Certain amount of gas is present in five litre vessels at 1.5atm pressure,one litre of water is filled in the vessels and it is further connected to two litre empty vessels.then find the partial final pressure of the gas in the vessels?

Question

Answer

The Problem

We have a 5-liter vessel containing a certain amount of gas at a pressure of 1.5 atm. We then add 1 liter of water to the vessel and connect it to two empty 2-liter vessels. We need to determine the partial final pressure of the gas in the vessels.

Understanding the Problem

To solve this problem, we need to consider the ideal gas law, which states that the pressure of a gas is directly proportional to its volume and inversely proportional to its temperature. In this case, the volume of the gas changes when water is added and the vessels are connected.

Solution

Step 1: Determine the initial volume of the gas

The initial volume of the gas is 5 liters.

Step 2: Determine the final volume of the gas

When 1 liter of water is added to the vessel, the total volume becomes 5 + 1 = 6 liters. Connecting it to two empty 2-liter vessels increases the total volume to 6 + 2 + 2 = 10 liters.

Step 3: Calculate the final pressure of the gas

To calculate the final pressure of the gas, we can use the formula:

P1V1 = P2V2

Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.

We know that the initial pressure P1 is 1.5 atm and the initial volume V1 is 5 liters. The final volume V2 is 10 liters.

Substituting these values into the formula, we have:

1.5 atm * 5 L = P2 * 10 L

Simplifying the equation, we get:

7.5 atm = P2 * 10 L

Dividing both sides by 10 L, we find:

P2 = 0.75 atm

Therefore, the partial final pressure of the gas in the vessels is 0.75 atm.

Conclusion

In summary, when 1 liter of water is added to the 5-liter vessel and connected to two empty 2-liter vessels, the final pressure of the gas in the vessels is 0.75 atm. This is calculated using the ideal gas law and considering the change in volume.

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