Problem 83 - Chemistry: An Atoms-Focused Approach

Question

Flavors 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

Answer: a. Molar mass of Vanillin = 152.16 g/mol; b. Molar mass of Oil of Cloves = 164.22 g/mol; c. Molar mass of Anise Oil = 148.22 g/mol; d. Molar mass of Oil of Cinnamon = 132.17 g/mol.

Step 1: Identify the elements present

In this molecule, we have Carbon (C), Hydrogen (H), and Oxygen (O).

Step 2: Find the mass of each element

Using the periodic table, we find the atomic mass of each element: Carbon (C) = 12.01 u, Hydrogen (H) = 1.01 u, Oxygen (O) = 16.00 u.

Step 3: Calculate the molar mass

To find the molar mass, we multiply the atomic mass of each element by its count in the molecule and sum these values: Molar mass of Vanillin = (8 × 12.01) + (8 × 1.01) + (3 × 16.00) = 96.08 + 8.08 + 48.00 = 152.16 g/mol - Oil of Cloves, C10H12O2:

Step 1: Identify the elements present

In this molecule, we have Carbon (C), Hydrogen (H), and Oxygen (O).

Step 2: Find the mass of each element

Using the periodic table, we find the atomic mass of each element: Carbon (C) = 12.01 u, Hydrogen (H) = 1.01 u, Oxygen (O) = 16.00 u.

Step 3: Calculate the molar mass

To find the molar mass, we multiply the atomic mass of each element by its count in the molecule and sum these values: Molar mass of Oil of Cloves = (10 × 12.01) + (12 × 1.01) + (2 × 16.00) = 120.10 + 12.12 + 32.00 = 164.22 g/mol - Anise Oil, C10H12O:

Step 1: Identify the elements present

In this molecule, we have Carbon (C), Hydrogen (H), and Oxygen (O).

Step 2: Find the mass of each element

Using the periodic table, we find the atomic mass of each element: Carbon (C) = 12.01 u, Hydrogen (H) = 1.01 u, Oxygen (O) = 16.00 u.

Step 3: Calculate the molar mass

To find the molar mass, we multiply the atomic mass of each element by its count in the molecule and sum these values: Molar mass of Anise Oil = (10 × 12.01) + (12 × 1.01) + (1 × 16.00) = 120.10 + 12.12 + 16.00 = 148.22 g/mol - Oil of Cinnamon, C9H8O:

Step 1: Identify the elements present

In this molecule, we have Carbon (C), Hydrogen (H), and Oxygen (O).

Step 2: Find the mass of each element

Using the periodic table, we find the atomic mass of each element: Carbon (C) = 12.01 u, Hydrogen (H) = 1.01 u, Oxygen (O) = 16.00 u.

Step 3: Calculate the molar mass

To find the molar mass, we multiply the atomic mass of each element by its count in the molecule and sum these values: Molar mass of Oil of Cinnamon = (9 × 12.01) + (8 × 1.01) + (1 × 16.00) = 108.09 + 8.08 + 16.00 = 132.17 g/mol Final results: a. Molar mass of Vanillin = 152.16 g/mol b. Molar mass of Oil of Cloves = 164.22 g/mol c. Molar mass of Anise Oil = 148.22 g/mol d. Molar mass of Oil of Cinnamon = 132.17 g/mol

Key Concepts

Chemical Compounds

Chemical compounds are substances formed by the combination of two or more different types of atoms. These compounds have unique properties that distinguish them from their elemental components.
For example, vanillin is made up of carbon, hydrogen, and oxygen atoms. These elements bond together in specific ratios to form the compound's unique structure and properties.

• Types of Bonds: Atoms in compounds are held together by chemical bonds. These can be covalent bonds, where atoms share electrons, or ionic bonds, where atoms transfer electrons.
• Formula Representation: Compounds are represented by chemical formulas that display the elements and their quantities, such as \(\mathrm{C}_8\mathrm{H}_8\mathrm{O}_3\) for vanillin.
• Properties: Chemical compounds have unique boiling points, melting points, flavors, and other properties that differ from their constituent elements.

Atomic Mass

Atomic mass is a crucial concept in understanding how to calculate the mass of chemical compounds. It is the mass of an individual atom, often measured in unified atomic mass units (u).
For accurate molar mass calculation, knowing the atomic mass of each element is essential.

• Individual Atomic Mass: Each element's atomic mass can be found on the periodic table. For example, carbon has an atomic mass of 12.01 u, hydrogen is 1.01 u, and oxygen is 16.00 u.
• Use in Molar Mass Calculation: The atomic mass is used to determine the molar mass by multiplying the atomic mass of each element by its quantity in the compound.
• Molar Mass Formula: For vanillin, \((8 \times 12.01) + (8 \times 1.01) + (3 \times 16.00)\)], the calculation results in 152.16 g/mol.

Periodic Table

The periodic table is an essential tool for chemists. It organizes all known chemical elements based on their properties and atomic number.
This organization helps in understanding elements and calculating molar masses effectively.

• Element Information: The periodic table provides vital information such as atomic mass, atomic number, and symbol for each element.
• Trend Analysis: Elements are arranged in a way that reveals periodic trends in properties like electronegativity, ionization energy, and atomic radii.
• Applications in Chemistry: With the periodic table, chemists can predict elemental behavior in reactions and accurately determine the molar masses of compounds.

Flavors in Chemistry

Flavors in chemistry refer to the unique tastes and aromas provided by chemical compounds, especially those found in food and spices.
Such compounds as vanillin, oil of cloves, anise oil, and oil of cinnamon contribute distinct flavors.

• Vanillin: Commonly used for vanilla flavoring, its structure determines its aromatic characteristics.
• Oil of Cloves: Known for its spicy aroma, it's used in both cooking and medicine.
• Anise Oil and Oil of Cinnamon: These provide licorice and sweet-spicy flavors respectively, adding complexity to culinary creations.
• Importance: Understanding the molar mass of these compounds can assist in quality control and flavor formulation in the food industry.