between fats and oils is that at room temperature, the former are solids and the latter are liquids. Fats are usually produced by animals, whereas oils are commonly found in plants. The melting points of these substances are determined by the number of $\mathrm{C}=\mathrm{C}$ bonds (or the extent of unsaturation) present-the larger the number of $\mathrm{C}=\mathrm{C}$ bonds, the lower the melting point and the more likely that the substance is a liquid. Explain. (d) One way to convert liquid oil to solid fat is to hydrogenate the oil, a process by which some or all of the $\mathrm{C}=\mathrm{C}$ bonds are converted to $\mathrm{C}-\mathrm{C}$ bonds. This procedure prolongs shelf life of the oil by removing the more reactive $\mathrm{C}=\mathrm{C}$ group and facilitates packaging. How would you carry out such a process (that is, what reagents and catalyst would you employ)? (e) The degree of unsaturation of oil can be determined by reacting the oil with iodine, which reacts with the $\mathrm{C}=\mathrm{C}$ bond as follows: