If 500 mL of gas A at 1000 torr and 1000 mL of gas B at 800 torr are placed in a 2 L container, the final pressure will be

Options

A. 100 torr
B. 650 torr
C. 1800 torr
D. 2400 torr

Explanation

To solve the problem of finding the final pressure when gases A and B are combined in a 2 L container, we can follow these steps:

### Step 1: Calculate the number of moles of gas A
Using the ideal gas equation \(PV = nRT\), we can rearrange it to find the number of moles \(n\):
\[ n_A = \frac{P_A V_A}{RT} \]
Where:
- \(P_A = 1000 \, \text{torr}\)
- \(V_A = 500 \, \text{mL} = 0.5 \, \text{L}\)

Substituting the values:
\[ n_A = \frac{1000 \, \text{torr} \times 0.5 \, \text{L}}{RT} \]

### Step 2: Calculate the number of moles of gas B
Similarly, for gas B:
\[ n_B = \frac{P_B V_B}{RT} \]
Where:
- \(P_B = 800 \, \text{torr}\)
- \(V_B = 1000 \, \text{mL} = 1.0 \, \text{L}\)

Substituting the values:
\[ n_B = \frac{800 \, \text{torr} \times 1.0 \, \text{L}}{RT} \]

### Step 3: Calculate the total number of moles
The total number of moles \(n_{total}\) is the sum of \(n_A\) and \(n_B\):
\[ n_{total} = n_A + n_B = \frac{1000 \times 0.5}{RT} + \frac{800 \times 1.0}{RT} \]
\[ n_{total} = \frac{500 + 800}{RT} = \frac{1300}{RT} \]

### Step 4: Calculate the final pressure
Using the ideal gas equation again for the total system:
\[ P_{final} = \frac{n_{total} RT}{V_{final}} \]
Where \(V_{final} = 2 \, \text{L}\):
\[ P_{final} = \frac{\frac{1300}{RT} \cdot RT}{2} = \frac{1300}{2} = 650 \, \text{torr} \]

### Final Answer
The final pressure when gases A and B are placed in a 2 L container is:
\[ \boxed{650 \, \text{torr}} \]

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