Problem 41 - Chemistry and Chemical Reactivity

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

Step-by-Step Solution

Answer

(a) Pb: 86.61%, S: 13.39%; (b) C: 81.68%, H: 18.32%; (c) C: 79.95%, H: 9.41%, O: 10.64%

Step 1: Calculate the Molar Mass of PbS

The molar masses of lead (Pb) and sulfur (S) are 207.2 g/mol and 32.07 g/mol, respectively. Thus, the molar mass of PbS is calculated as follows: \( 207.2 + 32.07 = 239.27 \) g/mol.

Step 2: Calculate Mass Percent of Lead in PbS

The mass percent of lead in PbS is calculated by the formula: \( \frac{\text{mass of Pb}}{\text{molar mass of PbS}} \times 100\). Substituting the values gives: \( \frac{207.2}{239.27} \times 100 \approx 86.61\% \).

Step 3: Calculate Mass Percent of Sulfur in PbS

Calculate the mass percent of sulfur by: \( \frac{\text{mass of S}}{\text{molar mass of PbS}} \times 100 \). This yields: \( \frac{32.07}{239.27} \times 100 \approx 13.39\% \).

Step 4: Calculate the Molar Mass of Propane (C3H8)

The molar mass of carbon (C) is 12.01 g/mol and that of hydrogen (H) is 1.01 g/mol. The molar mass of propane is: \( 3 \times 12.01 + 8 \times 1.01 = 44.11 \) g/mol.

Step 5: Calculate Mass Percent of Carbon in Propane

Calculate using the formula: \( \frac{\text{mass of 3} C}{\text{molar mass of C3H8}} \times 100 \). This results in: \( \frac{36.03}{44.11} \times 100 \approx 81.68\% \).

Step 6: Calculate Mass Percent of Hydrogen in Propane

Calculate the mass percent of hydrogen in C3H8: \( \frac{8.08}{44.11} \times 100 \approx 18.32\% \).

Step 7: Calculate the Molar Mass of Carvone (C10H14O)

The molar masses are 12.01 g/mol for carbon, 1.01 g/mol for hydrogen, and 16.00 g/mol for oxygen. Therefore, \( 10 \times 12.01 + 14 \times 1.01 + 1 \times 16.00 = 150.24 \) g/mol.

Step 8: Calculate Mass Percent of Carbon in Carvone

Calculate: \( \frac{120.1}{150.24} \times 100 \approx 79.95\% \).

Step 9: Calculate Mass Percent of Hydrogen in Carvone

Calculate: \( \frac{14.14}{150.24} \times 100 \approx 9.41\% \).

Step 10: Calculate Mass Percent of Oxygen in Carvone

Finally, calculate: \( \frac{16.00}{150.24} \times 100 \approx 10.64\% \).

Key Concepts

Understanding Molar Mass Calculation

To determine the mass percent composition of a compound, we first need to calculate its molar mass. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). It's calculated by summing the average atomic masses of all the atoms in a molecule.

Let's consider the example of lead(II) sulfide (PbS). The molar masses of lead and sulfur are 207.2 g/mol and 32.07 g/mol, respectively. When combined to form PbS, the molar mass is the sum: \(207.2 + 32.07 = 239.27\) g/mol.

Now, let's look at propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\). The molar mass of carbon (C) is 12.01 g/mol and hydrogen (H) is 1.01 g/mol. The molar mass of propane is \(3 \times 12.01 + 8 \times 1.01 = 44.11\) g/mol.

For carvone, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O}\), the molar masses are as follows: 12.01 g/mol for carbon, 1.01 g/mol for hydrogen, and 16.00 g/mol for oxygen. The final molar mass comes out to \(10 \times 12.01 + 14 \times 1.01 + 1 \times 16.00 = 150.24\) g/mol. Calculating the molar mass is the first vital step towards understanding a compound's composition.

Breaking Down Chemical Composition

Chemical composition tells us what elements and how much of each element are present in a compound. It's important in determining how a compound behaves in chemical reactions and its properties.

In lead(II) sulfide (PbS), for example, the composition involves lead and sulfur. For propane (\(\mathrm{C}_{3} \mathrm{H}_{8}\)), the compound is made of carbon and hydrogen atoms. In carvone (\(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O}\)), carbon, hydrogen, and oxygen are present. Each compound has a unique composition that defines its characteristics.

Knowing the chemical composition allows chemists to predict how substances will interact and change. It provides the foundation for the calculation of mass percent, a great way to express the concentration of each element in a compound. For example, in propane, if carbon makes up \(81.68\%\) of the mass, then this indicates the compound's characteristics very much depend on carbon's properties.

Elemental Analysis Unpacked

Elemental analysis is a crucial technique for determining the elemental composition of a compound. By performing this analysis, one calculates the mass percent of each element - a measure often needed in chemistry to understand a material's makeup.

To find the mass percent of an element, use the formula:

• \( \frac{\text{mass of the element in 1 mole of the compound}}{\text{molar mass of the compound}} \times 100 \)

This formula allows chemists to count each element's contribution to the total mass of the compound.

For instance, in PbS, the mass percent of lead is calculated as \(\frac{207.2}{239.27} \times 100 \approx 86.61\%\) whereas sulfur contributes \(\frac{32.07}{239.27} \times 100 \approx 13.39\%\). In carvone, the mass percent calculation reveals carbon as a major component at approximately \(79.95\%\) with oxygen making up \(10.64\%\).

Elemental analysis, therefore, highlights the precise contributions of each element within a compound, enabling a deeper understanding of its chemical nature. This is particularly useful for compound identification, quality control, and research purposes.