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The problem involves calculating the **mole fraction** and **partial pressure** of two gases, **dinitrogen monoxide** (N₂O) and **chlorine pentafluoride** (ClF₅), in a 6.00 L tank at 0.74°C, assuming ideal gas behavior.

We will use the following formulas:
1. **Mole fraction** of gas \( i \):
   \[
   X_i = \frac{n_i}{n_{\text{total}}}
   \]
   where \( n_i \) is the number of moles of gas \( i \), and \( n_{\text{total}} \) is the total moles of gas.

2. **Partial pressure** of gas \( i \):
   \[
   P_i = X_i \times P_{\text{total}}
   \]
   where \( P_{\text{total}} \) is the total pressure in the tank, which can be found using the ideal gas law:
   \[
   P_{\text{total}} V = n_{\text{total}} R T
   \]
   where:
   - \( V = 6.00 \, \text{L} \)
   - \( T = 0.74^\circ \text{C} = 273.74 \, \text{K} \)
   - \( R = 0.0821 \, \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}} \)

Next, we calculate the moles for each gas using their molar masses:
- **N₂O**: Molar mass \( = 44.013 \, \text{g/mol} \)
- **ClF₅**: Molar mass \( = 130.443 \, \text{g/mol} \)

Now, I will perform the calculations.Here are the calculations for the given gases:

1. **Moles** of each gas:
   - Moles of dinitrogen monoxide (N₂O): \( 0.216 \, \text{mol} \)
   - Moles of chlorine pentafluoride (ClF₅): \( 0.0495 \, \text{mol} \)

2. **Mole fractions**:
   - Mole fraction of N₂O: \( 0.813 \)
   - Mole fraction of ClF₅: \( 0.187 \)

3. **Partial pressures**:
   - Partial pressure of N₂O: \( 0.808 \, \text{atm} \)
   - Partial pressure of ClF₅: \( 0.185 \, \text{atm} \)

4. **Total pressure** in the tank: \( 0.993 \, \text{atm} \)

Would you like more details or have any questions? Here are five related questions:

1. How do changes in temperature affect the total pressure of gases in a container?
2. How is the mole fraction related to Dalton's Law of partial pressures?
3. What happens to the mole fraction if more dinitrogen monoxide is added to the tank?
4. How would the results differ if the gases did not behave ideally?
5. What is the significance of the gas constant \( R \) in the ideal gas law?

**Tip**: Always check units and temperature conversions when using the ideal gas law to avoid errors.

A 6.00 L tank at 0.74 °C is filled with 9.49 g of dinitrogen monoxide gas and 6.46 g of chlorine pentafluoride gas. You can assume both gases behave as ideal gases under these conditions. Calculate the mole fraction and partial pressure of each gas, and the total pressure in the tank.

Calculate the mole fraction and partial pressure of dinitrogen monoxide and chlorine pentafluoride in a 6.00 L tank at 0.74 °C. Understand the use of the ideal gas law and Dalton's Law of Partial Pressures in determining the total pressure. Suitable for AP Chemistry or College-level students.

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