A gaseous mixture has 7g of `N_2, 8g of He and 22g of CO_2`. Calculate the molefractions of component gaese in the mixture.

Answer

To calculate the mole fractions of the component gases in the mixture, we will follow these steps:

### Step 1: Calculate the molar masses of the gases.
- **Nitrogen (N₂)**: The molar mass of nitrogen is calculated as follows:
\[ \text{Molar mass of } N_2 = 2 \times 14 \, \text{g/mol} = 28 \, \text{g/mol} \]

- **Helium (He)**: The molar mass of helium is:
\[ \text{Molar mass of } He = 4 \, \text{g/mol} \]

- **Carbon Dioxide (CO₂)**: The molar mass of carbon dioxide is:
\[ \text{Molar mass of } CO_2 = 12 + 2 \times 16 = 44 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of each gas.
- **Moles of Nitrogen (N₂)**:
\[ \text{Moles of } N_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{7 \, \text{g}}{28 \, \text{g/mol}} = \frac{1}{4} \, \text{mol} \]

- **Moles of Helium (He)**:
\[ \text{Moles of } He = \frac{8 \, \text{g}}{4 \, \text{g/mol}} = 2 \, \text{mol} \]

- **Moles of Carbon Dioxide (CO₂)**:
\[ \text{Moles of } CO_2 = \frac{22 \, \text{g}}{44 \, \text{g/mol}} = \frac{1}{2} \, \text{mol} \]

### Step 3: Calculate the total number of moles in the mixture.
\[ \text{Total moles} = \left(\frac{1}{4} + 2 + \frac{1}{2}\right) = \frac{1}{4} + \frac{8}{4} + \frac{2}{4} = \frac{11}{4} \, \text{mol} \]

### Step 4: Calculate the mole fractions of each gas.
- **Mole fraction of Nitrogen (N₂)**:
\[ x_{N_2} = \frac{\text{Moles of } N_2}{\text{Total moles}} = \frac{\frac{1}{4}}{\frac{11}{4}} = \frac{1}{11} \]

- **Mole fraction of Helium (He)**:
\[ x_{He} = \frac{\text{Moles of } He}{\text{Total moles}} = \frac{2}{\frac{11}{4}} = \frac{8}{11} \]

- **Mole fraction of Carbon Dioxide (CO₂)**:
\[ x_{CO_2} = \frac{\text{Moles of } CO_2}{\text{Total moles}} = \frac{\frac{1}{2}}{\frac{11}{4}} = \frac{2}{11} \]

### Final Results:
- Mole fraction of Nitrogen (N₂): \( x_{N_2} = \frac{1}{11} \)
- Mole fraction of Helium (He): \( x_{He} = \frac{8}{11} \)
- Mole fraction of Carbon Dioxide (CO₂): \( x_{CO_2} = \frac{2}{11} \)