1. Chapter
14
The Behavior of Gases

2. OBJECTIVES:
 Explain why gases are easier to compress than solids or liquids are.
 Describe the three factors that affect gas pressure.
Compressibility
 Gases can ______________________ to fill its container, unlike solids or liquids
 The reverse is also true:
 They are easily __________________________, or squeezed into a
smaller volume
 Compressibility is a measure of how much the volume of matter decreases
under pressure
 This is the idea behind placing “air bags” in automobiles
 In an accident, the air compresses more than the steering wheel or dash
when you strike it
 The impact forces the gas particles closer together, because there is a
________________________________________________ between them
 At room temperature, the distance between particles is about 10x the diameter of
the particle
 This empty space makes gases good ____________________________(example:
windows, coats)
 How does the volume of the particles in a gas compare to the overall volume of
the gas?
Variables that describe a Gas
 The four variables and their common units:
1. _________________________ (P) in kilopascals
2. _________________________ (V) in Liters
3. _________________________ (T) in Kelvin
4. _________________________ (n) in moles
• The amount of gas, volume, and temperature are factors that affect gas pressure.
1. Amount of Gas
 When we inflate a balloon, we are __________________________ gas
molecules.
 Increasing the number of gas particles increases the number of collisions
 thus, the ____________________________________________
 If temperature is constant, then doubling the number of particles doubles the
pressure
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3. Pressure and the number of molecules are directly related
 More molecules means more collisions, and…
 Fewer molecules means fewer collisions.
 Gases naturally move from areas of
____________________________________________________, because there
is empty space to move into – a spray can is example.
Common use?
 A practical application is Aerosol (spray) cans
 gas moves from higher pressure to lower pressure
 a propellant forces the product out
 whipped cream, hair spray, paint
 Fig. 14.5, page 416
 Is the can really ever “empty”?
2. Volume of Gas
 In a smaller container, the molecules have less room to move.
 The particles hit the sides of the container more often.
 As volume decreases, pressure increases. (think of a syringe)
 Thus, volume and pressure are ___________________________________
to each other
3. Temperature of Gas
 Raising the temperature of a gas increases the pressure, if the volume is held
constant. __________________________________________________________
 The molecules hit the walls harder, and more frequently!
 Should you throw an aerosol can into a fire? What could happen?
 When should your automobile tire pressure be checked?
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4. Name ____________________________________________ Date _________________
Chapter 14 Section Review
1. How does kinetic theory explain the compressibility of gases?
2. What variables and units are used to describe a gas?
3. What affects do the changes in the amount of gas and in the volume of the
container have on gas pressure?
4. What is the effect of temperature change on the pressure of a contained gas?
5. What would you have to do to the volume of a gas to reduce its pressure to one-
quarter of the original value, assuming that the gas is at a constant temperature?
6. Keeping the temperature constant, how would you increase the pressure in a
container by one hundredfold?
7. The manufacturer of an aerosol deodorant packaged in a 150 mL container wishes
to produce a container of the same size that will hold twice as much gas. How will
the pressure of the gas in the new product compare with that of the gas in the
original container?
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5. Section 14.2
The Gas Laws
OBJECTIVES:
 Describe the relationships among the temperature, pressure, and volume of a gas.
 Use the combined gas law to solve problems.
The Gas Laws are mathematical
 The gas laws will describe HOW gases behave.
 Gas behavior can be predicted by the theory.
 The amount of change can be calculated with mathematical equations.
 You need to know both of these: the theory, and the math
#1. Boyle’s Law - 1662
Gas ___________________________________________________________________,
when temperature is held constant.
 Pressure x Volume = a constant
 Equation:
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6. Graph of Boyle’s Law
Boyle’s Law says the pressure is inverse to
the volume.
Note that when the volume goes up, the
pressure goes down
Example Problem
A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume when the helium
when the balloon rises to an altitude where the pressure is only 25.0 kPa? (assume the
temperature remains constant.
#2. Charles’s Law - 1787
 The volume of a fixed mass of gas is directly proportional to the Kelvin temperature,
when pressure is held constant.
 This extrapolates to zero volume at a temperature of zero Kelvin.
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7. Converting Celsius to Kelvin
• Gas law problems involving temperature will always require that the temperature
be in Kelvin. (Remember that no degree sign is shown with the kelvin scale.)
• Reason? There will never be a zero volume, since we have never reached
absolute zero.
Kelvin = °C + ___________ and °C = Kelvin - ___________
Example Problem
A balloon inflated in a room at 24 degrees Celsius has a volume of 4.00 L. The balloon is
then heated to a temperature of 58 degrees Celsius. What is the new volume if the
temperature remains constant?
#3. Gay-Lussac’s Law - 1802
The pressure and Kelvin temperature of a gas are directly proportional, provided that the
volume remains constant.
Example Problem
The gas left in a used aerosol can is at a pressure of 103kPa at 25 degrees Celsius. If this
can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928
degrees Celsius?
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8. #4. The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and
temperature of a fixed amount of gas.
 The combined gas law contains all the other gas laws!
 If the temperature remains constant...
 If the pressure remains constant...
 If the volume remains constant...
Example Problem
The volume of a gas filled balloon is 30.0 L at 40 degrees Celsius and 153kPa pressure.
What volume will the balloon have at standard temperature and pressure?
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9. Name __________________________________ Date ___________________________
14-2 Section Review
1. State Boyles law, Charles law, and Guy-Lussac’s law.
2. Explain how the combined gas law can be reduced to the other three gas laws.
3. Write the mathematical equation for Boyle’s law and explain the symbols. What
must be true about the temperature?
4. A given mass of air has a volume of 6.00 L at 101 kPa. What volume will it
occupy at 25.0 kPa if the temperature does not change?
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10. Section 14.3
Ideal Gases
OBJECTIVES:
 Compute the value of an unknown using the ideal gas law.
 Compare and contrast real an ideal gases.
5. The Ideal Gas Law #1
 Equation:
 Pressure times Volume equals the number of moles (n) times the Ideal Gas
Constant (R) times the Temperature in Kelvin.
 R = 8.31 (L x kPa) / (mol x K)
 The other units must match the value of the constant, in order to cancel out.
 The value of R could change, if other units of measurement are used for the other
values (namely pressure changes)
 We now have a new way to count moles (the amount of matter), by measuring T,
P, and V. We aren’t restricted to only STP conditions:
Ideal Gases
 We are going to assume the gases behave “ideally”- in other words, they
____________________________________________________under all
conditions of temperature and pressure
 An ideal gas does not really exist, but it makes the math easier and is a close
approximation.
 Particles have no volume? ______________________
 No attractive forces? __________________________
 There are no gases for which this is true (acting “ideal”); however,
 Real gases behave this way at
a) __________________________________________
b) __________________________________________
 Because at these conditions, a gas will stay a gas
Example Problem
You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas (N2) (g) to a
final pressure of 2.00 x 104 kPa at 28 degrees Celsius. How many moles of N2 (g) does
the cylinder contain?
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11. Example Problem 2
A deep underground cavern contains 2.24 x 106 L of methane gas (CH4) (g) at a pressure
of 1.50 x 103 kPa and a temperature of 42 degrees Celsius. How many kilograms of CH4
does this natural gas deposit contain?
#6. Ideal Gas Law 2
Equation:
 Allows LOTS of calculations, and some new items are:
 m = mass, in grams
 M = molar mass, in g/mol
Molar mass =
Density
 Density is mass divided by volume
so,
Real Gases and Ideal Gases
Ideal Gases don’t exist, because:
1. Molecules ___________ take up space
2. There _______________ attractive forces between particles
- otherwise there would be no liquids formed
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12. Real Gases behave like Ideal Gases...
 When the molecules are ___________________________
 The molecules do not take up as big a percentage of the space
 We can ignore the particle volume.
 This is at ____________________________________
 When molecules are moving fast
 This is at ______________________________________
 Collisions are harder and faster.
 Molecules are not next to each other very long.
 Attractive forces can’t play a role.
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13. Name ____________________________________________ Date _________________
14.3 – Section Review
1. How is it possible to determine the amount (moles) of a gas in a sample at given
conditions of temperature, pressure and volume?
2. What is the difference between an ideal gas and a real gas?
3. Explain the meaning of this statement: “No gas exhibits ideal behavior at all
temperatures and pressures.” At what conditions do real gases behave like ideal
gases? Why?
4. Determine the volume occupied by 0.582 mol of a gas at 15 degrees Celsius if the
pressure is 81.8 kPa
5. If 28.0 g of methane gas (CH4) are introduced into an evacuated 2.00 L gas
cylinder at a temperature of 35 degrees Celsius, what is the pressure inside the
cylinder? Note that the volume of the gas cylinder is constant.
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14. Section 14.4
Gases: Mixtures and Movements
OBJECTIVES:
 Relate the total pressure of a mixture of gases to the partial pressures of
the component gases.
 Explain how the molar mass of a gas affects the rate at which the gas
diffuses and effuses.
#7 Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = _____________________________
• P1 represents the “partial pressure”, or the contribution by that gas.
• Dalton’s Law is particularly useful in calculating the pressure of gases collected
over water.
 If the first three containers are all put into the fourth, we can find the
pressure in that container by adding up the pressure in the first 3:
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15. Sample Problem
Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is
the partial pressure of oxygen (PO ) at 101.3 kPa of total pressure if the partial pressures
2
of nitrogen, carbon dioxide, and other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa
respectively?
Diffusion is:
• Molecules moving from areas of ____________
concentration to ___________ concentration.
 Example: perfume molecules spreading across the
room.
• Effusion: Gas escaping through a tiny hole in a container.
• Both of these depend on the
_______________________________________________,
which determines the speed.
Effusion: a gas escapes through a tiny hole in its container
-Think of a nail in your car tire…
Diffusion and effusion are explained by the next gas law: Graham’s Law
8. Graham’s Law
 The rate of effusion and diffusion is ___________________________________
to the square root of the molar mass of the molecules.
Sample Problem
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16. Compare the rates of effusion of the air component nitrogen (molar mass = 28.0 g) and
helium (molar mass = 4.0 g)
 With effusion and diffusion, the type of particle is important:
 Gases of lower molar mass diffuse and effuse _______________________
than gases of higher molar mass.
 Helium effuses and diffuses __________________________ than nitrogen – thus,
helium escapes from a balloon quicker than many other gases
Name __________________________________________ Date ___________________
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17. 14.4 – Section Review Questions
1. How is the partial pressure of a gas in a mixture calculated?
2. Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and
helium if the partial pressures of the gases are as follows PO2 = 20.0 kPa, PN2 =
46.7 kPa, and PHe = 26.7 kPa
3. How is the rate of effusion of a gas calculated?
4. Compare the rates of effusion of helium and oxygen
5. At the same temperature, the rates of diffusion of carbon monoxide and nitrogen
are vitually identical. Explain how this happens?
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