If 720 litres of a gas were collected over water at `25^(@)C` and 720 mm then the volume of the dry gas at the same temperature and pressure is (aq. Tension of water at `25^(@)C` = 23.8 mm)

Options

A. 696.2 litres
B. 360 litres
C. 743.8 litres
D. 1440 litres

Answer

To solve the problem of finding the volume of dry gas collected over water, we will follow these steps:

### Step 1: Understand the Given Information
- Volume of gas collected over water (V1) = 720 liters
- Total pressure of the gas collected (P1) = 720 mm Hg
- Vapor pressure of water at 25°C (P_water) = 23.8 mm Hg

### Step 2: Calculate the Pressure of the Dry Gas
The pressure of the dry gas (P_dry) can be calculated using the formula:
\[ P_{dry} = P_{total} - P_{water} \]
Substituting the values:
\[ P_{dry} = 720 \, \text{mm Hg} - 23.8 \, \text{mm Hg} = 696.2 \, \text{mm Hg} \]

### Step 3: Use the Ideal Gas Law
Since we are looking for the volume of the dry gas at the same temperature and pressure, we can use the relationship between the pressures and volumes of the wet and dry gases. According to Boyle's Law:
\[ \frac{P_1}{V_1} = \frac{P_2}{V_2} \]
Where:
- \( P_1 = 720 \, \text{mm Hg} \) (pressure of wet gas)
- \( V_1 = 720 \, \text{liters} \) (volume of wet gas)
- \( P_2 = 696.2 \, \text{mm Hg} \) (pressure of dry gas)
- \( V_2 \) = ? (volume of dry gas)

### Step 4: Rearranging the Equation
Rearranging the equation to solve for \( V_2 \):
\[ V_2 = V_1 \times \frac{P_1}{P_2} \]

### Step 5: Substitute the Values
Substituting the known values into the equation:
\[ V_2 = 720 \, \text{liters} \times \frac{720 \, \text{mm Hg}}{696.2 \, \text{mm Hg}} \]

### Step 6: Calculate the Volume of Dry Gas
Calculating \( V_2 \):
\[ V_2 = 720 \times \frac{720}{696.2} \approx 720 \times 1.0343 \approx 743.1 \, \text{liters} \]

### Step 7: Conclusion
The volume of the dry gas at the same temperature and pressure is approximately **743.1 liters**.