`N_(2)` is found in a litre flask under `100 k Pa` pressure and `O_(2)` is found in another `3 litre` flask under `20 K Pa` pressure. If the two flask are connected, the resultant pressure is

Options

A. `310 kPa`
B. `210 kPa`
C. `420 kPa`
D. `265 kPa`

Explanation

To solve the problem of finding the resultant pressure when two flasks containing nitrogen (N₂) and oxygen (O₂) are connected, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- For N₂:
- Pressure (P₁) = 100 kPa
- Volume (V₁) = 1 L
- For O₂:
- Pressure (P₂) = 20 kPa
- Volume (V₂) = 3 L

2. **Calculate the Number of Moles of Each Gas**:
- Using the ideal gas equation:
\[ n = \frac{PV}{RT} \]
- For N₂:
\[ n_{N₂} = \frac{P₁ \cdot V₁}{RT} = \frac{100 \, \text{kPa} \cdot 1 \, \text{L}}{RT} \]
- For O₂:
\[ n_{O₂} = \frac{P₂ \cdot V₂}{RT} = \frac{20 \, \text{kPa} \cdot 3 \, \text{L}}{RT} \]

3. **Combine the Moles**:
- The total number of moles when the flasks are connected is:
\[ n_{total} = n_{N₂} + n_{O₂} = \frac{100 \cdot 1}{RT} + \frac{20 \cdot 3}{RT} \]
- Simplifying:
\[ n_{total} = \frac{100 + 60}{RT} = \frac{160}{RT} \]

4. **Calculate the Total Volume**:
- The total volume (V_total) when the flasks are connected:
\[ V_{total} = V₁ + V₂ = 1 \, \text{L} + 3 \, \text{L} = 4 \, \text{L} \]

5. **Calculate the Final Pressure**:
- Using the ideal gas equation again for the combined system:
\[ P_{final} = \frac{n_{total} \cdot RT}{V_{total}} = \frac{\left(\frac{160}{RT}\right) \cdot RT}{4} = \frac{160}{4} = 40 \, \text{kPa} \]

6. **Final Result**:
- The resultant pressure when the two flasks are connected is **40 kPa**.