If 1 litre of a gas A at 600 mm and 0.5 litre of gas B at 800 mm are taken in a 2-litre bulb, the resulting pressure is

Options

A. 1500mm
B. 1000 mm
C. 200mm
D. 500mm

Answer

To solve the problem of finding the resulting pressure when 1 liter of gas A at 600 mm and 0.5 liter of gas B at 800 mm are combined in a 2-liter bulb, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Volume of gas A (V_A) = 1 L
- Pressure of gas A (P_A) = 600 mm
- Volume of gas B (V_B) = 0.5 L
- Pressure of gas B (P_B) = 800 mm
- Total volume of the bulb (V_total) = 2 L

2. **Calculate the Number of Moles of Gas A:**
- Using the ideal gas equation \( PV = nRT \), we can express the number of moles (n) as:
\[ n_A = \frac{P_A \cdot V_A}{RT} \]
- Substituting the values:
\[ n_A = \frac{600 \, \text{mm} \cdot 1 \, \text{L}}{RT} = \frac{600}{RT} \]

3. **Calculate the Number of Moles of Gas B:**
- Similarly, for gas B:
\[ n_B = \frac{P_B \cdot V_B}{RT} \]
- Substituting the values:
\[ n_B = \frac{800 \, \text{mm} \cdot 0.5 \, \text{L}}{RT} = \frac{400}{RT} \]

4. **Calculate the Total Number of Moles:**
- The total number of moles (n_total) is the sum of the moles of gas A and gas B:
\[ n_{\text{total}} = n_A + n_B = \frac{600}{RT} + \frac{400}{RT} = \frac{1000}{RT} \]

5. **Use the Ideal Gas Law to Find the Resulting Pressure:**
- According to the ideal gas equation:
\[ P_{\text{total}} \cdot V_{\text{total}} = n_{\text{total}} \cdot RT \]
- Rearranging gives:
\[ P_{\text{total}} = \frac{n_{\text{total}} \cdot RT}{V_{\text{total}}} \]
- Substituting the values:
\[ P_{\text{total}} = \frac{\left(\frac{1000}{RT}\right) \cdot RT}{2 \, \text{L}} = \frac{1000}{2} = 500 \, \text{mm} \]

6. **Conclusion:**
- The resulting pressure in the 2-liter bulb is **500 mm**.