Chapter 3: Problem 41
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
Expert verified
(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 by step solution
01
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.
02
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: \( \frac{207.2}{239.27} \times 100 \approx 86.61\% \).
03
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: \( \frac{32.07}{239.27} \times 100 \approx 13.39\% \).
04
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.
05
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: \( \frac{36.03}{44.11} \times 100 \approx 81.68\% \).
06
Calculate Mass Percent of Hydrogen in Propane
Calculate the mass percent of hydrogen in C3H8: \( \frac{8.08}{44.11} \times 100 \approx 18.32\% \).
07
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.
08
Calculate Mass Percent of Carbon in Carvone
Calculate: \( \frac{120.1}{150.24} \times 100 \approx 79.95\% \).
09
Calculate Mass Percent of Hydrogen in Carvone
Calculate: \( \frac{14.14}{150.24} \times 100 \approx 9.41\% \).
10
Calculate Mass Percent of Oxygen in Carvone
Finally, calculate: \( \frac{16.00}{150.24} \times 100 \approx 10.64\% \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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.
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.
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:
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.
To find the mass percent of an element, use the formula:
- \( \frac{\text{mass of the element in 1 mole of the compound}}{\text{molar mass of the compound}} \times 100 \)
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.