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To solve this problem, we need to calculate the **mole fraction** and **partial pressure** of each gas, as well as the **total pressure** in the tank.

### Given Information:
- Volume of tank, \( V = 9.00 \, \text{L} \)
- Temperature, \( T = 7.58^\circ C = 280.73 \, \text{K} \) (converted to Kelvin)
- Mass of sulfur tetrafluoride (SF₄) = 10.3 g
- Mass of chlorine pentafluoride (ClF₅) = 18.3 g
- Assume both gases behave as ideal gases.

### Step-by-Step Approach:

1. **Convert Mass to Moles**:
   To find the moles of each gas, we use the molar masses:
   - Molar mass of SF₄ = 108.07 g/mol
   - Molar mass of ClF₅ = 130.44 g/mol

   The number of moles is calculated using:
   \[
   n = \frac{\text{mass}}{\text{molar mass}}
   \]

2. **Calculate Mole Fractions**:
   The mole fraction \( \chi \) of each gas is calculated as:
   \[
   \chi_{\text{gas}} = \frac{n_{\text{gas}}}{n_{\text{total}}}
   \]
   where \( n_{\text{total}} = n_{\text{SF}_4} + n_{\text{ClF}_5} \).

3. **Calculate the Total Pressure**:
   Use the **Ideal Gas Law** to calculate the total pressure in the tank:
   \[
   P_{\text{total}} = \frac{n_{\text{total}}RT}{V}
   \]
   where:
   - \( R = 0.0821 \, \text{L·atm/mol·K} \) (ideal gas constant)
   - \( T \) is the temperature in Kelvin (280.73 K)
   - \( V \) is the volume of the tank (9.00 L)

4. **Calculate Partial Pressures**:
   The partial pressure \( P_{\text{gas}} \) of each gas is:
   \[
   P_{\text{gas}} = \chi_{\text{gas}} \times P_{\text{total}}
   \]

Let me compute each of these values for you.Here are the results:

1. **Moles of each gas**:
   - Moles of sulfur tetrafluoride (SF₄): \( 0.0953 \, \text{mol} \)
   - Moles of chlorine pentafluoride (ClF₅): \( 0.1403 \, \text{mol} \)

2. **Mole fractions**:
   - Mole fraction of SF₄: \( 0.4045 \)
   - Mole fraction of ClF₅: \( 0.5955 \)

3. **Partial pressures**:
   - Partial pressure of SF₄: \( 0.244 \, \text{atm} \)
   - Partial pressure of ClF₅: \( 0.359 \, \text{atm} \)

4. **Total pressure in the tank**: \( 0.603 \, \text{atm} \)

Would you like any further clarifications or more details?

Here are 5 related questions to explore:
1. How does changing the temperature affect the total pressure?
2. What if we used a larger tank? How would the pressure change?
3. How would the mole fractions change if the masses of the gases were swapped?
4. How is the ideal gas law impacted by non-ideal gas behavior?
5. Can you apply this approach to a mixture of three or more gases?

**Tip**: Always ensure temperature is in Kelvin when using the ideal gas law for accurate results.

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. 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 pressure of sulfur tetrafluoride and chlorine pentafluoride gases in a 9.00 L tank at 7.58 °C using the ideal gas law. This example walks through the steps including mass to mole conversion and the application of the ideal gas equation.

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