Question

Calculate the mass percent of each element in the following compounds: (a) \(\mathrm{PbS}\), lead(II) sulfide, galena (b) \(\mathrm{C}_{3} \mathrm{H}_{8},\) propane (c) \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O},\) carvone, found in caraway seed oil

Short answer

(a) Pb: ≈86.53%, S: ≈13.42% (b) C: ≈81.68%, H: ≈18.32% (c) C: ≈79.98%, H: ≈9.41%, O: ≈10.65%

Step-by-step solution

Determine Molar Mass of PbS

To find the mass percent of each element in PbS, we first need to determine its molar mass. Lead (Pb) has an approximate atomic mass of 207.2 g/mol and sulfur (S) has an atomic mass of approximately 32.07 g/mol.Calculate the molar mass of PbS:\[\text{Molar mass of PbS} = 207.2\, \text{g/mol (Pb)} + 32.07\, \text{g/mol (S)} = 239.27\, \text{g/mol}\]

Calculate Mass Percent of Each Element in PbS

Next, use the molar mass to find the mass percent of each element.1. Mass percent of Pb:\[\text{Mass percent of Pb} = \frac{207.2}{239.27} \times 100\% \approx 86.53\%\]2. Mass percent of S:\[\text{Mass percent of S} = \frac{32.07}{239.27} \times 100\% \approx 13.42\%\]

Determine Molar Mass of C₃H₈

Now let's determine the molar mass of C₃H₈ (propane). Carbon (C) has an atomic mass of about 12.01 g/mol and hydrogen (H) has an atomic mass of approximately 1.01 g/mol.Calculate the molar mass of C₃H₈:\[\text{Molar mass of C₃H₈} = (3 \times 12.01) + (8 \times 1.01) = 44.11\, \text{g/mol}\]

Calculate Mass Percent of Each Element in C₃H₈

Now calculate the mass percent of each element in propane.1. Mass percent of C:\[\text{Mass percent of C} = \frac{36.03}{44.11} \times 100\% \approx 81.68\%\]2. Mass percent of H:\[\text{Mass percent of H} = \frac{8.08}{44.11} \times 100\% \approx 18.32\%\]

Determine Molar Mass of C₁₀H₁₄O

Finally, let's find the molar mass of C₁₀H₁₄O (carvone). Carvone contains 10 carbon atoms, 14 hydrogen atoms, and 1 oxygen atom. Oxygen (O) has an approximate atomic mass of 16.00 g/mol.Calculate the molar mass of C₁₀H₁₄O:\[\text{Molar mass of C₁₀H₁₄O} = (10 \times 12.01) + (14 \times 1.01) + 16.00 = 150.22\, \text{g/mol}\]

Calculate Mass Percent of Each Element in C₁₀H₁₄O

Calculate the mass percent of each element in carvone.1. Mass percent of C:\[\text{Mass percent of C} = \frac{120.1}{150.22} \times 100\% \approx 79.98\%\]2. Mass percent of H:\[\text{Mass percent of H} = \frac{14.14}{150.22} \times 100\% \approx 9.41\%\]3. Mass percent of O:\[\text{Mass percent of O} = \frac{16.00}{150.22} \times 100\% \approx 10.65\%\]

Key concepts

Molar Mass

The molar mass is a fundamental concept in chemistry that describes the mass of one mole of a chemical compound. It is expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule.
For example, in the case of lead(II) sulfide (\(\text{PbS}\)), we calculate the molar mass by adding together the atomic masses of lead (\(\text{Pb}: 207.2\,\text{g/mol}\)) and sulfur (\(\text{S}: 32.07\,\text{g/mol}\)).
This results in a molar mass of 239.27 g/mol for PbS.
Understanding how to find the molar mass is crucial in determining the mass percent of each element in a compound, as it provides the basis for calculating the proportion of each element relative to the entire compound.
The process is similar for other compounds, like propane and carvone, where we tally up the individual contributions from each atom in the molecules to find their respective molar masses, thus facilitating subsequent calculations of mass percent.

Chemical Compounds

Chemical compounds are substances formed by the combination of two or more different elements bonded together in fixed proportions. The types of elements and the number of each used in a compound define its unique chemical structure.
Chemical compounds can exist as simple molecules, such as water (H₂O), or more complex structures like carvone (C₁₀H₁₄O), a component of caraway seed oil.
To understand a compound, we must know the stoichiometry, which means the precise count of each type of atom. For example, propane (C₃H₈) is a compound with three carbons and eight hydrogens.
This not only helps in naming the compound but is also essential when calculating the molar mass and determining the elemental composition. The stability and reactions of a chemical compound are significantly influenced by its chemical structure, which defines the arrangement of atoms and thus its chemical behavior.

Elemental Composition

Elemental composition refers to the distribution of different elements within a chemical compound and their relative proportions. It is crucial for analyzing and understanding the compound's properties.
To calculate the mass percent of each element in a compound, you divide the mass of the specific element by the total mass of the compound and multiply by 100 to convert it to a percentage.

• For lead(II) sulfide (PbS), the mass percent of lead (Pb) is calculated as \(\frac{207.2}{239.27} \times 100\% ≈ 86.53\%\).
• The same method applies to sulfur (S), giving \(\frac{32.07}{239.27} \times 100\% ≈ 13.42\%\).

Calculating the elemental composition provides insights into the compound's makeup and is essential in applications such as synthesizing new materials, understanding biological interactions, or even in environmental assessments. Each element's contribution to the overall structure determines the compound's characteristics, and the calculation of mass percent aids in quantifying these relationships.