Question

Calculate the mass percent of each element in the following compounds: (a) 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: 86.64%, S: 13.36%; (b) C: 81.71%, H: 18.29%; (c) C: 79.98%, H: 9.40%, O: 10.65%

Step-by-step solution

Determine Molar Mass of PbS

The molar mass of a compound is the sum of the atomic masses of its elements. For PbS, the atomic mass of Pb (lead) is approximately 207.2 g/mol and that of S (sulfur) is approximately 32.07 g/mol. Therefore, the molar mass of PbS is calculated as follows:\[\text{Molar mass of PbS} = 207.2 + 32.07 = 239.27 \, \text{g/mol}\]

Calculate Mass Percent in PbS

To calculate the mass percent of each element, divide the atomic mass of the element by the molar mass of the compound, then multiply by 100.- Mass percent of Pb:\[\text{Mass percent of Pb} = \left(\frac{207.2}{239.27}\right) \times 100 \approx 86.64\%\]- Mass percent of S:\[\text{Mass percent of S} = \left(\frac{32.07}{239.27}\right) \times 100 \approx 13.36\%\]

Determine Molar Mass of C3H8

The atomic masses are approximately: C (carbon) = 12.01 g/mol, H (hydrogen) = 1.008 g/mol. Calculate the molar mass as follows:\[\text{Molar mass of } \text{C}_3\text{H}_8 = 3 \times 12.01 + 8 \times 1.008 = 44.094 \, \text{g/mol}\]

Calculate Mass Percent in C3H8

Use the molar mass to find the mass percent of each element.- Mass percent of C:\[\text{Mass percent of C} = \left(\frac{36.03}{44.094}\right) \times 100 \approx 81.71\%\]- Mass percent of H:\[\text{Mass percent of H} = \left(\frac{8.064}{44.094}\right) \times 100 \approx 18.29\%\]

Determine Molar Mass of C10H14O

Using atomic masses: C = 12.01 g/mol, H = 1.008 g/mol, O = 16.00 g/mol. Calculate the molar mass:\[\text{Molar mass of } \text{C}_{10}\text{H}_{14}\text{O} = 10 \times 12.01 + 14 \times 1.008 + 16.00 = 150.22 \, \text{g/mol}\]

Calculate Mass Percent in C10H14O

Calculate each element's mass percent:- Mass percent of C:\[\text{Mass percent of C} = \left(\frac{120.1}{150.22}\right) \times 100 \approx 79.98\%\]- Mass percent of H:\[\text{Mass percent of H} = \left(\frac{14.112}{150.22}\right) \times 100 \approx 9.40\%\]- Mass percent of O:\[\text{Mass percent of O} = \left(\frac{16.00}{150.22}\right) \times 100 \approx 10.65\%\]

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry. It's the weight of one mole of a given substance. To find the molar mass of a compound, sum up the atomic masses of all the atoms present in that compound. For a compound like PbS, you take the atomic mass of lead (Pb) and add it to the atomic mass of sulfur (S). This value is typically expressed in grams per mole (g/mol). Calculating the molar mass helps us understand how much one mole of a compound weighs and is crucial for calculating mass percent. In our original exercise, we learned that the molar mass of PbS is 239.27 g/mol, derived from adding the atomic masses of Pb (207.2 g/mol) and S (32.07 g/mol).

• Lead (Pb): 207.2 g/mol
• Sulfur (S): 32.07 g/mol

This combines to give us a complete molar mass for the compound PbS.

Elemental Composition

Elemental composition refers to the relative amounts of each element within a compound. It's essentially what percentage of the entire compound is made up of each element. This is calculated by dividing the atomic mass contribution of each specific element by the total molar mass of the compound and then multiplying by 100 to get a percentage value. Understanding elemental composition helps you see what your compound is mostly made of. For example, if you have a compound where one element constitutes 90% of the total mass, you'll know that element dominates the molecular structure.

• In PbS, lead makes up about 86.64% of the compound.
• Sulfur accounts for roughly 13.36% of PbS.

Grasping elemental composition is crucial when comparing different compounds or when considering chemical reactions, as it allows you to understand the balance and significance of the elements involved.

Chemical Compound Analysis

Chemical compound analysis involves breaking down the structure and composition of a chemical compound. This process can include identifying which elements are present, what quantities of each are contained within the compound, and determining the molar mass. Such analysis is fundamental in various fields like pharmacology, materials science, and environmental science. By analyzing compounds chemically, scientists can predict how they might react with others, their stability, and their potential uses. In our case study of calculating mass percent, chemical compound analysis helps in:

• Understanding the proportion of elements, such as lead and sulfur in PbS.
• Determining the utility and application of a compound based on its elemental makeup.
• Comparing properties, like mass percent, across different compounds such as propane and carvone.

By mastering chemical compound analysis, students and chemists can gauge the reactivity, usage, and even environmental impact of different compounds they encounter.