one liter flask contains air and some liquid water at a pressure of 200mm of Hg .if this is connected to a evacuated vessel of same volume what will be the final pressure in each container

To solve the problem of what happens when a one-liter flask containing air and liquid water at a pressure of 200 mm of Hg is connected to an evacuated vessel of the same volume, we need to consider the principles of gas laws and the behavior of gases under pressure changes.

Understanding the Initial Conditions

Initially, we have a flask with air and liquid water at a pressure of 200 mm of Hg. The liquid water contributes negligibly to the pressure since it is incompressible, so we can focus on the air. The air in the flask is at a certain temperature and volume, and we can assume it behaves ideally.

Connecting the Evacuated Vessel

When the flask is connected to an evacuated vessel, the air will expand into the evacuated space. Since both containers have the same volume, we can use the ideal gas law to find the final pressure.

Applying the Ideal Gas Law

The ideal gas law is given by the equation:

• PV = nRT

Where:

• P = pressure
• V = volume
• n = number of moles of gas
• R = ideal gas constant
• T = temperature in Kelvin

Initial and Final States

Initially, the air in the flask has a pressure of 200 mm of Hg and occupies a volume of 1 liter. When the flask is connected to the evacuated vessel, the total volume becomes 2 liters. Assuming the temperature remains constant, we can express the initial and final states of the gas:

• Initial state: P₁ = 200 mm Hg, V₁ = 1 L
• Final state: P₂ = ?, V₂ = 2 L

Calculating the Final Pressure

Using the relationship of pressure and volume for a constant temperature (Boyle's Law), we can set up the equation:

P₁V₁ = P₂V₂

Substituting the known values:

200 mm Hg * 1 L = P₂ * 2 L

Now, solving for P₂:

P₂ = (200 mm Hg * 1 L) / 2 L = 100 mm Hg

Final Outcome

After connecting the flask to the evacuated vessel, the final pressure in both the flask and the evacuated vessel will be 100 mm of Hg. This demonstrates how gases expand to fill available space, and the pressure decreases when the volume increases, assuming temperature remains constant.

In summary, when the air from the flask is allowed to expand into the evacuated vessel, the pressure equalizes at 100 mm of Hg in both containers. This example illustrates the fundamental principles of gas behavior and the application of Boyle's Law in real-world scenarios.