Problem 140 - Introductory Chemistry Atoms First

Question

Determine the mass percent of each element in aluminum sulfate.

Step-by-Step Solution

Answer

The mass percent of each element in aluminum sulfate (Al₂(SO₄)₃) is: Aluminum (Al): 15.77%, Sulfur (S): 28.10%, and Oxygen (O): 56.13%.

Step 1: Find the chemical formula of aluminum sulfate

The chemical formula of aluminum sulfate is Al₂(SO₄)₃.

Step 2: Calculate the molar mass of aluminum sulfate

To do this, first find the atomic masses of each element present in the formula, and then multiply their atomic masses by the number of atoms. Add these values together for the total molar mass. - Aluminum (Al): 26.98 g/mol - Sulfur (S): 32.06 g/mol - Oxygen (O): 16.00 g/mol Molar mass of aluminum sulfate: = 2 * 26.98 (Al) + 3 * (4 * 16.00 (O) + 32.06 (S)) = 2 * 26.98 + 3 * (64 + 32.06) = 53.96 + 3 * 96.06 = 53.96 + 288.18 = 342.14 g/mol

Step 3: Calculate the mass percent of each element

Now, divide the mass of each element in one mole of aluminum sulfate by the molar mass of aluminum sulfate and multiply by 100%. 1. Mass percent of aluminum (Al): = (53.96 g/mol (Al) / 342.14 g/mol (Al₂(SO₄)₃)) * 100% = (0.1577) * 100% = 15.77% 2. Mass percent of sulfur (S): = (3 * 32.06 g/mol (S) / 342.14 g/mol (Al₂(SO₄)₃)) * 100% = (96.18 g/mol (S) / 342.14 g/mol) * 100% = (0.2810) * 100% = 28.10% 3. Mass percent of oxygen (O): = (12 * 16.00 g/mol (O) / 342.14 g/mol (Al₂(SO₄)₃)) * 100% = (192.00 g/mol (O) / 342.14 g/mol) * 100% = (0.5613) * 100% = 56.13%

Step 4: Final Answer

The mass percent of each element in aluminum sulfate is: - Aluminum (Al): 15.77% - Sulfur (S): 28.10% - Oxygen (O): 56.13%.

Key Concepts

Aluminum Sulfate

Aluminum sulfate is a useful chemical compound commonly used in various industrial applications. It holds a chemical formula of \( \text{Al}_2(\text{SO}_4)_3 \). This indicates that each molecule of aluminum sulfate is composed of:

• 2 atoms of aluminum (\( \text{Al} \))
• 3 sulfate ions (\( \text{SO}_4 \)).

Within each sulfate ion, there are 4 oxygen atoms bonded to 1 sulfur atom. This configuration is essential for understanding how to calculate further properties like molar mass.

Molar Mass

The molar mass of a compound gives the weight of one mole of that compound. To find the molar mass of aluminum sulfate, for example, you need to sum up the individual atomic masses of all the atoms in its chemical formula: \( \text{Al}_2(\text{SO}_4)_3 \). The calculations include:

• 2 aluminum atoms: \( 2 \times 26.98 \text{ g/mol} = 53.96 \text{ g/mol} \)
• 3 sulfur atoms: \( 3 \times 32.06 \text{ g/mol} = 96.18 \text{ g/mol} \)
• 12 oxygen atoms: \( 12 \times 16.00 \text{ g/mol} = 192.00 \text{ g/mol} \)

Together, their combined molar mass becomes \( 342.14 \text{ g/mol} \). This total helps assess how much of each element contributes to the compound's overall mass.

Atomic Mass

Atomic mass represents the mass of individual atoms of an element, generally expressed in atomic mass units (amu) or grams per mole (g/mol). Each element in aluminum sulfate has its atomic mass:

• Aluminum (\(\text{Al}\)): 26.98 g/mol
• Sulfur (\(\text{S}\)): 32.06 g/mol
• Oxygen (\(\text{O}\)): 16.00 g/mol

These values are crucial when you calculate the molar mass, providing the essential weights for each element in a simple and standard format. Empirical data gathered via experiments informs these atomic masses, allowing them to be reliable and widely used benchmarks.

Chemical Formula

A chemical formula indicates the specific numbers and types of atoms in a given compound. For aluminum sulfate, the chemical formula \( \text{Al}_2(\text{SO}_4)_3 \) communicates the compound's composition:

• 2 atoms of aluminum (\(\text{Al}\))
• 3 groups of sulfate (\(\text{SO}_4\)), with each group containing 1 sulfur and 4 oxygens.

This formula helps chemists understand how elements interact to form compounds and is a foundation for further calculations. It provides an easy label for identifying substances and understanding how complex molecules are structured.