https://file.aiquickdraw.com/mathbot/file/1727573058448hq6mqlsy.jpg

To solve this problem, we need to calculate the mole fraction and partial pressures of sulfur hexafluoride (SF₆) and chlorine pentafluoride (ClF₅), as well as the total pressure in the tank. We'll proceed by finding the number of moles of each gas, use the ideal gas law to determine partial pressures, and calculate the mole fractions.

### Step 1: Find the Molar Masses
1. **Sulfur hexafluoride (SF₆)**:
   - S: 32.06 g/mol
   - F: 6 × 19.00 g/mol = 114.00 g/mol
   - Molar mass of SF₆ = 32.06 + 114.00 = **146.06 g/mol**

2. **Chlorine pentafluoride (ClF₅)**:
   - Cl: 35.45 g/mol
   - F: 5 × 19.00 g/mol = 95.00 g/mol
   - Molar mass of ClF₅ = 35.45 + 95.00 = **130.45 g/mol**

### Step 2: Calculate the Number of Moles
Given masses:
- **SF₆**: 2.53 g
- **ClF₅**: 12.7 g

Using the formula:
\[
n = \frac{m}{M}
\]

1. **Number of moles of SF₆**:
   \[
   n_{\text{SF₆}} = \frac{2.53 \, \text{g}}{146.06 \, \text{g/mol}} = 0.0173 \, \text{mol}
   \]

2. **Number of moles of ClF₅**:
   \[
   n_{\text{ClF₅}} = \frac{12.7 \, \text{g}}{130.45 \, \text{g/mol}} = 0.0974 \, \text{mol}
   \]

### Step 3: Calculate the Mole Fractions
The total number of moles is:
\[
n_{\text{total}} = n_{\text{SF₆}} + n_{\text{ClF₅}} = 0.0173 + 0.0974 = 0.1147 \, \text{mol}
\]

1. **Mole fraction of SF₆**:
   \[
   X_{\text{SF₆}} = \frac{n_{\text{SF₆}}}{n_{\text{total}}} = \frac{0.0173}{0.1147} = 0.151
   \]

2. **Mole fraction of ClF₅**:
   \[
   X_{\text{ClF₅}} = \frac{n_{\text{ClF₅}}}{n_{\text{total}}} = \frac{0.0974}{0.1147} = 0.849
   \]

### Step 4: Calculate the Total Pressure Using the Ideal Gas Law
The ideal gas law is:
\[
PV = nRT
\]

Where:
- \( P \) = Pressure in atm (unknown)
- \( V \) = Volume = 6.00 L
- \( n \) = Total moles = 0.1147 mol
- \( R \) = Ideal gas constant = 0.0821 L·atm/(mol·K)
- \( T \) = Temperature in Kelvin = \( 0.22^\circ C + 273.15 = 273.37 \, \text{K} \)

Rearrange for pressure \( P \):
\[
P = \frac{nRT}{V} = \frac{0.1147 \times 0.0821 \times 273.37}{6.00}
\]

Let's calculate the total pressure.

### Step 5: Calculate Partial Pressures
The partial pressure of each gas can be calculated using:
\[
P_i = X_i \times P_{\text{total}}
\]The total pressure in the tank is approximately **0.429 atm**.

### Step 6: Calculate the Partial Pressures
Now that we have the total pressure, we can find the partial pressures:

1. **Partial pressure of SF₆**:
   \[
   P_{\text{SF₆}} = X_{\text{SF₆}} \times P_{\text{total}} = 0.151 \times 0.429 = 0.0648 \, \text{atm}
   \]

2. **Partial pressure of ClF₅**:
   \[
   P_{\text{ClF₅}} = X_{\text{ClF₅}} \times P_{\text{total}} = 0.849 \times 0.429 = 0.364 \, \text{atm}
   \]

### Summary of Results
- **Mole Fraction of SF₆**: 0.151
- **Partial Pressure of SF₆**: 0.065 atm
- **Mole Fraction of ClF₅**: 0.849
- **Partial Pressure of ClF₅**: 0.364 atm
- **Total Pressure in Tank**: 0.429 atm

Would you like me to clarify any of these steps or need more details?

#### Related Questions:
1. How does temperature affect the partial pressures of the gases in the tank?
2. What is the significance of assuming ideal gas behavior in these calculations?
3. How would the results change if the tank volume was different?
4. What would happen to the total pressure if we added more ClF₅?
5. How can the concept of mole fractions be applied to real-world gas mixtures?

#### Tip:
Always ensure temperature is converted to Kelvin when using the ideal gas law, as the gas constant \(R\) is defined for temperatures in Kelvin.

A 6.00 L tank at 0.22°C is filled with 2.53 g of sulfur hexafluoride gas and 12.7 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 hexafluoride and chlorine pentafluoride in a 6.00 L tank using the ideal gas law. Includes step-by-step calculations for moles, mole fractions, and total pressure.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation