To find the partial pressure of oxygen in the 50 ml vessel after transferring the contents from the 100 ml vessel, we can use Dalton's Law of Partial Pressures and some basic principles of gas behavior. Let's break this down step by step.
Understanding the Initial Conditions
In the 100 ml vessel, the total pressure is 760 mm Hg, which consists of the vapor pressure of water and the partial pressure of oxygen. At 80°C, the vapor pressure of water is given as 355 mm Hg. Therefore, we can calculate the partial pressure of oxygen in the 100 ml vessel.
Calculating the Partial Pressure of Oxygen
Using Dalton's Law, we know that:
- Total Pressure = Partial Pressure of Water + Partial Pressure of Oxygen
Substituting the known values:
- 760 mm Hg = 355 mm Hg + Partial Pressure of Oxygen
Now, we can solve for the partial pressure of oxygen:
- Partial Pressure of Oxygen = 760 mm Hg - 355 mm Hg = 405 mm Hg
Transferring the Gas to a Smaller Vessel
Next, we need to consider what happens when we pump the contents into a 50 ml vessel. The temperature remains constant at 80°C, and we assume that the amount of water vapor does not change significantly during this process.
Applying the Ideal Gas Law
When the gas is transferred to the smaller vessel, we can use the concept of gas behavior under constant temperature. The partial pressure of a gas in a smaller volume can be calculated using the ratio of the volumes, assuming the number of moles of gas remains constant.
The relationship can be expressed as:
- Partial Pressure in 50 ml = (Volume of 100 ml / Volume of 50 ml) * Partial Pressure in 100 ml
Substituting the values:
- Partial Pressure in 50 ml = (100 ml / 50 ml) * 405 mm Hg
This simplifies to:
- Partial Pressure in 50 ml = 2 * 405 mm Hg = 810 mm Hg
Final Considerations
However, we must remember that the total pressure in the 50 ml vessel cannot exceed the vapor pressure of water at 80°C, which is 355 mm Hg. Therefore, the partial pressure of oxygen will be limited by the total pressure that can be exerted in the vessel.
Since the vapor pressure of water remains constant, the partial pressure of oxygen in the 50 ml vessel will actually be:
- Partial Pressure of Oxygen = Total Pressure - Vapor Pressure of Water
Thus, the maximum partial pressure of oxygen in the 50 ml vessel is:
- Partial Pressure of Oxygen = 760 mm Hg - 355 mm Hg = 405 mm Hg
In summary, the partial pressure of oxygen in the 50 ml vessel, after considering the constraints of vapor pressure, remains at 405 mm Hg. This illustrates how gas behavior and pressure relationships work in practical scenarios.
