## Saturday, 6 September 2014

### KINETIC THEORY OF GASES QUESTIONS AND PROBLEMS

KINETIC THEORY OF GASES

1. List six assumptions that you have to make about molecules when deriving the equation for the kinetic theory of gases.

2. (a) What is meant by the root mean square speed of gas molecules?
(b) what is the difference between the root mean square of  a group of gas molecules and their average speed?

3. (a) What do you see when looking at Brownian motion in air?
(b) What changes do you see if the air is heated?

4. (a) Sketch a graph to show the distribution of the number of molecules in a gas against their molecular speeds.
(b) Add a second line to show the same gas at a higher temperature

5. (a) A molecule of mass 3x10-26 kg moving at 4x102 ms-1 collides elastically with a wall. What is the change of momentum of the molecule?
(b) How long would it take this molecule to travel a distance of 0.4 m?

6. (a) Some bromine is added to a closed evacuated tube 0.4 m long.  Suggest the time that you might expect it to take for the brown bromine colour to move from one end of the tube to the other.
(b) Explain what would happen if the tube had been initially filled with air at atmospheric pressure and the experiment had been repeated.

7. Calculate the root mean square speeds for the following gases at a pressure of 105 Pa:
(a) air                    density 1.29 kgm-3                           (b) carbon dioxide          density 1.98 kgm-3
(c) nitrogen        density  1.25 kgm-3                          (d) chlorine                        density 3.21 kgm-3
(e) hydrogen     density 0.09 kgm-3

8. Calculate the pressure of three samples of air of density 1.29 kgm-3 with different root mean square speeds:
(a) 4.0x102 ms-1                 (b) 5.0x102 ms-1                                 (c) 6.0x102 ms-1

9. A sample of gas of volume 0.1 m3 and at a pressure of 2.0x105 Pa is enclosed in a cylinder. If the root mean square speed of the gas molecules is 5.5x102 ms-1 and the mass of each molecule is 3.5x10-26 kg calculate the number of gas molecules in the cylinder.

10 How does the motion of gas molecules affect the speed of sound through the gas?

11. A bottle of perfume is dropped onto the floor at one end of a long straight corridor. As it hits the floor it breaks. This event is observed by a student at the far end of the corridor.
Explain whether they will hear the sound or smell the scent first.

12. A sample of gas at a pressure of 1.5x105 Pa is contained in a cylinder with a volume of 0.05 m3. If there are 1.2x1025 molecules of gas in the cylinder with a root mean square speed of 350 ms-1 calculate the mass of one gas molecule.