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` ?

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 into a `1 L` vessel at `27°C`, we can follow these steps:

### Step 1: Calculate the Partial Pressure of Hydrogen (H2)

1. **Identify the known values:**
- Volume of H2 (V1) = 0.5 L
- Initial pressure of H2 (P1) = 0.8 bar
- Final volume of the vessel (V2) = 1 L
- Final pressure of H2 (P2) = ?

2. **Apply Boyle's Law:**
Boyle's Law states that \( P_1 V_1 = P_2 V_2 \).

Substituting the known values:
\[ 0.8 \, \text{bar} \times 0.5 \, \text{L} = P_2 \times 1 \, \text{L} \]

3. **Calculate P2:**
\[ P_2 = \frac{0.8 \times 0.5}{1} = 0.4 \, \text{bar} \]

### Step 2: Calculate the Partial Pressure of Oxygen (O2)

1. **Identify the known values:**
- Volume of O2 (V1) = 2.0 L
- Initial pressure of O2 (P1) = 0.7 bar
- Final volume of the vessel (V2) = 1 L
- Final pressure of O2 (P2) = ?

2. **Apply Boyle's Law:**
\[ 0.7 \, \text{bar} \times 2.0 \, \text{L} = P_2 \times 1 \, \text{L} \]

3. **Calculate P2:**
\[ P_2 = \frac{0.7 \times 2.0}{1} = 1.4 \, \text{bar} \]

### Step 3: Calculate the Total Pressure of the Gas Mixture

1. **Add the partial pressures:**
- Partial pressure of H2 = 0.4 bar
- Partial pressure of O2 = 1.4 bar

Total pressure (P_total) = Partial pressure of H2 + Partial pressure of O2
\[ P_{\text{total}} = 0.4 \, \text{bar} + 1.4 \, \text{bar} = 1.8 \, \text{bar} \]

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

---