Problem 30 - Chemistry: Principles and Reactions

Question

Calculate the mass in grams of \(13.5 \mathrm{~mol}\) of (a) vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), the starting material for a plastic. (b) capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\), the substance that makes red chili peppers "hot." (c) stearic acid, \(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\), used in soaps.

Step-by-Step Solution

Answer

The mass in grams of 13.5 moles of: (a) Vinyl Chloride (C2H3Cl) is 843.75 g. (b) Capsaicin (C18H27NO3) is 4123.71 g. (c) Stearic Acid (C18H36O2) is 3841.29 g.

Step 1: Finding the Molar Mass of Vinyl Chloride (C2H3Cl)

To find the molar mass of Vinyl Chloride, we need to know the atomic mass of each atom in the compound. Using the periodic table, we find that: - Carbon (C) has an atomic mass of 12.01 g/mol - Hydrogen (H) has an atomic mass of 1.01 g/mol - Chlorine (Cl) has an atomic mass of 35.45 g/mol Now, we can calculate the molar mass of Vinyl Chloride: Molar mass = (2 × 12.01) + (3 × 1.01) + (1 × 35.45) = 24.02 + 3.03 + 35.45 = 62.50 g/mol

Step 2: Mass of 13.5 mol Vinyl Chloride

Using the molar mass of Vinyl Chloride (62.50 g/mol) and the given amount of moles (13.5 mol), we can calculate the mass in grams: Mass = (13.5 mol) × (62.50 g/mol) = 843.75 g

Step 3: Finding the Molar Mass of Capsaicin (C18H27NO3)

To find the molar mass of Capsaicin, we need to know the atomic mass of each atom in the compound. Using the periodic table, we find that: - Nitrogen (N) has an atomic mass of 14.01 g/mol - Oxygen (O) has an atomic mass of 16.00 g/mol Now, we can calculate the molar mass of Capsaicin: Molar mass = (18 × 12.01) + (27 × 1.01) + (1 × 14.01) + (3 × 16.00) = 216.18 + 27.27 + 14.01 + 48.00 = 305.46 g/mol

Step 4: Mass of 13.5 mol Capsaicin

Using the molar mass of Capsaicin (305.46 g/mol) and the given amount of moles (13.5 mol), we can calculate the mass in grams: Mass = (13.5 mol) × (305.46 g/mol) = 4123.71 g

Step 5: Finding the Molar Mass of Stearic Acid (C18H36O2)

To find the molar mass of Stearic Acid, we can use the atomic masses we found earlier and calculate the molar mass: Molar mass = (18 × 12.01) + (36 × 1.01) + (2 × 16.00) = 216.18 + 36.36 + 32.00 = 284.54 g/mol

Step 6: Mass of 13.5 mol Stearic Acid

Using the molar mass of Stearic Acid (284.54 g/mol) and the given amount of moles (13.5 mol), we can calculate the mass in grams: Mass = (13.5 mol) × (284.54 g/mol) = 3841.29 g In conclusion, the mass in grams of \(13.5 \mathrm{~mol}\) of: (a) Vinyl Chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), is \(843.75 \mathrm{~g}\). (b) Capsaicin, \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\), is \(4123.71 \mathrm{~g}\). (c) Stearic Acid, \(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\), is \(3841.29 \mathrm{~g}\).

Key Concepts

Vinyl Chloride

Vinyl chloride is an important chemical compound used widely in the production of polyvinyl chloride (PVC), which is a common plastic material. Understanding the molar mass of vinyl chloride is crucial for practical applications in chemistry and industry. Vinyl chloride has the chemical formula \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\). Here's how to calculate its molar mass:

• Carbon (C) has an atomic mass of 12.01 g/mol.
• Hydrogen (H) has an atomic mass of 1.01 g/mol.
• Chlorine (Cl) has an atomic mass of 35.45 g/mol.

To find the molar mass of vinyl chloride:
\[(2 \times 12.01) + (3 \times 1.01) + (1 \times 35.45) = 24.02 + 3.03 + 35.45 = 62.50 \text{ g/mol}.\]Having a clear understanding of the molar mass helps in converting between moles and grams, crucial for practical lab work. It allows chemists to easily know how much of a substance is needed or used in a chemical reaction based on its moles.

Capsaicin

Capsaicin is the chemical compound that gives chili peppers their distinctive heat. From a chemistry perspective, it's known by its molecular formula \(\mathrm{C}_{18} \mathrm{H}_{27} \mathrm{NO}_{3}\). Determining the molar mass of capsaicin is key for studying its properties and effects in various applications.

To compute the molar mass of capsaicin, we use these atomic masses:

• Carbon (C): 12.01 g/mol
• Hydrogen (H): 1.01 g/mol
• Nitrogen (N): 14.01 g/mol
• Oxygen (O): 16.00 g/mol

Now calculate the molar mass:
\[(18 \times 12.01) + (27 \times 1.01) + (1 \times 14.01) + (3 \times 16.00) = 216.18 + 27.27 + 14.01 + 48.00 = 305.46 \text{ g/mol}.\]Knowing the molar mass of capsaicin is useful for biochemists and food scientists who are interested in the effects and applications of this compound in food, medicine, and even pest control.

Stearic Acid

Stearic acid is a significant component found in various products ranging from cosmetics to candles and even soaps. It has the molecular formula \(\mathrm{C}_{18} \mathrm{H}_{36} \mathrm{O}_{2}\). Calculating the molar mass of stearic acid is essential for understanding its role and behavior in chemical reactions and product formulations. Here's how to find its molar mass:

Using previously noted atomic masses, we perform the following calculation:\[(18 \times 12.01) + (36 \times 1.01) + (2 \times 16.00) = 216.18 + 36.36 + 32.00 = 284.54 \text{ g/mol}.\]Understanding the molar mass allows manufacturers and chemists to create and optimize products with precise chemical compositions, ensuring consistency and quality.

Moles to Grams Conversion

Conversion between moles and grams is a fundamental skill in chemistry, rooted in the concept of molar mass. This conversion is indispensable for translating chemical equations into real-world applications. Let's break down how to convert moles to grams using vinyl chloride as an example:

Given:

• Moles of vinyl chloride = 13.5 mol
• Molar mass = 62.50 g/mol

To find the mass in grams, we use the formula:\[\text{Mass in grams} = \text{Moles} \times \text{Molar Mass}\]Plug in the values:\[(13.5 \text{ mol}) \times (62.50 \text{ g/mol}) = 843.75 \text{ g}\]This approach applies to any compound; just plug in the respective molar mass and moles involved. Whether you are in a lab or engaged in industrial production, mastering this conversion is vital for ensuring precision and accuracy in chemical measurements.