At constant temperature `200 cm^(3)` of `N_(2)` at 720 mm and `400 cm^(3)` of `O_(2)` at 750 mm pressure are put together in a litre flask. The final pressure of mixture is

Options

A. 111 mm
B. 222 mm
C. 333 mm
D. 444 mm

Explanation

To find the final pressure of the mixture of gases (N₂ and O₂) in a 1-liter flask, we can use Dalton's Law of Partial Pressures. Here’s the step-by-step solution:

### Step 1: Understand the Given Information
We have:
- Volume of N₂ (V₁) = 200 cm³
- Pressure of N₂ (P₁) = 720 mmHg
- Volume of O₂ (V₂) = 400 cm³
- Pressure of O₂ (P₂) = 750 mmHg
- Total volume of the flask (V_total) = 1 L = 1000 cm³

### Step 2: Calculate the Partial Pressure of N₂
Using the formula for partial pressure:
\[ P_{N₂} = \frac{P₁ \times V₁}{V_{total}} \]

Substituting the values:
\[ P_{N₂} = \frac{720 \, \text{mmHg} \times 200 \, \text{cm³}}{1000 \, \text{cm³}} \]

Calculating:
\[ P_{N₂} = \frac{144000}{1000} = 144 \, \text{mmHg} \]

### Step 3: Calculate the Partial Pressure of O₂
Using the same formula for O₂:
\[ P_{O₂} = \frac{P₂ \times V₂}{V_{total}} \]

Substituting the values:
\[ P_{O₂} = \frac{750 \, \text{mmHg} \times 400 \, \text{cm³}}{1000 \, \text{cm³}} \]

Calculating:
\[ P_{O₂} = \frac{300000}{1000} = 300 \, \text{mmHg} \]

### Step 4: Calculate the Total Pressure of the Mixture
According to Dalton's Law:
\[ P_{total} = P_{N₂} + P_{O₂} \]

Substituting the partial pressures:
\[ P_{total} = 144 \, \text{mmHg} + 300 \, \text{mmHg} \]

Calculating:
\[ P_{total} = 444 \, \text{mmHg} \]

### Final Answer
The final pressure of the mixture is **444 mmHg**.

---