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To solve this problem, we need to start by analyzing the chemical reaction involving gaseous ammonia \((\text{NH}_3)\), oxygen gas \((\text{O}_2)\), nitrogen monoxide \((\text{NO})\), and water vapor \((\text{H}_2\text{O})\).

The balanced chemical equation is:

\[
4 \text{NH}_3 + 5 \text{O}_2 \rightarrow 4 \text{NO} + 6 \text{H}_2\text{O}
\]

### Steps to solve the problem:

1. **Identify the given value:**
   - You are given that 0.080 moles of nitrogen monoxide (\(\text{NO}\)) are produced.

2. **Use the stoichiometric ratios from the balanced equation:**
   - According to the balanced equation, 4 moles of \(\text{NO}\) are produced when 5 moles of \(\text{O}_2\) are consumed.
   - The ratio of moles of \(\text{NO}\) to moles of \(\text{O}_2\) is \(\frac{4}{5}\), meaning for every 4 moles of \(\text{NO}\), 5 moles of \(\text{O}_2\) are required.

3. **Set up the proportion:**
   To find how many moles of oxygen are needed for 0.080 moles of \(\text{NO}\):
   
   \[
   \frac{4 \, \text{mol NO}}{5 \, \text{mol O}_2} = \frac{0.080 \, \text{mol NO}}{x \, \text{mol O}_2}
   \]
   
4. **Solve for \(x\):**
   \[
   x = \frac{0.080 \, \text{mol NO} \times 5 \, \text{mol O}_2}{4 \, \text{mol NO}}
   \]
   \[
   x = 0.100 \, \text{mol O}_2
   \]

Thus, the moles of oxygen required to produce 0.080 mol of nitrogen monoxide are **0.100 mol**.

Would you like more details on this, or do you have any questions? 

Here are some related questions to consider:
1. How do you balance chemical equations?
2. What is the importance of stoichiometry in chemical reactions?
3. How do you calculate the limiting reactant in a chemical reaction?
4. What are the units used in molar calculations?
5. How does the law of conservation of mass apply to this reaction?

**Tip:** When solving stoichiometric problems, always check if the chemical equation is balanced before performing calculations!

Gaseous ammonia chemically reacts with oxygen gas to produce nitrogen monoxide gas and water vapor. Calculate the moles of oxygen needed to produce 0.080 mol of nitrogen monoxide. Be sure your answer has a unit symbol, if necessary, and round it to the correct number of significant digits.

Learn how to calculate the moles of oxygen required to react with ammonia to produce nitrogen monoxide using stoichiometry and a balanced chemical reaction. This problem demonstrates the use of molar ratios in chemical equations, suitable for high school chemistry students.

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