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To solve this problem, we need to calculate the **mole fractions** and **partial pressures** of dinitrogen monoxide (N₂O) and chlorine pentafluoride (ClF₅), followed by determining the **total pressure** in the tank.

### Given Data:
- **Volume (V)** = 9.00 L
- **Temperature (T)** = 6.91 °C = 280.06 K (using \( T(K) = T(°C) + 273.15 \))
- **Mass of dinitrogen monoxide (N₂O)** = 7.23 g
- **Mass of chlorine pentafluoride (ClF₅)** = 14.5 g
- Assume ideal gas behavior.

We will use the **Ideal Gas Law**: 
\[
PV = nRT
\]
Where:
- \( P \) = pressure (atm)
- \( V \) = volume (L)
- \( n \) = moles of gas
- \( R \) = ideal gas constant = 0.0821 L·atm/mol·K
- \( T \) = temperature in Kelvin

### Step 1: Calculate the moles of each gas.

- **Molar mass of N₂O** = 44.01 g/mol
- **Molar mass of ClF₅** = 130.443 g/mol

\[
n_{\text{N₂O}} = \frac{7.23 \, \text{g}}{44.01 \, \text{g/mol}}
\]
\[
n_{\text{ClF₅}} = \frac{14.5 \, \text{g}}{130.443 \, \text{g/mol}}
\]

### Step 2: Calculate the mole fractions of each gas.
The mole fraction \( \chi_i \) is given by:
\[
\chi_i = \frac{n_i}{n_{\text{total}}}
\]
Where:
\[
n_{\text{total}} = n_{\text{N₂O}} + n_{\text{ClF₅}}
\]

### Step 3: Calculate the partial pressures of each gas.
Using the Ideal Gas Law for each gas:
\[
P_{\text{N₂O}} = \frac{n_{\text{N₂O}}RT}{V}
\]
\[
P_{\text{ClF₅}} = \frac{n_{\text{ClF₅}}RT}{V}
\]

### Step 4: Calculate the total pressure in the tank.
The total pressure is the sum of the partial pressures:
\[
P_{\text{total}} = P_{\text{N₂O}} + P_{\text{ClF₅}}
\]

I will now calculate each step.### Calculations:

1. **Moles of dinitrogen monoxide (N₂O)**: 0.164 mol
2. **Moles of chlorine pentafluoride (ClF₅)**: 0.111 mol

3. **Mole fractions**:
   - Mole fraction of N₂O: \( \chi_{\text{N₂O}} = 0.596 \)
   - Mole fraction of ClF₅: \( \chi_{\text{ClF₅}} = 0.404 \)

4. **Partial pressures**:
   - Partial pressure of N₂O: \( P_{\text{N₂O}} = 0.420 \, \text{atm} \)
   - Partial pressure of ClF₅: \( P_{\text{ClF₅}} = 0.284 \, \text{atm} \)

5. **Total pressure in the tank**: \( P_{\text{total}} = 0.704 \, \text{atm} \)

Let me know if you need further clarification or details on any step!

### Related Questions:
1. How is the ideal gas law applied in different temperature and pressure conditions?
2. What assumptions does the ideal gas law make about gas behavior?
3. How do deviations from ideal gas behavior occur at high pressures?
4. What is the significance of mole fractions in gas mixtures?
5. How can partial pressures help in determining the composition of a gas mixture?

### Tip:
Remember that the ideal gas law works best at low pressures and high temperatures, where gases behave more ideally.

A 9.00 L tank at 6.91°C is filled with 7.23 g of dinitrogen monoxide gas and 14.5 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 fractions and partial pressures of dinitrogen monoxide (N₂O) and chlorine pentafluoride (ClF₅) in a 9.00 L tank at 6.91°C. Learn how to apply the Ideal Gas Law to determine the total pressure in the tank. This problem involves determining gas moles, mole fractions, and partial pressures.

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