Question

Allyl sulfide, \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{~S}\), is the substance that gives garlic, onions, and leeks their characteristic odor. a. How many moles of sulfur are in \(23.2 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{~S}\) ? b. How many moles of hydrogen are in \(0.75\) mole of \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{~S}\) ? c. How many grams of carbon are in \(44.0 \mathrm{~g}\) of \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{~S} ?\)

Short answer

a. 0.203 moles of S, b. 7.5 moles of H, c. 27.75 grams of C.

Step-by-step solution

Calculate the molar mass of C6H10S

To find the molar mass of \(\text{C}_{6}\text{H}_{10}\text{S}\), add the atomic masses of all the atoms in the molecule. The atomic masses are approximately: C = 12.01, H = 1.01, S = 32.07. Therefore, the molar mass is calculated as follows: \[\text{Molar Mass} = 6 \times 12.01 + 10 \times 1.01 + 1 \times 32.07 = 72.06 + 10.10 + 32.07 = 114.23 \text{ grams/mole}\]

Calculate moles of C6H10S for sulfur

Using the given mass of \(\text{C}_{6}\text{H}_{10}\text{S}\) and the molar mass from Step 1, calculate the moles of \(\text{C}_{6}\text{H}_{10}\text{S}\): \[\text{Moles of } \text{C}_{6}\text{H}_{10}\text{S} = \frac{23.2 \text{ grams}}{114.23 \text{ grams/mole}} = 0.203 \text{ moles}\]

Calculate moles of sulfur in given moles of C6H10S

Since each molecule of \(\text{C}_{6}\text{H}_{10}\text{S}\) contains one sulfur atom, the number of moles of sulfur is directly equal to the number of moles of \(\text{C}_{6}\text{H}_{10}\text{S}\): \[\text{Moles of Sulfur} = 0.203 \text{ moles}\]

Calculate moles of hydrogen in 0.75 moles of C6H10S

Since each molecule of \(\text{C}_{6}\text{H}_{10}\text{S}\) contains 10 hydrogen atoms, the number of moles of hydrogen in 0.75 moles of \(\text{C}_{6}\text{H}_{10}\text{S}\) is: \[\text{Moles of Hydrogen} = 0.75 \text{ moles } \times 10 = 7.5 \text{ moles}\]

Calculate moles of C6H10S for carbon

Using the given mass of \(\text{C}_{6}\text{H}_{10}\text{S}\) and the molar mass from Step 1, calculate the moles of \(\text{C}_{6}\text{H}_{10}\text{S}\): \[\text{Moles of } \text{C}_{6}\text{H}_{10}\text{S} = \frac{44.0 \text{ grams}}{114.23 \text{ grams/mole}} = 0.385 \text{ moles}\]

Calculate grams of carbon in given moles of C6H10S

Since each molecule of \(\text{C}_{6}\text{H}_{10}\text{S}\) contains 6 carbon atoms, the moles of carbon in 0.385 moles of \(\text{C}_{6}\text{H}_{10}\text{S}\) is: \[\text{Moles of Carbon} = 0.385 \text{ moles } \times 6 = 2.31 \text{ moles}\] Then, convert moles of carbon to grams using the atomic mass of carbon: \[\text{Grams of Carbon} = 2.31 \text{ moles} \times 12.01 \text{ g/mole} = 27.75 \text{ grams}\]

Key concepts

Molar Mass Calculation

The molar mass of a compound is simply the sum of the atomic masses of each element in the compound. To find the molar mass of \(\text{C}_{6}\text{H}_{10}\text{S}\), we start by identifying the atomic masses of carbon (C), hydrogen (H), and sulfur (S):
\(\text{C} = 12.01 \, \text{H} = 1.01 \, \text{S} = 32.07\). Next, we multiply these atomic masses by the number of each atom in the molecule:
\(\text{Molar Mass} = (6 \times 12.01) + (10 \times 1.01) + (1 \times 32.07) = 72.06 + 10.10 + 32.07 = 114.23 \text{ grams/mole}\). This final value, 114.23 grams/mole, is the molar mass of \(\text{C}_{6}\text{H}_{10}\text{S}\). Calculating the molar mass is an essential step in converting between moles and grams.

Moles of an Element

Moles represent a specific quantity (6.022 \times 10^{23}\ particles) of a substance. In this exercise, we need to calculate the moles of specific elements within a given amount of compound. For example, in 23.2 grams of \(\text{C}_{6}\text{H}_{10}\text{S}\), we can find how many moles of sulfur are present.
First, we convert the mass of the compound to moles by dividing by its molar mass:
\(\text{Moles of } \text{C}_{6}\text{H}_{10}\text{S} = \frac{23.2 \text{ grams}}{114.23 \text{ grams/mole}} = 0.203 \text{ moles}\). Since each molecule of \(\text{C}_{6}\text{H}_{10}\text{S}\) contains one sulfur atom, the moles of sulfur is the same as the moles of \(\text{C}_{6}\text{H}_{10}\text{S}\): 0.203 moles.

Moles to Grams Conversion

Converting moles to grams is a common calculation in chemistry when dealing with molecular substances. For instance, if you need to find the grams of carbon in a certain amount of \(\text{C}_{6}\text{H}_{10}\text{S}\), you must first find the moles of carbon.
For 44.0 grams of \(\text{C}_{6}\text{H}_{10}\text{S}\), we start by converting the mass to moles:
\(\text{Moles of } \text{C}_{6}\text{H}_{10}\text{S} = \frac{44.0 \text{ grams}}{114.23 \text{ grams/mole}} = 0.385 \text{ moles}\). Knowing there are 6 carbon atoms per molecule, you find the moles of carbon:
\(\text{Moles of Carbon} = 0.385 \text{ moles} \times 6 = 2.31 \text{ moles}\). Finally, convert moles to grams using carbon's atomic mass:
\(\text{Grams of Carbon} = 2.31 \text{ moles} \times 12.01 \text{ g/mole} = 27.75 \text{ grams}\).

Stoichiometry

Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It involves calculations that relate the quantities of substances involved in reactions based on the balanced chemical equation.
In this exercise, we focus on the stoichiometric relationships within a single compound, \(\text{C}_{6}\text{H}_{10}\text{S}\). For instance, with 0.75 moles of \(\text{C}_{6}\text{H}_{10}\text{S}\), we learn how to find the number of moles of hydrogen it contains by multiplying it by the number of hydrogen atoms per molecule:
\(0.75 \text{ moles of } \text{C}_{6}\text{H}_{10}\text{S} \times 10 = 7.5 \text{ moles of hydrogen}\). This type of calculation is fundamental in predicting the amounts of products and reactants in more complex chemical reactions.