## Saturday, 6 September 2014

### Kinetic theory of gases 2 PROBLEMS

Kinetic theory of gases 2

Ideal gas constant (R) = 8.31 Jmol-1K-1     Avogadro’s number (NA) = 6.02x1023 mol-1

1. Use the data given on this page to calculate the value of the Boltzmann constant (k)

2.Calculate:
(a) the kinetic energy of an individual  gas molecule of mass 3.5x10-26 kg moving at a speed of 600 ms-1.
(b) the kinetic energy of the gas molecules in a cylinder at a temperature of 20 oC

3. A cylinder contains 2 moles of a gas composed of molecules with a mass of 2.5x10-26 kg moving with an r.m.s. speed of 500 ms-1. Calculate the temperature of the gas.

4. Two gases of density 1.35 kgm-3 (gas A) and 1.68 kgm-3 (gas B) are released into the air. If gas A diffuses at a rate of 0.2 ms-1 what is the rate of diffusion of gas B?

5. State Avogadro’s law.

6. A container of volume 1.5 m3 is full of gas with a density of 1.8 kgm-3 at a pressure of 1.4x105
Pa.
(a) Calculate the root mean square velocity of the molecules within the gas.
(b) If the mass of an individual molecule of the gas is 3.0x10-27 kg calculate the number of molecules in the container
7. A deuterium plasma contains deuterium ions of mass 4.9x10-27 kg at a temperature of 150x106 K.
Calculate:
(a) the r.m.s. speed and
(b) the kinetic energy of a deuterium ion in the plasma

8. Degrees of freedom:
(a) What is meant by a "degree of freedom" of a gas molecule?
(b) Describe the nature of the degrees of freedom for a monatomic molecule
(c) Describe the nature of the degrees of freedom for a diatomic molecule
(d) Which degree of freedom in your answer to part (c) is associated with the least energy?