Problem 35 - Chemistry The Science in Context

Question

Calculate the molar masses of the following common flavors in food: a. vanillin, \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\). b. oil of cloves, \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\). c. anise oil, \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\). d. oil of cinnamon, \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\).

Step-by-Step Solution

Answer

Question: Calculate the molar masses of the following compounds: a. Vanillin (\(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\)) b. Oil of Cloves (\(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\)) c. Anise Oil (\(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\)) d. Oil of Cinnamon (\(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\)) Answer: a. The molar mass of Vanillin is 152.16 u. b. The molar mass of Oil of Cloves is 164.22 u. c. The molar mass of Anise Oil is 148.22 u. d. The molar mass of Oil of Cinnamon is 132.17 u.

Step 1: a. Calculation of Molar Mass of Vanillin (\(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\))

To calculate the molar mass of vanillin, we need to find the sum of the molar masses of all atoms in the formula, considering the number of each atom. The molecular formula of vanillin is \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\). Thus, the molar mass can be calculated as follows: Molar mass of vanillin = (8 x Molar mass of C) + (8 x Molar mass of H) + (3 x Molar mass of O) = (8 x 12.01 u) + (8 x 1.01 u) + (3 x 16.00 u) = 96.08 u + 8.08 u + 48.00 u = 152.16 u

Step 2: b. Calculation of Molar Mass of Oil of Cloves (\(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\))

To calculate the molar mass of oil of cloves, we need to find the sum of the molar masses of all atoms in the formula, considering the number of each atom. The molecular formula of oil of cloves is \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}_{2}\). Thus, the molar mass can be calculated as follows: Molar mass of oil of cloves = (10 x Molar mass of C) + (12 x Molar mass of H) + (2 x Molar mass of O) = (10 x 12.01 u) + (12 x 1.01 u) + (2 x 16.00 u) = 120.10 u + 12.12 u + 32.00 u = 164.22 u

Step 3: c. Calculation of Molar Mass of Anise Oil (\(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\))

To calculate the molar mass of anise oil, we need to find the sum of the molar masses of all atoms in the formula, considering the number of each atom. The molecular formula of anise oil is \(\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{O}\). Thus, the molar mass can be calculated as follows: Molar mass of anise oil = (10 x Molar mass of C) + (12 x Molar mass of H) + (1 x Molar mass of O) = (10 x 12.01 u) + (12 x 1.01 u) + (1 x 16.00 u) = 120.10 u + 12.12 u + 16.00 u = 148.22 u

Step 4: d. Calculation of Molar Mass of Oil of Cinnamon (\(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\))

To calculate the molar mass of oil of cinnamon, we need to find the sum of the molar masses of all atoms in the formula, considering the number of each atom. The molecular formula of oil of cinnamon is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\). Thus, the molar mass can be calculated as follows: Molar mass of oil of cinnamon = (9 x Molar mass of C) + (8 x Molar mass of H) + (1 x Molar mass of O) = (9 x 12.01 u) + (8 x 1.01 u) + (1 x 16.00 u) = 108.09 u + 8.08 u + 16.00 u = 132.17 u

Key Concepts

Molecular Formula

When you think about the ingredients of a chemical compound, the molecular formula is like the recipe. It tells you exactly how many atoms of each element are in a single molecule of the compound. For example, the molecular formula of vanillin is \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\). It informs us that each molecule consists of 8 carbon atoms, 8 hydrogen atoms, and 3 oxygen atoms. This formula is crucial because it lays the foundation for calculating the molar mass, a key step in understanding and working with chemical compounds.

Each element is represented by a symbol (like C for carbon, H for hydrogen, and O for oxygen), and the subscript numbers indicate the quantity of each type of atom. Understanding molecular formulas helps us recognize the basic structure of a compound and allows us to derive further details, like its molar mass.

Atomic Mass Units

Atomic mass units (AMU), often represented as 'u', serve as a convenient measure for expressing the masses of atoms and subatomic particles. The atomic mass of an element roughly equals the mass of one mole of its atoms, measured in grams. For practical purposes in chemistry, the atomic mass unit is defined such that the carbon-12 atom, \(^{12}\mathrm{C}\), has a mass of exactly 12 u.

For instance, the atomic mass of carbon is approximately 12.01 u, hydrogen is about 1.01 u, and oxygen is 16.00 u. These values are crucial when calculating the molar masses of chemical compounds. The molar mass of a compound is the sum of the atomic masses of its atoms, each multiplied by the number of times the element appears in the formula. By utilizing atomic mass units, chemists can easily compare different elements and predict how they will interact.

Chemical Compounds

Chemical compounds are substances that consist of two or more different types of atoms bonded together. These compounds can be broken down into two main categories: molecular compounds and ionic compounds, based on the nature of the bonding.

For example, vanillin is a molecular compound, composed of carbon, hydrogen, and oxygen atoms bonded covalently. The atoms in molecular compounds share electrons, creating a strong bond between them. Understanding the nature of chemical compounds helps determine their properties and reactions.

• Molecular compounds like those found in food flavors can be calculated for their molar mass by considering their molecular formulas.
• Different compounds with similar elements, like oil of cloves and anise oil, vary in the number of atoms and their arrangement but share common elements.

Investigating chemical compounds is essential for fields ranging from food chemistry to pharmaceuticals, as it aids in understanding their behavior and application.

Step by Step Calculation

Calculating the molar mass of a compound is like solving a puzzle. With the molecular formula at hand, you can find the total mass of all constituent atoms to understand more about the compound's nature. Here’s the step-by-step breakdown of how it’s done.

1. **Identify the Molecular Formula:** Start with the molecular formula of your compound, such as \(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\) for vanillin. This tells you how many of each atom you have.

2. **Determine Individual Atomic Masses:** Lookup the atomic masses from the periodic table—like carbon (12.01 u), hydrogen (1.01 u), and oxygen (16.00 u).

3. **Multiply & Sum:** Multiply each atomic mass by the number of atoms in the formula: - Carbon: \(8 \times 12.01\) - Hydrogen: \(8 \times 1.01\) - Oxygen: \(3 \times 16.00\)
4. **Add the Products:** Add these products together to get the molar mass: - \(= 96.08 + 8.08 + 48.00 = 152.16 \text{ u}\) for vanillin.

These steps give a numerical insight into the composition of chemical compounds, aiding in both academic studies and practical applications in chemistry.