Consider a sample containing 1.542x10-18 grams of Fe2O3. How many oxygen atoms are in the sample? Express your answer using at least three significant digits. 

To calculate the number of oxygen atoms in a sample of Fe₂O₃, we'll follow these steps:

### 1. **Determine the molar mass of Fe₂O₃**:
- The molar mass of iron (Fe) is approximately 55.85 g/mol.
- The molar mass of oxygen (O) is approximately 16.00 g/mol.
- Fe₂O₃ contains two iron atoms and three oxygen atoms.

So, the molar mass of Fe₂O₃ is:
\[
\text{Molar mass of Fe₂O₃} = (2 \times 55.85) + (3 \times 16.00) = 111.70 + 48.00 = 159.70 \, \text{g/mol}
\]

### 2. **Convert the mass of Fe₂O₃ to moles**:
The mass of Fe₂O₃ given is \( 1.542 \times 10^{-18} \, \text{grams} \). Using the molar mass, we can convert this to moles:

\[
\text{Moles of Fe₂O₃} = \frac{1.542 \times 10^{-18} \, \text{g}}{159.70 \, \text{g/mol}} = 9.655 \times 10^{-21} \, \text{mol}
\]

### 3. **Determine the number of oxygen atoms**:
Each mole of Fe₂O₃ contains 3 moles of oxygen atoms. Therefore, the number of moles of oxygen atoms in the sample is:

\[
\text{Moles of oxygen atoms} = 9.655 \times 10^{-21} \, \text{mol} \times 3 = 2.897 \times 10^{-20} \, \text{mol O atoms}
\]

Next, we use Avogadro's number (\( 6.022 \times 10^{23} \, \text{atoms/mol} \)) to convert moles of oxygen atoms to the number of atoms:

\[
\text{Number of oxygen atoms} = 2.897 \times 10^{-20} \, \text{mol O atoms} \times 6.022 \times 10^{23} \, \text{atoms/mol}
\]

\[
\text{Number of oxygen atoms} \approx 1.744 \times 10^{4} \, \text{atoms}
\]

### Final Answer:
The sample contains approximately \( 1.744 \times 10^{4} \) oxygen atoms.

Would you like more details on any of these steps, or do you have further questions?

Here are five related questions you might find interesting:
1. How is the molar mass of a compound determined?
2. What is the significance of Avogadro's number in chemistry?
3. How can you find the number of atoms in a mole of any element?
4. How does the atomic structure of Fe₂O₃ affect its chemical properties?
5. What are the practical applications of Fe₂O₃ in industry?

**Tip**: Always ensure that significant digits in your calculations match the precision of the data given to avoid rounding errors!

Consider a sample containing 1.542x10-18 grams of Fe2O3. How many oxygen atoms are in the sample? Express your answer using at least three significant digits.

Learn how to calculate the number of oxygen atoms in a 1.542x10-18 gram sample of Fe₂O₃ using molar mass, the mole concept, and Avogadro's number. This detailed solution is ideal for high school chemistry students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation