Ideal Gases

6. Compute (a) the number of moles and (b) the number of molecules in 1.00 cm³ of an ideal gas at a pressure of 100 Pa temperature of 220 K.

7. The best laboratory vacuum has a pressure of about . How many gas molecules are there per cubic centimeter in such vacuum?

11. Oxygen gas having a volume of 1000 cm³ at 40.0^CC and Pa expands until its volume is 1500 cm and its pressure is 1.06x10 Pa. Find (a) the number of moles of oxygen present and (b) the final temperature of the sample.

12. An automobile tire has a volume of 1000 cm³ and contains air at a gauge pressure (pressure above atmospheric pressure) of 165 kPa when the temperature is 0°C. What is the gauge pressure of the air in the tire when its temperature rises to 27.0°C and its volume increases to Pa.

m^J? Assume atmospheric pressure is 1.01 x 10 Pa.

13. A quantity of ideal gas at 10.0°C and 100 kPa occupies a volume of 2.50 m³. (a) How many moles of the gas are present?(b) If the pressure is now raised to 300 kPa and the temperature is raised to 30.0^CC, how much volume does the gas occupy? Assume no leaks.

3. Estimate the number of molecules in a flask of volume 5x10 m³ which contains oxygen gas at a pressure of 2x10⁵ Pa and temperature of 300 K. (2.5x10²² )

4. A mixture contains two types of gas A and В each of mass m kg. The partial pressures of A and В are and respectively. Show how the ratio of the relative molecular masses of A and В can be obtained from this information.

5. Hydrogen gas which has just been released in an electrolytic process consists of hydrogen atoms and not molecules. If all the hydrogen atoms pair off to form molecules, what will happen to the pressure of the gas at the same temperature and volume? (Pressure is halved)

Kinetic theory of ideal gas

3. Calculate the mean kinetic energy of each molecule for an ideal gas at a temperature of (a)300 К (b)10 000K. Does the kinetic energy calculated depend on the mass of the molecules? Explain. (Ans.6.21 xl0^-21 J, 2.07 xl0^-19 J, No.)

14. At what temperature is the rms speed of oxygen molecules equal to the rms speed of hydrogen molecules at 0°C?

15. A flask contains a mixture of mercury vapor, neon, and helium. Compare

1. the average kinetic energies of the three types of atoms;

2. the root-mean-square speeds.

The molecular masses are: helium, 4 g/mol; neon 20 g/mol; mercury 201 g/mol.

17. Smoke particles in the air typically have masses of the order of 10^-16 kg. The Brownian motion of these particles resulting from collisions with air molecules can be observed with a microscope.

a)Find the root-mean-square speed of Brownian motion for such a particle in air at 300 К.

b) Would the speed be different if the particle were in hydrogen gas at the same temperature? Explain.

18. What is the average translational kinetic energy of a molecule of oxygen at a temperature of 300 K?

1. What is the average value of the square of its speed?

2. What is the root-mean-square speed?

3. What is the momentum of an oxygen molecule traveling at this speed?

4. Suppose a molecule traveling at this speed bounces back and forth between opposite sides of a cubical vessel 0.10 m on a side. What is the average force it exerts on the walls of the container? (Assume that the molecule's velocity is perpendicular to the two sides that it strikes.)

6. What is the average force per unit area?

7. How many molecules traveling at this speed are necessary to produce an average pressure of 1 atm?

h) Compute the number of oxygen molecules actually contained in a vessel of this size, at 300 К and atmospheric pressure.

i) Your answer for (h) should be three times as large as the answer for (g). Where does this discrepancy arise?

19. Calculate the rms speed of helium atoms at 1000 K.

19. The lowest possible temperature in outer space is 2.7 K. What is the root-mean-square speed of hydrogen molecules at this temperature?

19. Find the rms speed of argon atoms at 313 K.

22. The temperature and pressure in the Sun's atmosphere are К

and 0.0300 Pa. Calculate the rms speed of free electrons (mass =9.1x10^-19 kg) mere, assuming they are an ideal gas.

The internal energy of a fixed mass of ideal gas depends on

A its pressure

В its temperature

С its volume

D its pressure and volume

2. The effective number of degree of freedom for N₂ gas at room temperature is

A 3 В 5\ С 6 D 7

3. The mean kinetic energy of CO₂ gas molecules at temperature Г is

A ~ В С D

4. The pressure of an ideal gas in a closed container is , and the mean kinetic energy of the molecules is E. If the mean kinetic energy increases to 9E, what is the pressure of the gas?

А З 'B 9 С 27 D 81

5. The r.m.s. speed of the molecules of an ideal gas at pressure and volume is . What is the r.m.s. speed of the molecules?

А З В 4 С 6 D 9

6. The mean kinetic energy of molecules of an ideal diatomic gas at a temperature is E. What is the mean kinetic energy of molecules of an ideal monoatomic gas at a temperature 2 ?

A 0.5E В 0.6Е С 1.2Е D 2E

7. Starting from the kinetic theory equation > and the ideal gas equation , derive an expression for the internal energy of one mole of ideal

monoatomic gas in terms of R, the molar gas constant and .