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Questions on Kinetic Theory and the Gas Laws

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R = 8.31JK^-1mol^-
k = 1.38 x 10-23 JK-1
standard atmospheric pressure 100.3kPa
mass of hydrogen molecule = 3.32x10-27kg


1. A fixed mass of gas at a constant temperature has a pressure of 50000Pa, and a volume of 3.2m^2. The pressure is changed to 80000Pa. What is the new volume?
2. Some gas enclosed by a piston is compressed isothermally from a volume of 5m^3 to 3m^3. If the initial pressure on it was 30kPa, what is the new pressure?
3. Some air in a sealed container at atmospheric pressure (100kPa) was heated from 20C to 100C. What is the new pressure inside the container?
4. Some gas contained within a syringe was heated from a temp of 25C to 95C, while the volume was allowed to expand from 50cm^3 to 55cm^3. If the initial pressure was 95000Pa, what is the new pressure?
5. To what temp (stated in C) should a sample of gas at 20C be heated if its volume is to rise by 25%, while the pressure falls by 10%?

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Solution Preview

1. For fixed mass and temperature, P1 * V1 = P2 * V2
Therefore, 50000 * 3.2 = 80000 * V2 => V2 = 2 (m^3)

2. Again, P1 * V1 = P2 * V2

Solution Summary

The solution provides quick step-by-step calculations for each question described on kinetic theory and the gas laws.

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Vacuum Question

vacuum chamber and pumper
large marshmallow

Wear safety goggles.

1. Place one large marshmallow in the vacuum chamber.
2. Cover the chamber with the dome and insert the pumper into the rubber septum.
3. Raise and lower the pumper slowly and observe what happens to the marshmallow.
4. The more times you pump, the more air is drawn out of the chamber.
5. After you have made your observations, you can release the vacuum and allow the pressure inside to return to atmospheric pressure. Do this by removing the pumper and squeezing the rubber septum as indicated.
6. Observe what happens to the marshmallow when the vacuum is released.
7. Remove the marshmallow.

Now try it with a balloon
1. Inflate the balloon to about an inch or two and tie a knot in it. It must fit in the chamber with room to spare so do not inflate it too much.
2. Place the small, inflated balloon in the chamber. Repeat steps 2 through 7.

The marshmallow has a large amount of air trapped in the pores of its carbohydrate structure. As the air is drawn out of the vacuum chamber, the pressure outside the marshmallow is reduced. The pressure of the air inside the marshmallow causes the air inside to expand. Thus you should have observed a change in the size of the marshmallow. A similar phenomenon occurs when the small, inflated balloon is placed in the chamber. As the air is removed from the chamber and the pressure is reduced on the outside walls of the balloon, the air pressure inside the balloon is greater than outside. It pushes the rubber walls of the balloon outward. You should observed a change in the size of the balloon.

In both experiments with the marshmallow and the balloon, once the vacuum was released, the air pressure inside the chamber increased back to atmospheric pressure.

1. Why does the air inside the marshmallow or balloon fill a larger volume when some of the air outside them is removed?
2. Why does the balloon return to its original size when the vacuum is released?
3. Can you explain this phenomenon in terms of the kinetic molecular theory of gases?
4. What gas law is being demonstrated by this expanding volume of gas as the pressure is being reduced?

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