400 ml gas at 500 torr and 666.6 ml gas at 600 torr taken in a container of 3 litre then the total pressure of mixture

Options

A. 200 torr
B. 400 torr
C. 600 torr
D. 50 torr

Answer

To find the total pressure of the gas mixture in a container, we can use Dalton's Law of Partial Pressures. Here’s how to solve the problem step by step:

### Step 1: Identify the given values
- For the first gas:
- Volume (V1) = 400 ml
- Pressure (P1) = 500 torr

- For the second gas:
- Volume (V2) = 666.6 ml
- Pressure (P2) = 600 torr

- Total volume of the container (Vf) = 3 liters = 3000 ml

### Step 2: Calculate the partial pressure of the first gas in the final volume
Using the formula for partial pressure:
\[ P_{1f} = P_1 \times \frac{V_1}{V_f} \]

Substituting the values:
\[ P_{1f} = 500 \, \text{torr} \times \frac{400 \, \text{ml}}{3000 \, \text{ml}} \]
\[ P_{1f} = 500 \, \text{torr} \times \frac{400}{3000} \]
\[ P_{1f} = 500 \, \text{torr} \times 0.1333 \]
\[ P_{1f} = 66.66 \, \text{torr} \]

### Step 3: Calculate the partial pressure of the second gas in the final volume
Using the same formula for the second gas:
\[ P_{2f} = P_2 \times \frac{V_2}{V_f} \]

Substituting the values:
\[ P_{2f} = 600 \, \text{torr} \times \frac{666.6 \, \text{ml}}{3000 \, \text{ml}} \]
\[ P_{2f} = 600 \, \text{torr} \times \frac{666.6}{3000} \]
\[ P_{2f} = 600 \, \text{torr} \times 0.2222 \]
\[ P_{2f} = 133.33 \, \text{torr} \]

### Step 4: Calculate the total pressure of the mixture
The total pressure (P_f) is the sum of the partial pressures:
\[ P_f = P_{1f} + P_{2f} \]
\[ P_f = 66.66 \, \text{torr} + 133.33 \, \text{torr} \]
\[ P_f = 200 \, \text{torr} \]

### Final Answer
The total pressure of the mixture is approximately **200 torr**.

---