The Behavior of Gases

Review of KMT of Gases Assumptions

1. Gases consist of tiny particles far apart from one another

2. Collision between gas particles are elastic, with no loss of KE

3. Gas particles are in constant, rapid motion.

4. No forces of attraction or repulsion exist between gas particles

5. Average KE of particles depends on absolute temperature of the gas

Review of PressurePressure is force force

per unit areaper unit areaSI unit of forceforce is

the NewtonNewton (N)SI unit of pressurepressure

is the pascalpascal 1Pa = 1N/m2 Pascals

meter

NewtonsP

A

FP

area

forcepressure

2

14.1 Properties of GasesCompressibilityFactors affecting Gas Pressure

Amount of gas (n)number of particles, i.e. moles of gas

Volume (V)space occupied by the gas

Temperature (T, absolute temperature)Recall TK = TC + 273

14.2 The Gas LawsThe gas laws describe the relationship of

the 4 important variables that describe gas behavior

Pressure (P)Moles (n)Volume (V)Temperature (T in Kelvins)

Boyle’s Law:Pressure & Volume

Volume is inversely related to PressureWhen Pressure increases, Volume

decreasesIf temperature and moles are constant

2211

1

VPVP

kPVP

V

Practice Problemspage 419

1. Given a volume of 2.50 L, if the pressure of N2O (an anesthetic) decreases from 105 kPa to 40.5 kPa, what is its new volume? (assume n & T are constant)

2. If 4.00 L of NH3 at 205 kPa is allowed to expand to 12.0L, what is the new pressure if T and n remain constant?

Charles’ Law:Volume and Temperature

Volume is directly proportional to absolute temperature

When temperature of an enclosed gas increases, its volume increases

If pressure is constant

2

2

1

1

T

V

T

V

kTV

TV

Sample Problemspage 421

1. If a sample of CO2 occupies a volume of 6.80 L at 325ºC, what will its volume be at 25ºC if the pressure does not change?

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

Gay-Lussac Law:Pressure and TemperaturePressure is directly proportional to absolute

temperatureAs the temperature of an enclosed gas increases,

its pressure increases if volume is constant

2

2

1

1

T

P

T

P

kTP

TP

Gay-Lussac Law

Sample Problemspage 423

1. A sample of N2 gas has a pressure of 6.58 kPa at 539K. If the volume does not change, what will the pressure be at 211K?

2. 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?

The Combined Gas Law:Pressure, Volume and Temperature

Combines Boyle’s, Charles’, and Gay-Lussac’s Laws

Relates pressure, volume and temperature

2

22

1

11

T

VP

T

VP

kT

PV

Sample Problemspage 424

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

2. A 5.00 L sample of air has a pressure of 107 kPa at 50.0ºC. If the temperature is raised to 102ºC and the volume expands to 7.00 L, what will the new pressure be?

14.3 Ideal GasesGases at ordinary temperatures and

pressures comply with the assumptions of the KMT of gases

These are called ideal gasesGases at extremely low temperatures

and/or extremely high pressures do notThese are called real gases

Avagadro’s Law:Moles & Volume

The volume of a confined gas is directly proportional to moles of a gas

If the moles of gas increases, the volume of the gas increases

If temperature and pressure are constantn = kV n/V = kn1/V1 = n2/V2

Practice Problem A cylinder of gas with a moveable piston

contains 2.00 mol N2 with a volume of 11.0 L. What is the new volume if 1.50 mol of CO2 is injected into the cylinder? Assume that pressure and temperature are unchanged and that the N2 and CO2 do not react with one another.

19.3 L

Molar Volume of Gases:Remember This!At STP, the standard

molar volume of any gas is 22.4L

One mole of a gas has a volume of 22.4L at STP

Use this as a conversion factor when solving stoichiometry problems involving gases

mol

L

1

4.22

Practice Problems1. A chemical reaction produces

0.0680 mol of oxygen gas. What is the volume of the gas at

STP?2. A reaction produced 98.0 mL of

SO2 gas at STP. a. How many moles of SO2 were produced?

b. What was the mass in grams of the gas?c. What is the density of the gas?

14.3 Ideal Gas Law:Pressure, Volume, Moles, Temperature

A single law that relates pressure, volume, moles, and temperature of a gas

PV=nRTn is number of moles of gasR is the ideal gas constant

Value of R varies depending on units used for pressure and volume

The Ideal Gas Constant

082.0

314.8

Kelvinmoles

LiteratmR

Kelvinmoles

LiterkPaR

nT

PVR

nRTPV

Sample Problems1. A rigid hollow sphere containing 685 L He has

a temperature of 621K and a pressure of 1.89 x 103 kPa. How many moles of He are in the sphere? (251 mol)

2. What volume will 12.0 g of methane gas (CH4) occupy at a temperature of 25ºC and pressure of 0.52 atm?

3. A gaseous product of a reaction is collected in a 30.0 L container at 25ºC. The measured pressure of the gas was 150 kPa. The mass of gas produced was about 116 g. What is the molar mass of the gas?

Ideal Gases and Real GasesIdeal gases are real gases which comply

with the ideal gas equationReal gases deviate from the ideal gas

equation at low temperatures and high pressures

This is because the assumptions of KMT are no longer valid at low T and high P

Real Gases Deviate from the Ideal

14.4 Gas Mixtures and MovementsVery often gases are mixtures

Pure substancesHomogeneous mixturesSolutions

The total pressure of a mixture of gases is the sum of the pressures of each individual gas (component gas) in the mixture

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial PressuresThe total pressure of a mixture of

gases is the sum of the partial pressure of each component of the mixture

Partial pressure is the pressure of each gas within a mixture of gases

...321 PPPPT

Example of Dalton’s LawIf you mix 2 moles O2 at 0.12 atm with 2 moles of N2 at 0.12 atm, the total pressure is the sum of

the partial pressures.

Do Problem 32, p. 434

atm24.0

atm12.0atm12.022

T

T

NOT

P

P

PPP

Mole Fraction can be used to calculate partial pressuresThe mole fraction of a gas is the moles of a

gas divided by the total moles of gas in a mixture

X = moles x/ total molesIn a mixture of 200 moles of O2 and 500

moles N2, what is the mole fraction of O2?

XO2 = 200 mol O2/700 mol = 0.29Suppose this mixture had a total pressure of

600 kPa. What is the PO2?

PO2 = XO2 · Ptotal = 0.29 x 600 kPa = 174 kPa

Graham’s Law of EffusionDiffusion

Movement of molecules from an area of higher concentration to lower concentration

EffusionEffusion

Movement of gas molecules through a pinhole

Rate of effusionHow much gas effuses per secondSometimes velocity is used

Graham’s Law of EffusionAt a given

temperature, lower mass molecules diffuse and effuse faster than greater mass molecules

This is because they have the same KE

KE = ½ mv2

A

B

B

A

m

m

R

R

A

B

B

A

massmolar

massmolar

Rate

Rate