#360. Independent Study Unit on the Gas Laws

Science, level: Senior
Posted Fri Mar 20 10:30:20 PST 1998 by Michael Edmondson (medmond@hotmail.com).
Hardaway High School/MCSD, Columbus, GA. USA
Materials Required: Paper, Pencil, Calculator
Activity Time: Several Days
Concepts Taught: Boyle's, Charles' and Combined Gas Laws

This is the first part of the unit. If you would like the whole unit, I can send it as a text file to you. (It is about 51K.)

GAS LAWS INDEPENDENT STUDY UNIT
BOYLE'S, CHARLES, AND THE COMBINED GAS LAWS

Michael H. Edmondson
Hardaway High School
medmond@hotmail.com

CONTENTS

Part A - Individual Unit........................................1

Objectives......................................................2

Concepts........................................................3

Pretest.........................................................4

Topic Introduction and Unit.....................................8

Boyle's Law Practice Problems..................................25

Boyle's Law - Computer Drill...................................27

Charles' Law Practice Problems.................................33

Charles' Law - Computer Drill..................................35

Combined Boyle's and Charles' Laws Practice Problems...........40

Combined Boyle's and Charles' Laws - Computer Drill............42

Posttest.......................................................44

Part B - Answer Keys...........................................46

PART A

INDEPENDENT STUDY UNIT
BOYLE'S, CHARLES, AND THE COMBINED GAS LAWS

Individual Unit
Gas Laws
Introductory Theory, Boyle's, Charles, and Combined Gas Laws
M. Edmondson

These are the objectives and concepts related to this individual unit on introductory theory to gas laws, Boyle's Law, Charles' Law, and the Combined Gas Law. The objectives are the major things which you need to be able to do at the completion of this unit. The concepts are the major ideas which are trying to be conveyed to you. Study them carefully, paying very close attention to the major items which you should ultimately be able to do.
The concepts have a small c beside them and match to the objective with the same number.

Objectives:

1. Use the Kinetic Theory as a model to explain the gas phase

2. Describe specific examples that show that gas molecules move

3. Describe the forces that become important when gases liquefy and why gases liquefy at different temperatures

4. State Boyle's Law mathematically and calculate changes in pressure or volume of gases using the law

5. Define different temperature scales

6. Convert to and from Celsius and Kelvin temperature scales

7. State Charles' Law mathematically and calculate changes in volume and/or temperature using the law

8. State the combined gas law mathematically and solve for temperature, pressure or volume when given all other conditions

Concepts:

1c. Gases exhibit definite behaviors that may be identified and analyzed.

2c. Gas molecules are in constant motion in all directions as demonstrated by diffusion.

3c. Van der Waals forces exist between all molecules and are necessary to explain the liquefaction of gases.

4c. Gas volume varies inversely with pressure.

5c. Temperature is a measure of the average kinetic energy of the molecule, represented by various temperature scales.

6c. oK = oC + 273

7c. Gas volume varies directly with temperature changes.

8c. Temperature, pressure and volume are all interrelated and several changes may occur simultaneously.

Directions: Choose the letter of the best or most correct answer. Write that letter on your answer sheet. DO NOT WRITE ON HERE. Choices not given on each question, but which may be used with any question are:

(e) More than one of the above
(f) All of the above
(g) None of the above

The correct answers are given in section B, after the individual unit.

1. What is standard temperature in Kelvin?
(a) 0 degrees Kelvin
(b) 273.25 degrees Kelvin
(c) 273 Kelvin
(d) 0 Kelvin

2. When pressure on a gas goes down what happens to volume?
(a) goes down
(b) stays the same
(c) rises, then falls
(d) falls

3. The rate of diffusion depends on what?
(a) speed, diameter of the molecule and attractive forces in the molecule
(b) speed and diameter of the molecule
(c) attractive forces in the molecules
(d) diameter of the molecule

4. The volume of a gas goes up. What is happening to the temperature?
(a) going up
(b) going down
(c) staying the same
(d) goes down, then up

5. What is absolute zero?
(a) the lowest temperature that has ever been reached
(b) the point at which all molecular motion stops
(c) standard temperature
(d) the point at which a gas occupies exactly 22.4 liters

6. How was the Kelvin temperature scale arrived at?
(a) it is arbitrary
(b) by adding 273 to the Celsius temperature
(c) through the observation that for each temperature increment the volume of an observed gas increases 1/273rd of the original volume
(d) the origin is uncertain

7. When pressure goes down, what happens to volume?
(a) goes up
(b) goes down
(c) remains the same
(b) goes up, then down

8. A gas has a probability of being located at any point in its container, no matter how large the container. This is a statement of the property of gases known as:
(a) low density
(b) diffusion
(c) expansion
(d) pressure

9. If volume is held constant and temperature goes down what happens to pressure?
(a) goes up
(b) goes down
(c) goes up, then down
(d) goes down, then up

10. Movement of a substance from a region of higher concentration to a region of lower concentration is a definition of what property of gases?
(a) low density
(b) diffusion
(c) expansion
(d) pressure

11. What is standard pressure in mm Hg?
(a) 760.
(b) 760.0
(c) 760.00
(d) 760.000

12. The abbreviation for standard conditions of temperature and pressure is
(a) STP
(b) STPV
(c) TP
(d) PV = nRT

13. What is the numerical value of absolute zero?
(a) -273.15 K
(b) 0.015 deg C
(c) 273 K
(d) 0 deg C

14. The temperature and volume of a gas are directly related. This is a statement of:
(a) the Combined Gas Laws
(b) Charles' Law
(c) Boyle's Law
(d) the Ideal Gas Law

15. P1 V1 P2 V2
_________ = ___________
T1 T2

The above is a mathematical statement of
(a) Boyle's Law
(b) Charles' Law
(c) Ideal Gas Law
(d) Combined Gas Law

16. An ideal gas
(a) exists at low temperatures
(b) is one that perfectly obeys the Ideal Gas Law
(c) is one that exists at high pressures
(d) has high attractive forces between the atoms in the molecule

17. The four observed properties of a gas are
(a) expansion, diffusion, low pressure, and low density
(b) expansion, diameter of molecules, diffusion, and pressure
(c) expansion, speed of the molecules, density, and temperature of the molecules
(d) expansion, low density, diffusion, and pressure

18. The volume of a gas is inversely proportional to the pressure on the gas. This statement reflects
(a) Boyle's Law
(b) Charles' Law
(c) the Ideal Gas Law
(d) the Combined Gas Laws

19. When temperature goes down, what happens to volume?
(a) goes down
(b) goes up, then down
(c) goes up
(d) goes down, then up

20. The mathematical statement of Charles' Law is
(a) T1 V1 = T2 V2
(b) T1 V2 = T2 V1
(c) T2 V1 = T1 V2
(d) T2 V2 = T1 V1

21. At which temperature would a gas most likely be moving the most rapidly (possess the most energy of motion)?
(a) 27 deg C
(b) 300 K
(c) 37 deg C
(d) 401 K

Directions: Read the following. As you go through, answer the questions that are asked of you, as completely and accurately as possible. This is Part A. On Part B, you will find the answers to each of the questions in this unit. The answers are numbered according to the question numbers in this part. Read the directions at the top of Part B for further instructions and information.

1. We know that matter exists in four forms.

These are called phases of matter.

Those phases are solid, liquid, gas, and plasma.

Chemistry deals with the first three (3) of these phases.

We will be studying the gas laws and gas properties in this "booklet."

2. Name the three states of matter that we study in Chemistry.

3. Name the state of matter that we will study now.

4. Matter is made up of atoms, molecules, and/or ions.

5. In Chemistry and Physics, there is a theory which is used to explain the properties of gases, liquids, and solids - the Kinetic Molecular Theory, also just called the Kinetic Theory.

6. Name the three types of particles which may compose matter.

7. What is the purpose of the Kinetic Theory?

8. The Kinetic Theory explains the properties of matter in terms of (1) the forces between the particles of matter and (2) the energy these particles possess.

9. What are the three basic particles of which matter is composed?

10. Most of the information in support of the Kinetic Theory comes from indirect observation.

(It is almost impossible at our present level of technology to directly observe the behavior of individual atomic particles.)

However, scientists can observe the behavior of large groups of particles, and can then make observations and draw conclusions from these observations.

11. What are the two ways in which the Kinetic Theory helps to explain the properties of matter?

12. The Kinetic Theory makes these three basic assumptions:

12a. Matter is composed of very tiny particles.

12b. The particles of matter are in continual motion.

12c. The particles of matter do not lose energy in collisions.

13. Let's look at these assumptions individually.

14. First -- matter is composed of very tiny particles.

This is to say that the chemical properties of matter depend upon the composition of the particles which compose matter.

For instance: an atom with 16 protons differs from one with 17 or 18 (or any other number) of protons.

The type and number of particles cause each type of matter to have its own set of chemical properties.

15. What are the three basic assumptions of the Kinetic Theory?

16. Secondly -- the particles of matter are in continual motion.

Their average kinetic energy (which is the type of energy possessed by anything in motion) depends upon the temperature.

As the temperature rises, the speed of the molecules increases.

As the temperature falls, the molecules slow down.

The temperature, then, determines the average kinetic energy of the molecules.

17. What do the chemical properties of matter depend on?

18. What does the kinetic energy of a molecule depend on?

19. What happens to the kinetic energy of a molecule as the temperature falls?

20. Lastly -- the molecules of matter do not lose energy in collisions.

When particles collide with each other or the sides of their containers, there is no energy loss (ideally).

These types of collisions are said to be elastic.

21. When no energy is lost in collisions, the collisions are said to be _________________.

22. Gases have four (4) characteristic properties:

22a. Expansion

22b. Pressure

22c. Low density

22d. Diffusion

23. Do molecules lose energy in collisions (ideally)?

24. What are the four characteristic properties of a gas?

25. Looking at the properties of a gas individually:

Expansion.

A gas does not have a definite shape or volume.

It will expand to completely fill any container to which it is added.

If you put a milliliter of hydrogen into a sphere the size of the universe, the gas will fill the sphere.

There would be a great deal of room introduced in between the molecules of hydrogen, but they would nevertheless be spread out all over the container.

What this really means is that there is, at any given moment, a chance of finding at least one molecule of the hydrogen gas in any location within the container, given the time necessary to traverse from one side of the container to the other.

26. What property of a gas have we just been over?

27. A gas has no definite ________________ or ________________.

28. A gas will completely fill any container into which it is added. True or false?

29. If you add two (2) molecules of oxygen to an otherwise empty room, will the oxygen molecules fill the room?

30. Next -- Pressure.

A balloon becomes larger when inflated because of increased pressure on the inside surface.

Then when you let air out, it shrinks because pressure is decreasing.

If you warm the balloon, it inflates because of the expansion of the gas and the following increase in pressure due to the faster speed of the molecules.

Pressure increases with increasing temperature, so long as volume is held constant.

31. Low density.

The density of a gas is about 0.001 (one thousandth) that of

the same substance in the solid state.

The difference in density is explained by the fact that the gas takes up more room, and since more volume is occupied, but the same amount of mass is present, the density decreases.

32. How is pressure affected by temperature?

33. Does a gas have a high or low density, as compared to the solid state of the same substance?

34. Which of these would you expect has a greater density - solid oxygen or liquid oxygen?

35. Lastly: Diffusion.

A gas will spread out spontaneously (without help) to uniformly occupy a space.

This is a process called diffusion.

This is characteristic of all gases.

36. The process of uniformly and spontaneously spreading out to fill a space is _______________________.

37. According to the Kinetic Theory, a gas consists of very small independent particles.

These particles move at random (in no certain direction) in space and experience perfectly elastic collisions.

That is to say they lose no energy in collisions.

This theoretical description of an imaginary gas that perfectly obeys the Kinetic Theory is a description of an ideal gas.

38. This gas is imaginary because no molecules can collide and retain all their energy.
Some energy is transferred; therefore, some energy is lost.

But, real gases at normal conditions (that is, not at high

pressures or extremely low temperatures) reasonably fit the ideal gas descriptions.

39. A _________ consists of very small independent particles. These particles move at ___________ and experience _____________ collisions.

40. The imaginary gas which we have described above is called a(n) _______________________.

41. Do molecules normally lose energy in collisions?

42. Would a gas under very high pressure fit the description of an ideal gas?

43. Gases consist of very small independent __________________.

44. Substances which are gases at room temperature consist of molecules. Some of these substances have only two atoms in them (ex. HCl); others have more than two atoms (ex. NH3).

Matter in the gaseous phase, as explained earlier, is much less dense than the same matter in either the solid or liquid phase.

In spite of this, 1 ml of a gas at 0 degrees Celsius and 1 atmosphere pressure still contains about 3 x 1019 molecules.

45. In gases, molecules are widely separated.

46. The kinetic energy of molecules of a gas (except at the condensation temperature) overcomes the attractive forces between the molecules.

The molecules of a gas are on the average essentially independent particles.

47. The molecules of a gas travel in random directions at high speeds.

48. The speed of molecules at 0 degrees Celsius and 1 atmosphere pressure is on the order of 1000 m/sec.

49. Substances which are gases at room temperature consist of ______________.

50. Molecules in gases are close together. True or false?

51. Matter is less dense in the ___________ phase.

52. Molecules travel in _________ directions at __________ speeds.

53. Kinetic energy overcomes the ____________ ______________ between molecules except near the condensation temperature of the gas.

54. At the average speed of 1000 m/sec, molecules are separated by about 10-7 m and undergo about 5 x 109 collisions per second.

55. The expansion and diffusion of gases are both explained by the fact that gas molecules are essentially independent particles, as said earlier.

Diffusion is slowed by the presence of other gas molecules, but the diffusion is not stopped.

56. Gas molecules are separated by (large, small, very small) distances.

57. The fact that gas molecules are essentially independent particles explains both ________________ and _________________.

58. The rate of diffusion of one gas through another depends on three properties of the intermingling gas particles:

58a. Speed of the molecules

58b. Diameter of the molecules
58c. Attractive forces between the molecules

59. Gas pressure results from the collisions of billions of

particles with the walls of the container.

60. Name three (3) factors which determine the rate of diffusion of one gas through another gas.

61. The result of billions of particles striking the sides of a container is ______________________.

62. Raising the temperature of a container raises the average kinetic energy of the molecules in the container.

63. Pressure drops when the number of molecules is lowered or when the temperature is lowered.

64. Molecules of a gas do not all have the same speed.

65. The temperature of a gas provides an indication of the average kinetic energy of the molecules present in the gas.

66. Name two ways to lower pressure in a container:
(a)
(b)

67. Molecules do not all have the same ___________________.

68. The average kinetic energy of molecules is indicated by the ___________________.

69. The lowest temperature at which a substance can exist as a gas at atmospheric pressure is the condensation temperature.

70. A gas below its condensation temperature does not have sufficient kinetic energy to keep the molecules apart.

It therefore condenses.

71. Studying condensation temperatures, then, gives an idea of how strong the attractive forces are between the molecules in a gas.

72. The weaker the attractive forces between molecules, the greater the ability for those molecules to stay apart.

Therefore, the condensation temperature will be lower.

The stronger the attractive forces between molecules, the higher the condensation temperature.

73. Define condensation temperature.

74. Why do gases condense?

75. An indication of the attractive forces between molecules is given by _____________________.

76. If a gas liquefies at a very low temperature, would the gas have very strong or very weak attractive forces?

77. Water condenses at 100 degrees Celsius.

Methane condenses at -161 degrees Celsius.

Which of the two gases has the greatest attractive force between molecules?

78. Ionic substances have the highest condensation temperatures of all.

Therefore, we can conclude that the strongest type of attractive forces exist in ionic compounds.

79. Which of the following has the highest condensation temperature?
(a) SO3
(b) CaS

80. Which compound of the following two have the strongest attractive forces between the atoms which compose it?
(a) SO3
(b) CaS

81. The attractive forces between molecules are known as van der Waal's forces.

82. Van der Waal's forces are important only when molecules are close together.

83. There are two types of van der Waal forces:

(a) dispersion interaction

(b) dipole-dipole interaction

84. Dispersion interaction exists between all molecules.

85. The strength of dispersion interaction depends upon the number of electrons present in the molecule and the strength with which they are bound.

86. Nonpolar molecules possess only dispersion interaction between the molecules.

87. The attractive forces between molecules are known as __________________.

88. The attractive forces between molecules are important only when the molecules are ___________ together.

89. Name the two (2) types of van der Waal's forces:
(a)
(b)

90. Where does dispersion interaction exist?

91. What determines the strength of dispersion interaction?

92. True or False: Nonpolar molecules do not possess dispersion interaction.

93. A given number of molecules can occupy widely different

volumes.

They can be compressed to a few cubic centimeters or can expand to fill a room.

94. Since the pressure that a gas exerts is a measure of the number of molecules colliding with the sides of the container, then to increase the pressure one must do something to increase the number of collisions with the sides of the container holding the gas.

95. Increasing temperature (if the volume which a gas occupies is constant) gives the molecules more energy and thus causes a rise in the number of collisions of molecules with the sides of the container.

This results in an increase in pressure.

96. Are gases very compressible?

97. Name one way to increase the pressure in a container.

98. If you decrease the number of collisions of molecules with the sides of its container, what will be the result?

99. Another way to increase the pressure is to decrease the volume which the gas is occupying.

The molecules have a shorter distance to travel, they conserve energy (by not traveling so far) and the collisions increase.

100. The result is the fact that, in measuring the volume of a gas, the pressure and temperature must be considered.

101. The volume of a gas depends on the pressure and the temperature.

102. Therefore, it is very important to have the advantage of a standard temperature and a standard pressure.

The purpose of the standard would be to compare other temperatures and pressures to the standard in order to

measure a gas' volume.

103. Name a second way to increase gas pressure.

104. In measuring the volume of a gas, both ____________ and __________ must be considered.

105. The volume of a gas depends on _________________ and _______________.

106. What is the purpose of having a standard temperature and pressure?

107. STP stands for standard temperature and pressure.

108. Standard temperature is 0 degrees Celsius.

109. Standard pressure is 760 mm Hg.

This is the pressure exerted by the atmosphere on a column of mercury at sea level.

The column of mercury rises 760 mm into a tube, which is closed on one end and has a vacuum existing within the tube.

110. Gas pressure varies with volume.

111. When you squeeze a hollow rubber ball, the volume decreases and the pressure within the ball increases.

When the squeezing ceases, the volume increases and the pressure decreases (falls) within the ball.

112. Robert Boyle, an English scientist, was the first person to make accurate observations showing how pressures and volumes were related.
113. STP stands for what?

114. What is 0 degrees Celsius also referred to as?

115. What is standard temperature?

116. What is standard pressure?

117. What is the abbreviation for standard temperature and pressure?

118. Gas pressure varies with _________________.

119. Who was Robert Boyle?

120. Boyle formulated a law relating to gases.

This law bears his name.

121. Boyle's Law states: The volume of a definite quantity of dry gas is inversely proportional to the pressure, provided the temperature remains constant.

122. This law means that if pressure increases, volume decreases.

123. This law also means that if pressure decreases, volume increases.

124. The mathematical expression for Boyle's Law is:

P1 V2
___ = ___
P2 V1

125. P1 represents the original pressure.

126. V1 represents the original volume.

127. P2 represents the final pressure.

128. V2 represents the final volume.

129. What was Boyle's Law concerned with?

130. If pressure increases, volume _____________. (increases, decreases)

131. If volume decreases, pressure _____________. (increases, decreases)

132. If volume increases, pressure _____________. (increases, decreases)

133. If pressure decreases, volume _____________. (increases, decreases)

134. Give the mathematical formula for Boyle's Law.

135. You know that with increasing pressure, volume decreases.

Let us say that you start with 700. mm Hg pressure and end with 800. mm Hg pressure.

The volume at 700. mm Hg pressure is 10.0 liters.

The pressure has increased.

136. You know that since pressure has increased, the new volume is less than the old volume.

So, the new volume is some fraction of the old volume.

To make the new volume smaller than the old volume, you must set up the pressure part of the problem so that it, when multiplied by the old volume, gives you a smaller number for the final volume.

Remember, this is what you would expect since the pressure is rising and naturally, the volume should be getting smaller.
137. To make the pressure side of the Boyle's Law equation a number which will make the volume to decrease, it must be a number less than one, since a number greater than 1 will

(when multiplied by the old volume) give you a larger number.

This would not be reasonable, nor (quite honestly) what you want.

138. If you have two (2) numbers, (in this case, 700. and 800.) you have two choices as to how to arrange them into a fraction.

How would you set them up to result in a number less than 1 as a result of their division?

139. It would not be 800./700., since that gives 1 and 1/7, which is more than one.

You do not want a number more than one.

140. If you use 700./800., then you obtain a number less than one.

It gives you, upon simplification, 7/8.

That is less than 1.

141. If you multiply 7/8 times 10.0 liters, then you get a number less than the original volume.

The new volume would be 8.750 liters.

The old volume did decrease.

142. Try this example.

The old pressure was 200. mm Hg.

The new pressure is 150. mm Hg.

The old volume was 10. ml.

The new volume is what?

143. The pressure has decreased this time, so what must the volume do?

144. Must the pressure fraction be more or less than one?

145. Does the volume increase or decrease?

146. How must the pressure fraction be set up?

147. Set up the pressure fraction.

148. What must you multiply the pressure fraction by to get the new volume?

149. What is the old volume?

150. What is the new volume?

151. Did the volume increase or decrease?

152. Did the volume do what it should do?

153. Another way to work these type problems is to substitute into the Boyle's Law equation.

154. Using the first example:
P1 = 700. mm Hg
P2 = 800. mm Hg
V1 = 10.0 liters
V2 = x liters

155. Boyle's Law equation:

P1 V2
____ = ____
P2 V1

156. 700. mm Hg V2
____ = ____ The problem is set up.
800. mm Hg 10.0 liters Next, cross-multiply.

157. (700. mm Hg)(10.0 liters)
V2 = _____________
(800. mm Hg)

158. 7000.
V2 = _____ liters
800.

159. V2 = 8.750 liters (mm Hg cancelled out, leaving you with the correct units of liters)