Problem 132 - Chemistry Matter and Change

Question

Garlic Determine the molar mass of allyl sulfide, the compound responsible for the smell of garlic. The chemical formula of allyl sulfide is \(\left(\mathrm{C}_{3} \mathrm{H}_{5}\right)_{2} \mathrm{S}\) .

Step-by-Step Solution

Answer

The molar mass of allyl sulfide \((\left(\mathrm{C}_{3} \mathrm{H}_{5}\right)_{2} \mathrm{S})\) can be calculated by summing the molar masses of its constituent elements: 6 carbon atoms, 10 hydrogen atoms, and 1 sulfur atom. The molar mass of allyl sulfide is approximately \(114.23 \ g/mol\).

Step 1: Find the molar mass of Carbon (C)

First, we need to find the molar mass of carbon. From the periodic table, we know that the molar mass of carbon is approximately 12.01 g/mol.

Step 2: Find the molar mass of Hydrogen (H)

Next, we need to find the molar mass of hydrogen. From the periodic table, the molar mass of hydrogen is approximately 1.01 g/mol.

Step 3: Find the molar mass of Sulfur (S)

Lastly, we need to find the molar mass of sulfur. From the periodic table, the molar mass of sulfur is approximately 32.07 g/mol.

Step 4: Calculate the molar mass of C6H10S

Now that we have the molar mass of carbon, hydrogen, and sulfur, we will calculate the total molar mass of allyl sulfide by summing the molar masses of the constituent elements. Molar mass of C6H10S = (6 × Molar mass of C) + (10 × Molar mass of H) + (1 × Molar mass of S) = (6 × 12.01 g/mol) + (10 × 1.01 g/mol) + (1 × 32.07 g/mol) = 72.06 g/mol + 10.1 g/mol + 32.07 g/mol = 114.23 g/mol The molar mass of allyl sulfide, the compound responsible for the smell of garlic, is approximately 114.23 g/mol.

Key Concepts

Understanding Allyl Sulfide

Allyl sulfide is an organic compound known for its distinctive smell, famously recognized as the aroma of garlic. This compound plays a critical role in culinary flavors and has various uses in medicinal applications.
Identified by its chemical formula \((\mathrm{C}_{3} \mathrm{H}_{5})_{2} \mathrm{S}\), allyl sulfide is composed of three elements:

• Carbon (C)
• Hydrogen (H)
• Sulfur (S)

These elements are bonded together in specific arrangements, creating the unique structure of allyl sulfide. Understanding its composition helps in grasping how to calculate its molar mass, which is essential for various chemical calculations and applications.

Decoding the Chemical Formula

A chemical formula is a concise way of representing the atomic composition of a substance. For allyl sulfide, the formula \((\mathrm{C}_{3} \mathrm{H}_{5})_{2} \mathrm{S}\) is used. This formula tells us several important things:

• Each molecule of allyl sulfide contains two groups of \(\mathrm{C}_{3} \mathrm{H}_{5}\).
• It also includes one sulfur (S) atom.

In total, this leads to the presence of:

• 6 carbon atoms \((3 + 3)\)
• 10 hydrogen atoms \((5 + 5)\)
• 1 sulfur atom

These values are crucial when calculating the molar mass, which relies on multiplying the number of each type of atom by their respective atomic masses.

Navigating the Periodic Table

The periodic table is an essential tool in chemistry, providing vital information about each chemical element. For calculating the molar mass of allyl sulfide, it is indispensable in determining the atomic masses of its constituent elements:

• Carbon (C): Often found on the table with an atomic mass of about 12.01 g/mol.
• Hydrogen (H): With a much lighter atomic mass, commonly listed as approximately 1.01 g/mol.
• Sulfur (S): Known for its distinctive yellow color in solid form, sulfur has an atomic mass around 32.07 g/mol.

These values are used to ascertain the molar mass of allyl sulfide by combining the atomic masses according to the chemical formula’s composition.

Calculating the Mass of Elements

To find the molar mass of allyl sulfide, we perform a series of straightforward calculations. Here's how:

• Carbon: Multiply the number of carbon atoms (6) by the molar mass of carbon (12.01 g/mol): \(6 \times 12.01 = 72.06 \text{ g/mol}\).
• Hydrogen: Multiply the number of hydrogen atoms (10) by the molar mass of hydrogen (1.01 g/mol): \(10 \times 1.01 = 10.10 \text{ g/mol}\).
• Sulfur: Since there's only one sulfur atom, multiply it by the sulfur molar mass: \(1 \times 32.07 = 32.07 \text{ g/mol}\).

Adding these results: \[ 72.06 \text{ g/mol} + 10.10 \text{ g/mol} + 32.07 \text{ g/mol} = 114.23 \text{ g/mol} \]This final value represents the molar mass of allyl sulfide, providing us with a way to measure the mass of one mole of this compound.