Problem 78 - Chemistry: An Atoms-Focused Approach

Question

One of the ingredients in the Native American stomachache remedy derived from common chokecherry is caffeic acid. a. Combustion of 100 mg of caffeic acid yielded \(220 \mathrm{mg}\) \(\mathrm{CO}_{2}\) and \(40.3 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) Determine the empirical formula of caffeic acid. b. \(A\) solution of \(0.272 \mathrm{g}\) caffeic acid in \(10.0 \mathrm{g}\) carbon tetrachloride causes the freezing point of the solution to decrease by \(4.47^{\circ} \mathrm{C} .\) Given that \(K_{\mathrm{f}}\) for \(\mathrm{CCl}_{4}\) is \(29.8^{\circ} \mathrm{C} / \mathrm{m}\) and that caffeic acid is a nonelectrolyte, calculate the molar mass and molecular formula of caffeic acid.

Step-by-Step Solution

Answer

Short Answer: The empirical formula of caffeic acid is CH, and the molecular formula is C14H14.

Step 1: Moles of carbon and hydrogen

First, let's convert the given masses of CO2 and H2O to moles. For \(\mathrm{CO}_{2}\): \(220 \mathrm{mg} \times \frac{1 \mathrm{g}}{1000\mathrm{mg}} \times \frac{1 \mathrm{mol}}{44.01\mathrm{g}} = 0.005\mathrm{mol}\) For \(\mathrm{H}_{2}\mathrm{O}\): \(40.3 \mathrm{mg} \times \frac{1 \mathrm{g}}{1000\mathrm{mg}} \times \frac{1 \mathrm{mol}}{18.02\mathrm{g}} = 0.00224\mathrm{mol}\) Since each mole of \(\mathrm{CO}_{2}\) has one mole of carbon, and each mole of \(\mathrm{H}_{2}\mathrm{O}\) has two moles of hydrogen, we can find the moles of carbon and hydrogen in the caffeic acid. Carbon: \(0.005\mathrm{mol}\) Hydrogen: \(0.00224 \mathrm{mol} \times 2 = 0.00448\mathrm{mol}\)

Step 2: Empirical formula

To find the empirical formula, let's divide the moles of each element by the smallest value (carbon in this case) and round to the nearest whole number. For carbon: \(0.005\mathrm{mol} / 0.005\mathrm{mol} = 1\) For hydrogen: \(0.00448\mathrm{mol} / 0.005\mathrm{mol} \approx 0.9\) Since these values are close to whole numbers, the empirical formula is \(\mathrm{C}_{1}\mathrm{H}_{0.9}\), which can be rounded to \(\mathrm{CH}\).

Step 3: Molar mass from freezing point depression

We will use the given information about the freezing point depression to calculate the molar mass of caffeic acid. First, calculate the molality (mol solute/kg solvent) of the solution. Molality: \(\frac{\Delta T}{K_{\mathrm{f}}} = \frac{4.47^{\circ}\mathrm{C}}{29.8^{\circ}\mathrm{C} \cdot \mathrm{mol}^{-1}} \approx 0.150\,\mathrm{mol}\cdot\mathrm{kg}^{-1}\) Now, use the molality and mass of caffeic acid to find the molar mass. Molar mass: \(\frac{0.272\,\mathrm{g}}{0.150\,\mathrm{mol}\cdot\mathrm{kg}^{-1} \times 0.010\,\mathrm{kg}} \approx 180.7\,\mathrm{g/mol}\)

Step 4: Molecular formula

Based on the empirical formula (\(\mathrm{CH}\)) and the molar mass (180.7 g/mol), we can find the molecular formula. Empirical formula mass: \(12.01\mathrm{g/mol} + 1.008\mathrm{g/mol} = 13.018\mathrm{g/mol}\) Molecular formula multiplier: \(\frac{180.7\mathrm{g/mol}}{13.018\mathrm{g/mol}} \approx 13.88 \approx 14\) Now, multiply the empirical formula by the multiplier to get the molecular formula. Molecular formula: \(\mathrm{C}_{14}\mathrm{H}_{14}\)

Key Concepts

Caffeic Acid

Caffeic acid is a naturally occurring compound found in various plants, including the chokecherry, where it's traditionally been used as a remedy for stomachaches. This compound belongs to a class of chemicals known as phenolic acids, which possess antioxidant properties that make them beneficial in protecting cells from damage. Caffeic acid's structure includes a hydroxyl group attached to an aromatic ring, contributing to its ability to scavenge free radicals. In experiments, it is important to understand the chemical makeup of such compounds to explore their full potential and applications in health and medicine.

Combustion Analysis

Combustion analysis is a vital technique in chemistry used to determine the empirical formula of a compound, particularly ones containing carbon and hydrogen. This method involves burning the compound to produce carbon dioxide and water, which can then be precisely measured. In our exercise, the combustion of caffeic acid produced 220 mg of CO2 and 40.3 mg of H2O. By calculating the number of moles of these products, we can deduce the number of moles of carbon and hydrogen originally present in the sample. This step is key in empirically deducing the ratio of elements present within the compound.

Molecular Formula

The molecular formula represents the actual number of atoms of each element in a compound. Unlike the empirical formula, which gives the simplest ratio of elements, the molecular formula conveys the total count. To derive it from the empirical formula, one must know the compound's molar mass. From the provided information, we determined the empirical formula of caffeic acid as CH. With further experiment, we calculated its molar mass to be approximately 180.7 g/mol. By comparing this with the mass of the empirical formula unit, we deduced a multiplier, which in this case was 14. Therefore, caffeic acid's molecular formula became C14H14, showing precisely the number of carbon and hydrogen atoms present.

Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point due to the addition of a solute. In the exercise, caffeic acid dissolved in carbon tetrachloride caused the freezing point to drop by 4.47°C. This change helps us calculate the molality of the solution. For calculations, the constant for freezing point depression ( K_f ) must be known, which in this case is 29.8°C/m for CCl4. Using these parameters, we determined the molality to find the molar mass, which then allowed us to explore more properties of caffeic acid.

Molar Mass Calculation

Molar mass calculation is crucial in bridging the gap between empirical and molecular formulas. It allows one to convert measurable properties into known quantities of atoms and molecules. In determining the molar mass, the exercise utilized both a freezing point depression setup and subsequent calculations. Using the determined molality from the freezing point data and the mass of the caffeic acid dissolved, the molar mass was calculated to be approximately 180.7 g/mol. This value was essential to verifying the molecular formula, ensuring that the empirical and calculated mole ratios matched experimental observations. Molar mass calculations often serve as a final piece in understanding the full molecular structure of chemical compounds.