If 1 L of gas A at 600 torr and 500 mL of gas B at 1000 torr are placed in 2 L flask , the final pressure will be

Options

A. 500 torr
B. 550 torr
C. 1000 torr
D. 1100 torr

Answer

To solve the problem of finding the final pressure when gas A and gas B are combined in a 2 L flask, we can use Dalton's Law of Partial Pressures. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Information
- Volume of gas A (V_A) = 1 L = 1000 mL
- Pressure of gas A (P_A) = 600 torr
- Volume of gas B (V_B) = 500 mL
- Pressure of gas B (P_B) = 1000 torr
- Total volume of the flask (V_F) = 2 L = 2000 mL

### Step 2: Calculate the Partial Pressure of Gas A
Using the formula for partial pressure:
\[ P_{A,final} = \frac{P_A \cdot V_A}{V_F} \]
Substituting the values:
\[ P_{A,final} = \frac{600 \, \text{torr} \cdot 1000 \, \text{mL}}{2000 \, \text{mL}} \]
\[ P_{A,final} = \frac{600000 \, \text{torr mL}}{2000 \, \text{mL}} \]
\[ P_{A,final} = 300 \, \text{torr} \]

### Step 3: Calculate the Partial Pressure of Gas B
Using the same formula for gas B:
\[ P_{B,final} = \frac{P_B \cdot V_B}{V_F} \]
Substituting the values:
\[ P_{B,final} = \frac{1000 \, \text{torr} \cdot 500 \, \text{mL}}{2000 \, \text{mL}} \]
\[ P_{B,final} = \frac{500000 \, \text{torr mL}}{2000 \, \text{mL}} \]
\[ P_{B,final} = 250 \, \text{torr} \]

### Step 4: Calculate the Total Final Pressure
According to Dalton's Law, the total pressure (P_F) in the flask is the sum of the partial pressures:
\[ P_F = P_{A,final} + P_{B,final} \]
Substituting the values:
\[ P_F = 300 \, \text{torr} + 250 \, \text{torr} \]
\[ P_F = 550 \, \text{torr} \]

### Final Answer
The final pressure in the flask is **550 torr**.

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