Problem 195 - Chemistry Matter and Change

Question

Which of these compounds has the greatest percent of oxygen by mass: \(\mathrm{TiO}_{2}, \mathrm{Fe}_{2} \mathrm{O}_{3},\) or \(\mathrm{Al}_{2} \mathrm{O}_{3} ?\)

Step-by-Step Solution

Answer

The compound with the greatest percent of oxygen by mass is \( \text{Al}_2\text{O}_3 \).

Step 1: Calculate Molar Mass of Each Compound

First, we find the molar mass for each compound.**For \( \text{TiO}_2 \):** Titanium (Ti): 47.87 g/mol Oxygen (O): 16 g/mol \( \text{Molar mass of } \text{TiO}_2 = 47.87 + 2 \times 16 = 79.87 \text{ g/mol} \).**For \( \text{Fe}_2\text{O}_3 \):** Iron (Fe): 55.85 g/mol Oxygen (O): 16 g/mol \( \text{Molar mass of } \text{Fe}_2\text{O}_3 = 2 \times 55.85 + 3 \times 16 = 159.7 \text{ g/mol} \).**For \( \text{Al}_2\text{O}_3 \):** Aluminum (Al): 26.98 g/mol Oxygen (O): 16 g/mol \( \text{Molar mass of } \text{Al}_2\text{O}_3 = 2 \times 26.98 + 3 \times 16 = 101.96 \text{ g/mol} \).

Step 2: Calculate Percent Oxygen by Mass for Each Compound

Next, calculate the percent oxygen by mass for each compound using the formula:\[ \text{Percent }\text{Oxygen} = \left( \frac{\text{Total Mass of Oxygen Atoms}}{\text{Molar Mass of Compound}} \right) \times 100 \]**For \( \text{TiO}_2 \):** \( \text{Percent Oxygen} = \left( \frac{2 \times 16}{79.87} \right) \times 100 \approx 40.13\% \)**For \( \text{Fe}_2\text{O}_3 \):** \( \text{Percent Oxygen} = \left( \frac{3 \times 16}{159.7} \right) \times 100 \approx 30.06\% \)**For \( \text{Al}_2\text{O}_3 \):** \( \text{Percent Oxygen} = \left( \frac{3 \times 16}{101.96} \right) \times 100 \approx 47.08\% \)

Step 3: Compare the Percent Oxygen by Mass

Now, we compare the percent oxygen by mass calculated for each compound.- \( \text{TiO}_2 \) has approximately 40.13% oxygen.- \( \text{Fe}_2\text{O}_3 \) has approximately 30.06% oxygen.- \( \text{Al}_2\text{O}_3 \) has approximately 47.08% oxygen.The compound with the greatest percent of oxygen by mass is \( \text{Al}_2\text{O}_3 \).

Key Concepts

Molar Mass Calculation

To determine the molar mass of a chemical compound, you need to sum up the atomic masses of all the atoms in the molecule. This is a crucial step because the molar mass is used in various calculations, such as finding the percent composition.

The atomic mass of each element can be found on the periodic table. For example:

• Titanium (Ti) has an atomic mass of 47.87 g/mol.
• Oxygen (O) has an atomic mass of 16 g/mol.
• Iron (Fe) has an atomic mass of 55.85 g/mol.
• Aluminum (Al) has an atomic mass of 26.98 g/mol.

To calculate the molar mass of a compound, consider its chemical formula. Each element’s atomic mass is multiplied by the number of times the element appears in the compound. Then, add all these values together. For example, for \( \text{TiO}_2 \):

Titanium contributes 47.87 g/mol and two oxygens contribute \( 2 \times 16 = 32 \) g/mol. Therefore, the molar mass of \( \text{TiO}_2 \) is \( 47.87 + 32 = 79.87 \) g/mol.

Performing these calculations accurately helps you get to the right answers, especially when calculating percent compositions.

Oxygen by Mass

Understanding the percent of oxygen by mass in a compound is fundamental in chemistry for practical applications like material selection and chemical reactions.

To find the percent of oxygen by mass, use the formula:
\[ \text{Percent Oxygen by Mass} = \left( \frac{\text{Total Mass of Oxygen Atoms}}{\text{Molar Mass of Compound}} \right) \times 100 \]

Let's use \( \text{Al}_2\text{O}_3 \) as an example. Aluminum oxide contains three oxygen atoms. First, calculate the total mass of oxygen in \( \text{Al}_2\text{O}_3 \): 6\( 3 \times 16 = 48 \) g/mol.

Then, you'll divide this by the molar mass of the compound, which is 101.96 g/mol, and multiply by 100 to find the percentage. Thus, \( \frac{48}{101.96} \times 100 = 47.08\% \)

This percentage tells you how much of the compound’s mass is due to oxygen. In practical situations, knowing this can help you determine suitable compounds for oxygen delivery or storage.

Chemical Compounds Comparison

When comparing chemical compounds, especially to determine which one has certain properties like the greatest percent of oxygen by mass, the steps are crucial to follow.

Start by calculating the molar mass and the percent of each element by mass within each compound, as described above. For this specific exercise, comparing oxygen by mass among \( \text{TiO}_2 \), \( \text{Fe}_2\text{O}_3 \), and \( \text{Al}_2\text{O}_3 \) gives you concrete data to make an informed decision.

For instance, in this case:

• \( \text{TiO}_2 \) contains about 40.13% oxygen.
• \( \text{Fe}_2\text{O}_3 \) contains about 30.06% oxygen.
• \( \text{Al}_2\text{O}_3 \) contains about 47.08% oxygen.

From these calculations, you determine that \( \text{Al}_2\text{O}_3 \) has the greatest percentage of oxygen by mass.

Such comparisons are vital in various chemical applications, helping scientists select the right mixture or element for reactions or materials based on their properties. Understanding how to calculate and compare these compositions allows for better decision-making in both academic and industrial settings.