SUPPLEMENTARY QUESTIONS

IDEAL GASES: Kinetic Model for Ideal Gases.

1. Give non mathematical explanations, in terms of molecules, for the

following:

a. A gas exerts a pressure on the walls of its container,

b. The gas pressure increases as the temperature increases.

2. State two quantities that increase when the temperature of a given

mass of a gas is increased at constant volume.

3. Eight molecules have the following speeds:

300, 400, 400, 500, 600, 600, 700, 900 m s-1.

Calculate their r.m.s speed. [579 m s-1]

4. The following table shows the distribution of speed of 20 particles:

Speed / m s-1 10 20 30 40 50 60

Number of

particles

1 3 8 5 2 1

Find:

a. The most probable speed [30 m s-1]

b. The average speed [34 m s-1]

c. The r.m.s speed [35 m s-1]

5. A cylinder of volume 30 10-3 m3contains 0.20 kg of oxygen gas at a

temperature of 300 K. Calculate:

a. the number of molecules of gas in the container, (the mass of a

mole of oxygen molecules is 0.032 kg) [3.80 1024]

b. the pressure exerted by the gas, [5.2 105 Pa]

c. the r.m.s speed of the molecules. [480 m s-1]

6. The r.m.s speed of helium at STP (1.01 105 Pa, 0 C) is 1.30 km s-1.

Calculate the density of helium at STP. [0.179 kg m-3]

7. The r.m.s speed of nitrogen molecules at 127 C is 600 m s-1. Calculate

the r.m.s speed at 1127 C. [1.12 km s-1]

8. According to the kinetic theory, the pressure p of an ideal gas is givne

by the equation =

< >, where is the density of the gas and

< > is the mean squared speed of the molecules.

a. Express in terms of the number of molecules N, each of mass m,

in a volume V.

b. It is assumed that kinetic theory that the mean kinetic energy is

directly proportional temperature, T in Kelvin. Use this

assumption, and the equation above to show that under certain

conditions p is directly proportional to T.

9. Air contains oxygen and nitrogen molecules. State, with a reason,

whether the following are the same for oxygen and nitrogen molecules

in air at a given temperature:

a. the average kinetic energy per molecule;

b. the r.m.s speed.

10.

a. State an algebraic relationship between the molar mass M of an

ideal gas and the mass m of one of its molecules. Identify any

other symbol used.

b. The Earths atmosphere at ground level consists principally of

oxygen (molar mass 0.032 kg) and nitrogen (molar mass 0.028

kg), both gases being at the same temperature. Calculate the ratio

of the r.m.s speeds of the molecules of the gases. [0.935]

11.

a. Write down an equation relating the pressure p and the volume V

of an ideal gas and the mean square speed < > of the

molecules of the ideal gas. Define any other terms that appear in

the equation.

b. A volume of 71 200 cm3 of a certain ideal gas contains 1.02 1024

atoms. The gas has a density 0.800 kg m-3.

i Calculate the mass of one atom of the gas [5.53 10-26 kg]

ii The pressure exerted by this gas is measured, and is found to

be 80.0 kPa.

I. Calculate the r.m.s speed of the atoms of the gas [548 m s-

1]

II. Calculate the temperature of the gas [401 K]

12. Two moles of argon have a mass of 0.036 kg and occupy a rigid

container of volume 4.0 10-2 m3 at a pressure of 1.0 105 Pa.

Calculate:

a. the root mean square of an argon atom, [580 m s-1]

b. the temperature of the argon gas, [241 K]

c. the total internal energy of the gas atoms. [6000 J]

The safety valve in the container will open if the pressure of the gas

inside it exceeds 1.5 105 Pa. If the gas is now heated, calculate:

d. the temperature at which the safety valve will open [361 K]

13. Describe how the concept of absolute zero of temperature is explained

in terms of

a. the ideal gas laws,

b. the kinetic theory of gases.

14. Calculate, for ideal gas molecules, the ratio ..

.. [1.38]