To solve the problem of determining the final volume of nitrogen dioxide (NO₂) formed when 20 mL of nitric oxide (NO) combines with 10 mL of oxygen (O₂) at standard temperature and pressure (STP), we can follow these steps:
### Step 1: Write the balanced chemical equation
The balanced chemical equation for the reaction between nitric oxide and oxygen is:
\[ 2 \text{NO} + \text{O}_2 \rightarrow 2 \text{NO}_2 \]
### Step 2: Determine the initial volumes of reactants
We have:
- Volume of NO = 20 mL
- Volume of O₂ = 10 mL
### Step 3: Calculate the moles of each reactant
At STP, the volume of one mole of gas is 22,400 mL. We can calculate the moles of each gas using the formula:
\[ \text{Moles} = \frac{\text{Volume}}{\text{Molar Volume}} \]
For NO:
\[ \text{Moles of NO} = \frac{20 \, \text{mL}}{22,400 \, \text{mL/mol}} = \frac{20}{22,400} \, \text{mol} \]
For O₂:
\[ \text{Moles of O}_2 = \frac{10 \, \text{mL}}{22,400 \, \text{mL/mol}} = \frac{10}{22,400} \, \text{mol} \]
### Step 4: Determine the limiting reagent
From the balanced equation, we see that 2 moles of NO react with 1 mole of O₂. Therefore, the mole ratio is:
- 2 moles of NO : 1 mole of O₂
Now, we can find the required moles of O₂ for the available moles of NO:
- Required moles of O₂ for 20 mL of NO:
\[ \text{Required moles of O}_2 = \frac{10}{22,400} \, \text{mol} \]
Now, we can find the moles of NO needed to react with the available O₂:
- Available moles of NO for 10 mL of O₂:
\[ \text{Required moles of NO} = 2 \times \frac{10}{22,400} = \frac{20}{22,400} \, \text{mol} \]
Since we have equal amounts of NO and O₂ in terms of their stoichiometric ratios, both reactants will be completely consumed.
### Step 5: Calculate the moles of NO₂ produced
From the balanced equation, 2 moles of NO produce 2 moles of NO₂. Thus, the moles of NO₂ produced will be equal to the moles of NO consumed:
\[ \text{Moles of NO}_2 = \text{Moles of NO} = \frac{20}{22,400} \, \text{mol} \]
### Step 6: Calculate the volume of NO₂ produced
Using the volume formula:
\[ \text{Volume of NO}_2 = \text{Moles of NO}_2 \times \text{Molar Volume} \]
\[ \text{Volume of NO}_2 = \frac{20}{22,400} \times 22,400 \, \text{mL} = 20 \, \text{mL} \]
### Final Answer
The final volume of nitrogen dioxide (NO₂) produced is **20 mL**.
---