Sure! Let's calculate the number of moles of dinitrogen trioxide (N₂O₃) given a mass of 75.0 grams.
### Step-by-Step Solution:
1. Understand the Problem:
- We are given:
- The mass of dinitrogen trioxide (N₂O₃) is 75.0 grams
- We need to find the number of moles in this mass.
2. Recall the Formula:
- To find the number of moles, we can use the formula:
[tex]\[
\text{Number of moles} = \frac{\text{mass (in grams)}}{\text{molar mass (in g/mol)}}
\][/tex]
3. Identify the Molar Mass:
- For dinitrogen trioxide (N₂O₃), the molar mass is approximately 76.01 g/mol. This value is typically found using atomic masses from the periodic table:
- Nitrogen (N): approximately 14.01 g/mol
- Oxygen (O): approximately 16.00 g/mol
- For N₂O₃: [tex]\(2 \times 14.01 \text{ g/mol} + 3 \times 16.00 \text{ g/mol} = 28.02 \text{ g/mol} + 48.00 \text{ g/mol} = 76.02 \text{ g/mol}\)[/tex]
- Note: We use the given precise molar mass of 76.01 g/mol for accuracy.
4. Plug in the Values and Solve:
- Using the given mass and molar mass:
[tex]\[
\text{Number of moles} = \frac{75.0 \text{ grams}}{76.01 \text{ g/mol}}
\][/tex]
5. Compute the Result:
- Carry out the division to find the number of moles:
[tex]\[
\text{Number of moles} \approx 0.9867
\][/tex]
### Final Answer:
The number of moles in 75.0 grams of dinitrogen trioxide is approximately 0.9867 moles.
