In a container of 10 L volume, 20 g `O_2(g)` and 2.8 g CO(g) are taken at a total pressure of 2 atm and `(27 ^0 C)`. Partial pressure and partial volume occupied by oxygen gas in container respectively are

Options

A. `[50/29 atm]` ,`[250/29]L`
B. `[17/50 atm]` ,`[250/29]L`
C. `[14/50 atm]` ,`[40/29]L`
D. `[50/29 atm]` ,`[100/29]L`

Answer

To solve the problem, we need to find the partial pressure and partial volume occupied by oxygen gas (O₂) in a container with a total volume of 10 L, containing 20 g of O₂ and 2.8 g of CO at a total pressure of 2 atm and a temperature of 27 °C.

### Step-by-Step Solution:

**Step 1: Calculate the number of moles of O₂ and CO.**

- The molar mass of O₂ (oxygen) is approximately 32 g/mol.
- The molar mass of CO (carbon monoxide) is approximately 28 g/mol.

**Moles of O₂:**
\[ \text{Moles of O₂} = \frac{\text{mass of O₂}}{\text{molar mass of O₂}} = \frac{20 \, \text{g}}{32 \, \text{g/mol}} = 0.625 \, \text{mol} \]

**Moles of CO:**
\[ \text{Moles of CO} = \frac{\text{mass of CO}}{\text{molar mass of CO}} = \frac{2.8 \, \text{g}}{28 \, \text{g/mol}} = 0.1 \, \text{mol} \]

**Step 2: Calculate the total number of moles in the container.**

\[ \text{Total moles} = \text{Moles of O₂} + \text{Moles of CO} = 0.625 \, \text{mol} + 0.1 \, \text{mol} = 0.725 \, \text{mol} \]

**Step 3: Calculate the mole fraction of O₂.**

\[ \text{Mole fraction of O₂} = \frac{\text{Moles of O₂}}{\text{Total moles}} = \frac{0.625}{0.725} \approx 0.8621 \]

**Step 4: Calculate the partial pressure of O₂.**

Using Dalton's Law of Partial Pressures:
\[ \text{Partial pressure of O₂} = \text{Mole fraction of O₂} \times \text{Total pressure} \]
\[ \text{Partial pressure of O₂} = 0.8621 \times 2 \, \text{atm} \approx 1.7242 \, \text{atm} \]

**Step 5: Calculate the partial volume occupied by O₂.**

Using the formula for partial volume:
\[ \text{Partial volume of O₂} = \text{Mole fraction of O₂} \times \text{Total volume} \]
\[ \text{Partial volume of O₂} = 0.8621 \times 10 \, \text{L} \approx 8.621 \, \text{L} \]

### Final Results:
- **Partial Pressure of O₂:** Approximately 1.7242 atm
- **Partial Volume of O₂:** Approximately 8.621 L