What will be the pressure of the gas mixture when `0.5 L` of `H_(2)` at `0.8` bar `2.0 L` of oxygen at `0.7` bar are introduced in a `1L` vessel at `27^(@)C` ?

Options

A. 1.8 bar
B. 2.8 bar
C. 3.0 bar
D. 5 bar

Explanation

To solve the problem of finding the pressure of the gas mixture when `0.5 L` of `H₂` at `0.8` bar and `2.0 L` of oxygen at `0.7` bar are introduced in a `1 L` vessel at `27°C`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- For Hydrogen (H₂):
- Volume (V₁) = 0.5 L
- Pressure (P₁) = 0.8 bar
- For Oxygen (O₂):
- Volume (V₂) = 2.0 L
- Pressure (P₂) = 0.7 bar
- Final Volume (V_f) = 1 L
- Temperature = 27°C = 300 K (converted to Kelvin)

2. **Use the Ideal Gas Law:**
The ideal gas law states that \( P \times V = n \times R \times T \). However, in this case, we can use the principle of partial pressures since we are dealing with a mixture of gases.

3. **Calculate the Partial Pressures in the Final Volume:**
The final pressure of the gas mixture can be calculated using the formula:
\[ P_f = \frac{P_1 \times V_1 + P_2 \times V_2}{V_f} \]
where:
- \( P_f \) = final pressure of the gas mixture
- \( P_1 \) = initial pressure of H₂
- \( V_1 \) = volume of H₂
- \( P_2 \) = initial pressure of O₂
- \( V_2 \) = volume of O₂
- \( V_f \) = final volume of the mixture

4. **Substitute the Values:**
\[ P_f = \frac{(0.8 \, \text{bar} \times 0.5 \, \text{L}) + (0.7 \, \text{bar} \times 2.0 \, \text{L})}{1 \, \text{L}} \]

5. **Calculate Each Term:**
- For H₂: \( 0.8 \, \text{bar} \times 0.5 \, \text{L} = 0.4 \, \text{bar} \cdot \text{L} \)
- For O₂: \( 0.7 \, \text{bar} \times 2.0 \, \text{L} = 1.4 \, \text{bar} \cdot \text{L} \)

6. **Add the Results:**
\[ P_f = \frac{0.4 + 1.4}{1} = \frac{1.8}{1} = 1.8 \, \text{bar} \]

7. **Final Answer:**
The pressure of the gas mixture in the 1 L vessel at 27°C is **1.8 bar**.