If 1 litre of a gas A at 500 mm and 0.5 litre of gas B at 800 mm are taken in a 2−litre bulb, the resulting pressure is:

Options

A. 200
B. 300
C. 450
D. 500

Answer

To solve the problem of finding the resulting pressure when gas A and gas B are combined in a 2-litre bulb, we can use the Ideal Gas Law, which states that \( PV = nRT \). Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the number of moles of gas A
Given:
- Volume of gas A, \( V_A = 1 \) L
- Pressure of gas A, \( P_A = 500 \) mm

Using the Ideal Gas Law, we can rearrange the formula to find the number of moles (\( n \)):
\[ n_A = \frac{P_A \cdot V_A}{R \cdot T} \]
Substituting the values:
\[ n_A = \frac{500 \, \text{mm} \cdot 1 \, \text{L}}{R \cdot T} = \frac{500}{RT} \]

### Step 2: Calculate the number of moles of gas B
Given:
- Volume of gas B, \( V_B = 0.5 \) L
- Pressure of gas B, \( P_B = 800 \) mm

Using the same formula:
\[ n_B = \frac{P_B \cdot V_B}{R \cdot T} \]
Substituting the values:
\[ n_B = \frac{800 \, \text{mm} \cdot 0.5 \, \text{L}}{R \cdot T} = \frac{400}{RT} \]

### Step 3: Calculate the total number of moles
Now, we can find the total number of moles (\( n_{total} \)):
\[ n_{total} = n_A + n_B = \frac{500}{RT} + \frac{400}{RT} = \frac{900}{RT} \]

### Step 4: Calculate the resulting pressure in the 2-litre bulb
The final volume of the bulb is given as \( V_{final} = 2 \) L. We can use the Ideal Gas Law again to find the pressure (\( P \)):
\[ PV = nRT \]
Rearranging for pressure:
\[ P = \frac{nRT}{V} \]
Substituting the total number of moles and the final volume:
\[ P = \frac{\left(\frac{900}{RT}\right)RT}{2} = \frac{900}{2} = 450 \, \text{mm} \]

### Final Result
The resulting pressure in the 2-litre bulb is **450 mm**.

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