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To solve the problem presented in the image, we will use the ideal gas law to determine the partial pressures and mole fractions of sulfur tetrafluoride (SF₄) and chlorine pentafluoride (ClF₅).

### Step-by-step approach:

1. **Determine the number of moles of each gas**:
   Use the molar mass to convert the mass of each gas into moles:
   
   \[
   n = \frac{m}{M}
   \]
   where:
   - \( m \) is the mass of the gas (in grams),
   - \( M \) is the molar mass of the gas (in g/mol),
   - \( n \) is the number of moles of the gas.
   
   - Molar mass of sulfur tetrafluoride (SF₄): \( 146.06 \, \text{g/mol} \)
   - Molar mass of chlorine pentafluoride (ClF₅): \( 130.44 \, \text{g/mol} \)

2. **Calculate the total moles**:
   Add the moles of sulfur tetrafluoride and chlorine pentafluoride to get the total moles of gas in the container.

3. **Calculate the mole fraction of each gas**:
   The mole fraction \( X \) is calculated as:
   
   \[
   X = \frac{n_{\text{gas}}}{n_{\text{total}}}
   \]
   where \( n_{\text{gas}} \) is the moles of the individual gas, and \( n_{\text{total}} \) is the total number of moles.

4. **Use the ideal gas law to find total pressure**:
   The ideal gas law is:
   
   \[
   PV = nRT
   \]
   where:
   - \( P \) is the pressure (in atm),
   - \( V \) is the volume of the tank (9.00 L),
   - \( n \) is the total number of moles,
   - \( R \) is the ideal gas constant (\( 0.0821 \, \text{L} \cdot \text{atm}/\text{mol} \cdot \text{K} \)),
   - \( T \) is the temperature (in Kelvin, so convert from \( 7.58 \, ^\circ\text{C} \) to K by adding 273.15).

5. **Calculate the partial pressure of each gas**:
   The partial pressure of a gas is:
   
   \[
   P_{\text{gas}} = X_{\text{gas}} \cdot P_{\text{total}}
   \]

Let me first calculate the moles, mole fractions, and pressures based on this plan.### Results:

1. **Moles of each gas:**
   - Moles of sulfur tetrafluoride (SF₄): \( 0.0705 \, \text{mol} \)
   - Moles of chlorine pentafluoride (ClF₅): \( 0.1403 \, \text{mol} \)

2. **Mole fractions:**
   - Mole fraction of sulfur tetrafluoride (SF₄): \( 0.335 \)
   - Mole fraction of chlorine pentafluoride (ClF₅): \( 0.665 \)

3. **Partial pressures:**
   - Partial pressure of sulfur tetrafluoride (SF₄): \( 0.181 \, \text{atm} \)
   - Partial pressure of chlorine pentafluoride (ClF₅): \( 0.359 \, \text{atm} \)

4. **Total pressure in the tank:**
   - Total pressure: \( 0.540 \, \text{atm} \)

Would you like further details on any of the steps or calculations? Here are some related questions you might find useful:

1. How is the ideal gas law used for calculating pressure?
2. How do mole fractions affect partial pressures?
3. Why is temperature converted to Kelvin in gas law calculations?
4. Can you explain the concept of partial pressure in a gas mixture?
5. How would changes in temperature affect the total pressure?

**Tip:** Always ensure to convert all units to the appropriate system (e.g., Kelvin for temperature) when using the ideal gas law!

A 9.00 L tank at 7.58°C is filled with 10.3 g of sulfur tetrafluoride gas and 18.3 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.

Learn how to calculate the mole fraction and partial pressures of sulfur tetrafluoride and chlorine pentafluoride in a 9.00 L tank at 7.58°C using the ideal gas law. This problem covers gas law principles and ideal gas behavior under specified conditions. Suitable for undergraduate students.

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