Chapter

14

The Behavior of Gases

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 kilopascals2. _________________________ (V) in Liters3. _________________________ (T) in Kelvin4. _________________________ (n) in moles

• The amount of gas, volume, and temperature are factors that affect gas pressure.

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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

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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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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Section 14.2The 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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Graph of Boyle’s Law

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.

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Boyle’s Law says the pressure is inverse to the volume.

Note that when the volume goes up, the pressure goes down

#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.

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

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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?

#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...

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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?

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?

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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?

Section 14.3Ideal 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:

P ressure 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:

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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?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:

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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 space2. There _______________ attractive forces between particles

- otherwise there would be no liquids formed

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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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?

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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.

Section 14.4Gases: 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.

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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:

Sample Problem

Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (PO2) at 101.3 kPa of total pressure if the partial pressures 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.

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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 ProblemCompare 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

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Name __________________________________________ Date ___________________

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

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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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