A 200.0 liter container of nitrogen gas has a pressure 6250 torr. If the container was compressed until its volume become exactly half of what it was, what is the pressure inside the container now in torr? Assume that the temperature remained the same.
Question
A 200.0 liter container of nitrogen gas has a pressure 6250 torr. If the container was compressed until its volume become exactly half of what it was, what is the pressure inside the container now in torr? Assume that the temperature remained the same.
Solution
This problem can be solved using Boyle's Law, which states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. In other words, if the volume decreases, the pressure increases, and vice versa.
The formula for Boyle's Law is P1V1 = P2V2, where:
- P1 is the initial pressure
- V1 is the initial volume
- P2 is the final pressure
- V2 is the final volume
Given in the problem:
- P1 = 6250 torr
- V1 = 200.0 liters
- V2 = 200.0 liters / 2 = 100.0 liters (since the volume is halved)
We need to find P2.
Substitute the given values into the formula:
6250 torr * 200.0 liters = P2 * 100.0 liters
Solve for P2:
P2 = (6250 torr * 200.0 liters) / 100.0 liters = 12500 torr
So, the pressure inside the container after it is compressed is 12500 torr.
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