Ethyl caprate is an ester used in the manufacture of wine bouquets. It is sometimes called "cognac essence." Combustion analysis of a sample of ethyl caprate shows it to be 71.89\(\% \mathrm{C}\) , 12.13\(\%\) hydrogen, and 15.98\(\%\) O by mass. Hydrolysis (reaction with water) of the ester produces ethanol and a carboxylic acid. The molar mass of the carboxylic acid is 172 \(\mathrm{g} / \mathrm{mol}\) , and the \(\mathrm{R}\) group attached to the COOH group of the acid is a straight chain alkane. What is the structure of ethyl caprate?

In order to convert mass percentages to molar percentages, we need to use the molar masses of carbon, hydrogen, and oxygen. Divide the mass percentages by their respective molar masses: Carbon: \(\frac{71.89\%}{12.01 \text{ g/mol}} = 5.99\text{ moles}\) Hydrogen: \(\frac{12.13\%}{1.01 \text{ g/mol}} = 12.01\text{ moles}\) Oxygen: \(\frac{15.98\%}{16.00 \text{ g/mol}} = 1.00\text{ moles}\)

Now we can find the ratio of carbon, hydrogen, and oxygen in the compound. To do this, divide the number of moles of each element by the smallest number of moles: Carbon: \(\frac{5.99 \text{ moles}}{1.00 \text{ mole}} = 6\) Hydrogen: \(\frac{12.01 \text{ moles}}{1.00 \text{ mole}} = 12\) Oxygen: \(\frac{1.00 \text{ moles}}{1.00 \text{ mole}} = 1\) The empirical formula for ethyl caprate is C6H12O.

We know that the molar mass of the carboxylic acid is 172 g/mol. The empirical formula of the COOH group is CH2O2, which has a molar mass of 45 g/mol. Subtracting the molar mass of the COOH group from the total molar mass of the carboxylic acid will give us the molar mass of the R group: Molar mass of R group: 172 g/mol - 45 g/mol = 127 g/mol Since the R group is a straight chain alkane, which consists of carbon (C) and hydrogen (H2) atoms, we can determine the number of carbon atoms by dividing the molar mass of the R group by (12.01 g/mol + 2(1.01 g/mol)): Number of carbon atoms in the R group: \(\frac{127 \text{ g/mol}}{(12.01 \text{ g/mol} + 2(1.01 \text{ g/mol}))} = 10\) Therefore, the molecular formula of the carboxylic acid is C11H22O2.

We know that ethyl caprate hydrolyzes to form ethanol (C2H5OH) and the carboxylic acid with a molecular formula of C11H22O2. The ethyl group in ethyl caprate comes from the ethanol, and the carboxylic acid group comes from the carboxylic acid molecule. Thus, the structure of ethyl caprate is given by combining the molecular formulas of ethanol and the carboxylic acid without the hydroxyl (OH) group and the hydrogen atom, respectively: Ethyl caprate structure: C2H5O - C11H21O The structure of ethyl caprate is C13H26O2.