Chapter 10

The Three Common States of Matter

• Solids– shape & volume ?

• Liquids – shape & volume ?

• Gases – shape & volume ?

solids

liquids

gases

Kinetic Theory - Gases• Kinetic Theory- matter is made of tiny particles

that are in constant motion (Kinetic energy)

• Gas is composed of molecules or atoms that are considered to be small, hard spheres that have insignificant volume.

• Gas particles are far apart, and have no attractive or repulsive forces between them.

Kinetic Theory - Gases

• Gas particles move rapidly in constant random motion in straight paths independent of each other.

– O2 molecules in air travel 1700 km/hr (> 500 mph)

• Gases fill their containers and diffuse into space without limit.

Kinetic Theory - Gases

• Gas particles move extremely fast until they strike another particle or side of the container

• Collisions are perfectly elastic meaning that during a collision, kinetic energy is transferred without loss so kinetic energy stays constant

Gas Pressure• Why does the water stay in the cup?

• Gas Pressure – The force exerted by a gas per unit surface area of an object

• Atmospheric pressure results from collisions of air molecules with objects. It is based on the mass of one square inch of air reaching to the top of the atmosphere (75 miles!!) The weight is 14.7 pounds. The pressure is 14.7 PSI (pounds per sq. inch)

Barometers and Air Pressure• Older barometers measured the

height of mercury in a tube which depended on the pressure created by collisions of air molecules with the surface of Hg.

• At sea level, the pressure supports a column of Hg at 760 mm high. So 1 atmosphere = 760 mm Hg

= 101.3 kPa = 14.7 PSI

Measuring Pressure

• Si unit of pressure is pascal (Pa).

• Atmospheric pressure at sea level is ~101.3 kilopascals (kPa)

• Other units are millimeters of mercury• ( 760 mm Hg) and atmospheres ( 1 atm)

STP = OºC and 101.3 kPa

Kinetic Energy and Kelvin Temperature

• When a substance is heated, the average kinetic energy of the substance increases (there is a wide range of speeds that molecules are moving so we use average kinetic energy).

• Temperature is the measurement of the average kinetic energy of a substance

• Kelvin scale reflects relationship between temperature and average kinetic energy

• Absolute zero is the temperature where all particles cease movement

Temperature Conversions• Absolute zero is the lowest possible

temperature: Equal to 0 Kelvin = -273.15°C

• The Kelvin scale has no degree symbol • Zero Celsius is 273 Kelvin:

K = °C + 273 °°C = K - 273 °

• Standard temperature is 0°C or 273 K

3 Properties of Gases1. Compressibility is measure of how much the

volume of matter decreases with increased pressure. Gases are easily compressed because of the space between molecules

2. No attractive or repulsive forces exist between atoms or molecules

3. Gas particles move rapidly in constant random motion in straight paths independently of each other

4 Variables That Describe a Gas1. Pressure- (P) in kilopascals2. Volume- (V) in liters3. Temperature- (T) in Kelvins4. Number of moles- (n)• Gas laws will enable you to predict

gas behavior at specific conditions

Factors Affecting Gas Pressure

Amount, Volume, and Temperature

Amount of Gas

• Increasing the number of particles increases the number of collisions so the pressure increases (↑)

• Keeping the temperature constant, doubling the number of particles doubles the pressure

• When a sealed container of gas under pressure is opened, the gas moves from the region of higher pressure to the region of lower pressure

Volume

• Pressure can be raised by reducing the volume of the gas• The more the gas is compressed, the greater the pressure it

exerts inside the container• Reducing volume by half doubles the pressure• Increasing the volume has the opposite effect of decreasing

the pressure• Doubling the volume halves the pressure

Temperature

• Speed and kinetic energy of gas particles increase as particles absorb thermal energy

• Faster moving particles impact the walls of their container with more energy, exerting more pressure

• If average kinetic energy of gas doubles, the Kelvin temperature doubles, and pressure of the enclosed gas also doubles

The Gas Laws

Boyle’s, Charles’, Gay-Lussac’s, and the Combined Gas Laws

Boyle

Charles

Pressure-Volume RelationshipBoyle’s Law

• For a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure

• If volume goes, pressure goes • If pressure goes , volume goes

• The product of pressure and volume at any 2 sets of conditions at given temp is constant so…… P1 x V1 = P2 x V2

A high altitude balloon contains 30.0 L of He gas at 103 kPa. What is the volume when balloon increases altitude to when pressure is 25.0 kPa?

• P1 x V1 = P2 x V2

– P1 = 103 kPa

– P2 = 25.0 kPa

– V1 = 30.0 L

• V2 = ?

• 103 kPa x 30.0 L = V2 x 25.0 kPa

• V2 = 124 L• Does this make sense? Yes, a decrease in

pressure at constant temperature corresponds to a proportional increase in volume.

• The pressure on 2.50 L of anesthetic gas changes from 105 kPa to 40.5 kPa. What will be the new volume if the temperature remains constant?

• What is the unknown?• What will happen to the size of the unknown?

• Answer:(2.5 L) (105 kPa) = (? L) (40.5 kPa)

? = 6.5 L

• A gas with a volume of 4.0 L at a pressure of 205 kPa is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant?

• What will happen to the pressure as volume increases?

• Answer:(4.0 L) (205 kPa) = (12.0 L) (? kPa) ? = 68.3

kPa

Temperature -Volume Relationship

Charles’ Law

Charles’s Law

• 1n 1787, French physicist and balloonist Jacques Charles investigated the effect of temperature on volume of a gas at constant pressure

• Found increase in volume with every increase in temperature that he studied

Graph of Temperature-Volume Relationship

• T vs. V yields a straight line graph• Graphs of all gas samples, when extrapolated to a

volume of zero, intersect at the same point, -273.15 ºC (Why?)

• William Thomson (Lord Kelvin) realized the importance of this number and identified it as absolute zero where theoretically the average kinetic energy of gas particles is zero

Charles’s Law• Volume of a fixed mass

of gas is directly proportional to its Kelvin temperature if the pressure is constant

2

2

1

1

T

V

T

V

A balloon inflated @ 24 ºC has a volume of 4.00 L. The balloon is heated to 61ºC. What is the new

volume if the pressure remains constant?

• V1 = 4.00 L T1 = 24ºC T2 = 61 ºC V2 = ?

• V2 = 4.5 L

• Does this make sense? Yes, from kinetic theory the volume should increase with increase in temperature at constant pressure.

1

212 T

TxVV

2

4.00 334

297

L x KV

K

2

2

1

1

T

V

T

V

Sample Problems

• If a gas occupies 6.80 L at 325ºC, what is the volume at 25 ºC if no change in pressure? Will the volume go up or down?

• Answer: • 5.00 L of air at – 50.0 ºC is warmed to 100.0

ºC. What is new volume @ constant pressure? What direction will the volume move?

• Answer:

Temperature-Pressure Relationship

Gay-Lussac’s Law

Gay-Lussac’s Law• In 1802, Joseph Gay-

Lussac, a French chemist stated that the pressure of a gas is directly proportional to the Kelvin temperature if the volume stays constant. 2

2

1

1

T

P

T

P

• Gas left in a used aerosol can is at a pressure of 103 kPa @ 25ºC. If thrown into a fire, what is the pressure at 928 ºC?

• P1 = 103 kPa T1 = 25 ºC T2 = 928 ºC P2 =?

• Remember temperature must be in Kelvin!

K

KxkPa

T

TxPP

298

1201103

1

212

2

2

1

1

T

P

T

P

• A gas has a pressure of 6.58 kPa at 539K. What will be pressure @ 211K given constant volume?

• Pressure in an automobile tire is 198 kPa @ 27 ºC. At the end of the trip, the pressure has risen to 225 kPa. What is the temperature of the air in the tire?

So you think you’ve had a bad day?

The Combined Gas Law

Combines the 3 gas laws

2

22

l

11

T

xVP

T

VxP

Holding one value constant, you can obtain the other gas laws

Can be used when none of the variables are constant

Volume of a gas-filled balloon is 30.0 L @ 40 ºC and 153 kPa. What volume will the balloon have at STP?

– V1 = 30.0 L

– T1 = 40 ºC

– T2 = 273K

– P1 = 153 kPa

– P2 = 101.3 kPa

• V2 = ?

2

22

l

11

T

xVP

T

VxP

V2 = 39.5 L

temperature ratio is 1 ( 273K/313K) volume decreasespressure ratio is 1 (153kPa/ 101.3kPa) volume increases

When both effects are combined, volume increases

KxkPa

KxkPaxL

TxP

TxPxVV

3133.101

2731530.302

12

211

Dalton’s Law• Particles in a mixtures of gases (ex: Air) are at

the same temperature so they have the same average kinetic energy

• Gas pressure depends only on # of particles in a given volume and their average kinetic energy

• If you know the pressure exerted by each gas in the mixture, the pressures can be added to find the total gas pressure.

Partial Pressure

• One form of Dalton’s law of partial pressures:

• Ptotal = P1 + P2 + P3 + P4……..@ constant volume and temperature

• Fractional contribution to pressure by each gas in a mixture does not change with changes in temperature, volume or pressure

• This is very important in the area of anesthesiology.

Sample Problem

• Air contains O2, N2, CO2, and trace amounts of other gases. What is the partial pressure of oxygen PO2 at 101.30kPa 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

• Ptotal = P02 + (PN2+PCO2 + Pothers)

• PO2 = 21.22 kPa

Sample Problems

• Determine the total pressure of a gas mixture that contains O2, N2, and He if the partial pressures of the gases are as follows:PO2=20.0 kPa, PN2=46.7 kPa, PHe = 26.7kPa.

• Answer:• A gas mixture containing O2, N2, and CO2

has a total pressure of 32.9 kPa. If PO2 = 6.6 kPa and PN2 = 23.0 kPa, what is PCO2?

• Answer:

End of Chapter 10

Chapter 11

Molecular Composition of GasIdeal Gas Laws

Avogadro’s Hypothesis

• Equal volumes of gases, at the same temperature and pressure contain equal numbers of particles

• This is possible because there is so much space between the particles that it doesn’t matter how large or small the particles are

• So 1 mole of any gas occupies 22.4 Liters at STP conditions

Sample Problem

• Determine the volume in L occupied by 0.202 mol of a gas at STP

• Does this make sense? Yes, because 1 mol of gas occupies 22.4 L at STP so 0.202 mol of gas would occupy about 1/5 of that volume

L52.4mol1

L4.22xsmol202.0V

4th Variable – Moles!• Amount of gas in system affects pressure and volume

of gas at constant temperature.• volume or pressure depends on the # of gas particles

– Moles!• Moles are expressed as “n”. • Divide each side of the combined gas equation by n

22

22

l1

11

nxT

VxP

nxT

VxP

• (P x V)/(T x n) is a constant for ideal gases• If you evaluate (P x V)/(T x n) , # of moles of

gas at any specified P, V, and T can be calculated - symbolized by R, the ideal gas constant

• Since 1 mol of gas occupies 22.4 L @STP, substitute #’s in to calculate R

molxK

kPaxL31.8

mol1xK273

L4.22xkPa3.101

nxT

VxPR

Ideal Gas Law

• Rearranging the equation, you get:

• P x V = n x R x T or PV = nRT

• This allows you to solve for the # of moles when P, V, and T are known

Fill a rigid steel cylinder that has a volume of 20.0 L with N2 gas to a final pressure of 2.00 x 104 kPa @ 28ºC. How many moles

does the cylinder contain?

• P=2.00 x 104 kPa, V= 20.0L, R=8.31 L kPa/K mol, ∙ ∙T= 301K

molxKkPaxL

xK

LxkPax

TxR

VxPn

31.8301

0.201000.2 4

A deep underground cavern contains 2.24 x 106 L of CH4(g) at a pressure of 1.50 x 103 kPa and temperature of 42ºC. How many kilograms of CH4 does

this natural-gas deposit contain?

• P = 1.50 x 103 kPa V = 2.24 x 106 L T = 42ºC• Mass = ?

molxKkPaxL

8.31x315K

L2.24x10xkPax105.1

TxR

VxPn

63

• Convert moles of methane to grams

• Convert to kilograms = 2.05 x 104 kg CH4

• Does this make sense? Yes, volume and pressure are very large so should be large mass of methane

6 644 4

4

16.0gCH1.28x10 mol CH x 20.5x10 g CH

1molCH

Sample Problems• A child has a lung capacity of 2.20L. How many

grams of air do her lungs hold at a pressure of 102kPa and a normal body temperature of 37ºC? (Molar mass of air ~29g/mol)

• Answer: • What volume will 12.0 g of oxygen gas occupy at

25ºC and a pressure of 52.7kPa?• Answer:

Ideal Gas Law and Kinetic Theory

• Ideal gas is one that follows the gas laws at all conditions of pressure and temperature

• Assumes gas conforms precisely to the kinetic theory– Particles have no volume and could not be

attracted to each other at all. – There are no ideal gases but at high

temperature and low pressure, real gases behave much like ideal.

Real Gases – Non Ideal

• Important difference is that real gases can be liquefied and sometimes solidified by cooling and applying pressure where ideal gases cannot.

• Gases become more “non ideal” at low temperatures and high pressures - Why? Gas molecules are more likely to stick together in these conditions.

Departures from Ideal Gas Law

• Deviations from ideal are based on 2 factors, attractions between molecules and volume of the gas molecules

• Gases could not be liquefied if there was no attraction between molecules

• Actual gases are made of actual particles that have volume

• Liquid O2 - occurs at -183 ºC

• Liquid N2 - occurs at - 196 ºC

• Coldest recorded temperature on EarthVostok, Antartica – 1983 - 89 ºC (-129 ºF)

• How many oxygen molecules are in 3.36 L of oxygen gas at STP?

• Convert from volume moles molecules

• = 9.03 x 1022 molecules

• Determine the volume of 14.0 g of nitrogen gas @ STP• Convert mass moles volume

2

223

2

22 Omol1

Omolecules10x02.6x

OL4.22

Omol1xOL36.3

22

2

2

22 LN2.11

molN1

LN4.22x

gN0.28

Nmol1xgN0.14

• What volume is occupied by 4.02 x 1022 molecules of helium gas @STP?

• Answer:• What is the volume of a container that

holds 8.80 g of carbon dioxide @STP?• Answer:• A container holds 6.92 g of hydrogen gas

@STP. What is the volume of the container?• Answer:

Graham’s Law

• Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout

• Effusion is the process where a gas escapes through a tiny hole in its container

• Thomas Graham (in 1840’s) studies effusion• Proposed that the rate of effusion is inversely

proportional to the square root of its molar mass

• KE = ½mv2 so…. If 2 bodies of different

masses have the same kinetic energy, the lighter body must move faster

• Particles at the same temperature have the same kinetic energy so the particles with lower molar mass must move faster

• The rates of effusion are inversely proportional to the square roots of their molar masses

A

B

B

A

massmolar

massmolar

Rate

Rate

Sample Problem• Compare rates of effusion of the air

component nitrogen (molar mass = 28.0g) and helium gas (molar mass = 4.0g)

7.2g0.2

g3.5

g0.4

g0.28

Rate

Rate

2N

He

Behavior of Gases