Chapter 14 The Behavior of Gases

Chapter 14The Behavior of Gases

Did you hear about the chemist who was reading a book about Helium?  He just couldn't put it down.

14.1 Properties of Gases

OBJECTIVES:Explain why gases are easier to compress than solids or liquids are

Describe the three factors that affect gas pressure

CompressibilityGases can ______ to fill its

container, unlike solids or liquidsThe reverse is also true:

They are easily compressed, or squeezed into a smaller volume

Compressibility is a measure of how much the ______ of matter decreases under _________

Compressibility 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 gas particles closer together, which is possible because there is a ___________between them

Compressibility At __oC, the distance between particles is

about 10x the diameter of the particle Fig. 14.2Shows spacing betweenO2 and N2 moleculesin air

This empty space makes gases good _________ down & fur keep animals warm because the air ________

in them prevents heat from escaping the animal’s body) How does the volume of the particles in a gas

compare to the overall volume of the gas (kinetic theory)?

Variables that describe a Gas The four variables and their common

units:1. ________ (P) in kilopascals2. volume (V) in Liters3. temperature (T) in Kelvin4. ______ (n) in moles

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

1. Amount of GasWhen we inflate a balloon, we are

adding gas molecules. Increasing the number of gas

particles increases the number of _______thus, pressure increases

If temperature is constant, then doubling the number of particles doubles the ________

Pressure and the number of molecules are directly related

More molecules means more _______, and…

Fewer molecules means ______ collisions.

Gases naturally move from areas of high pressure to _____ pressure, because there is empty space to move into

Using Gas Pressure A practical application is

aerosol (spray) cansgas moves from higher

pressure to lower pressure

a _______ 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 _____ room to move.

The particles hit the _____ of the ________ more often.

As volume decreases, pressure increases. (syringe example)Thus, volume and pressure are

________ related to each other

3. Temperature of Gas Raising the temperature of a gas increases the pressure, if

the volume is held _________. (T and P are directly related) The faster moving molecules hit the walls harder, and

more frequently! Should you throw an aerosol can into a fire? When should your automobile tire pressure be checked?

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 mathematicalThe gas laws will describe HOW

gases behave.Gas behavior can be predicted by

the _______.The ______________ can be

calculated with mathematical equations.

You need to know both of these: the theory, and the math

Robert Boyle(1627-1691)

• Boyle was born into an aristocratic _____ family

• Became interested in ______ and the new science of Galileo and studied chemistry. 

• A founder and an influential fellow of the Royal Society of London

• Wrote extensively on science, philosophy, and theology.

Don’t you love my swell

scarf??

#1. Boyle’s Law - 1662Gas pressure is ________ proportional to volume, at a constant _________ (Check out this cool animation)

Pressure x Volume = a constant Equation: P1V1 = P2V2 (at a constant T)

As volume increases, pressure decreasesAn inverse relationship!

- Page 419

Jacques Charles (1746-1823)• French Physicist• Part of a scientific

balloon flight in 1783 – one of three passengers in the second balloon ascension that carried humans

• This is how his interest in gases started

• It was a _________ filled balloon – good thing they were careful!

#2. Charles’ Law - 1787For a fixed ____ (moles), gas volume is directly proportional to the _____ temperature, when pressure is _______.This extrapolates to zero volume at a temperature of zero Kelvin.

Charles’ Law Animation

VT

VT

P1

1

2

2 ( constant)

Converting Celsius to Kelvin•Gas law problems involving temperature always require Kelvin temperature.

Kelvin = C + 273 °C = Kelvin - 273and

- Page 421

Practice Problems 9-109. If a sample of gas occupies 6.80 L at

325oC, what will its volume be at 25oC if the pressure does not change?

10.Exactly 5.00 L of air at –50.0oC is warmed to 100.0oC. What is the new volume if the pressure remains constant?

Joseph Louis Gay-Lussac (1778 – 1850)

____ chemist and physicist

Known for his studies on the _________ properties of gases.

In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes.

#3. Gay-Lussac’s Law - 1802•The pressure and Kelvin temperature of a gas are directly proportional, provided that the ________ remains constant.

2

2

1

1

TP

TP

• How does a pressure cooker affect the time needed to cook food? (Note page 422)

Practice Problems 11-1211. A sample of nitrogen gas has a pressure of 6.58

kPa at 539 K. If the volume does not change, what will the pressure be at 211 K?

12. The pressure in a car tire is 198 kPa at 27oC. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire (assume the volume is constant).

#4. The Combined Gas LawThe combined gas law expresses the relationship between ______, volume and _________ of a fixed amount of gas.

2

22

1

11

TVP

TVP

Practice Problems 13-14

13. A gas at 155 kPa and 25oC has an initial volume of 1.00 L. The pressure of the gas increases to 605 kPa as the temperature is raised to 125oC. What is the new volume?

14. A 5.00 L air sample has a pressure of 107 kPa at – 50oC. If the temperature is raised to 102oC and the volume expands to 7.00 L, what will the new pressure be?

See Sample Problem 14.4, page 424 if needed

The combined gas law contains all the other gas laws!

If the temperature remains constant...

P1 V1

T1

x = P2 V2

T2

x

______ Law

The combined gas law contains all the other gas laws!

If the pressure remains constant...

P1 V1

T1

x = P2 V2

T2

x

________ Law

The combined gas law contains all the other gas laws!

If the volume remains constant...

P1 V1

T1

x = P2 V2

T2

x

_________ Law

14.3 Ideal Gases

OBJECTIVES:Compute the value of an

unknown using the ____ gas law

Compare and contrast real an ideal gases

5. The Ideal Gas Law #1 Equation: P x V = n x R x T Pressure times Volume equals the number

of moles (n) times the _________________ (R) times the Temperature in Kelvin.

R = ______ (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)

Units and the Ideal Gas Law

R = 8.31 L·kPa/K·mol (when P in kPa) R = ______ L·atm/K·mol (when P in atm) R = 62.4 L·mmHg/K·mol (when P in mmHg)

Temperature always in _______!!

We now have a new way to count _____ (the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions:

P x V R x T

The Ideal Gas Law

n =

Practice Problems A rigid container holds 685 L of He(g). At a

temperature of 621 K, the pressure of the gas is 1.89 x 103 kPa. How many grams of gas does the container hold?

A child’s lungs hold 2.20 L. How many moles of air (mostly N2 and O2) do the lungs hold at 37oC and a pressure of 102 kPa.

Ideal Gases We are going to assume the gases

behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure

Ideal gases do not really exist, but it makes the math easier and is a very close approximation.

Particles have no volume? ______! No attractive forces __________!

Ideal Gases There are no gases that are absolutely

“ideal” however… Real gases do behave “ideally” at

high temperature, and low pressure Because under these conditions, the

gas particles themselves are so far apart they take up a very small proportion of the gas’s volume and the IM forces are so weak that they can be ignored

Ideal Gas Law: Useful Variations PV = nRT

Replace n with _________ mass1. P x V = m x R x T

M m = mass, in grams M = molar mass, in g/mol

Rearrange equation 1 Molar mass = M = m R T

P V

n (moles) = mass (g) molar mass (g/mol)

Using Density in Gas Calculations ______ is mass divided by volume m V so, we can use a density value to give

us two values needed in PV = nRT Volume (usually 1 L) and… -, if we know the _________, because we

can calculate itgrams (from D) x 1 mole

grams

D =

Using Density in Gas Calculations

What is the pressure of a sample of CO2 at 25oC, with a density of 2.0 g/L?

PV = nRT P = V = 1 L, R = 8.31 L·kPa/mol·K n = 2.0 g x 1 mole/44.0 g = 0.045 mole

P = _____________________ = 113 kPa1 L

nRTV

Ideal Gases don’t exist, because:1. Molecules __ take up space2. There ____ ________ forces between

particles- otherwise there would be no liquids

Real Gases behave like Ideal Gases...

When the molecules are far apart.

The molecules take up a very small percentage of the space We can ignore the particle

volume. True at low pressures

and/or high temperatures

Real Gases behave like Ideal Gases…

When molecules are moving fast = _____________

Collisions are harder and ____. Molecules are not next to each other

very long. __________ forces can’t play a role.

Real Gases do NOT Behave Ideally…

When temperature is very low Because the low KE means particles

may ________ with one another for longer periods of time, _______ weaker IM forces to have an effect

When the pressure are _____ Because the particles are _______

together more closely and thus occupy a much ________ percentage of the volume

14.4 Gas Mixtures & Movements

OBJECTIVES:Relate the total pressure of a

mixture of gases to the partial pressures of its component gases

Explain how the molar mass of a gas affects the rate at which it diffuses and effuses

#7 Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

• P1 represents the “___________”, or the contribution by that gas.

•Dalton’s Law is useful in calculating the pressure of gases ________ over water – a common lab technique

Collecting a Gas over Water

A common lab technique for collecting and measuring a gas produced by a chemical reaction

The bottle is filled with water and inverted in a pan of water

As the gas is produced in a separate container, tubing is used to carry it to the bottle where it displaces the water in the bottle

When the level of the gas in the bottle is even with the water in the pan, the pressure in the bottle = atmospheric pressure

A graduated cylinder is often used to collect the gas (for ease of measuring the gas volume)

Atmosphericpressure

Gas beingproduced

Dalton’s Law of Partial Pressures If the gas in containers 1, 2 & 3 are all put into the

fourth, the pressure in container 4 = the ____ of the pressures in the first 3

2 atm + 1 atm + 3 atm = _ atm

1 2 3 4

Practice Problems Determine the total pressure of a gas

mixture containing oxygen, nitrogen and helium: PO2

= 20.0 kPa, PN2 = 46.7 kPa, PHe

= 20.0 kPa.

A gas mixture containing oxygen, nitrogen and carbon dioxide has a total pressure of 32.9 kPa. If PO2

= 6.6 kPa and PN2 = 23.0

kPa, what is the PCO2 ?

Diffusion and Effusion

Effusion = gas particles escaping through a tiny hole in a container

Both diffusion and effusion depend on the molar mass of the particle, which determines the _______ at a given ________ (= average KE)

Diffusion = molecules moving from areas of ____ to areas of ____ concentration

Is mathematical phenomenon caused by random movements of gas particles

Diffusion• describes the mixing of gases

• Molecules move from areas of high concentration to low concentration

• A function of probability

• Fig. 14.18, p. 435Two gases mix after the wall separating them is removed.

Effusion: a gas escapes through a tiny hole in its container - balloons slowly lose air over time

Diffusion and effusion are explained by the next gas law: Graham’s

8. Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar masses (M) of the gases.

Relationship based on: KE = ½ mv2

At a given temperature (avg KE) larger molecules will have lower velocities

RateA MB

RateB MA

=

Graham’s Law Explained Temperature is a measure of the average KE of

the particles in a sample of matter At a given temperature (say 25oC), the molecules

of a lighter gas will be moving faster than molecules of a heavier one, so…

Faster-moving particles spread out faster!

Light Gas = N2 (mw = 28 g/mol)

Heavy Gas = CO2 (mw = 44 g/mol)

KE = ½ mv2 KE = ½ mv2

Sample: compare rates of effusion of Helium (He) with Nitrogen (N2) – p. 436

With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

Helium effuses and diffuses 2.7 times faster than nitrogen – thus, helium escapes from a balloon quicker than air, which is ~79% N2!

Graham’s Law