Chapter 12 1

GasesGases

Chapter 12Chapter 12

Chapter 12 2

Characteristics of GasesCharacteristics of Gases

- Expand to fill a volume (expandability)- Compressible- Readily forms homogeneous mixtures with other gases

Chapter 12 3

PressurePressurePressure - force acting on an object per unit area.

AF

P

Chapter 12 4

PressurePressure- Conversion Factors

- 1 atm (atmosphere) = 760 mmHg - 1 atm (atmosphere) = 760 torr - 1 atm (atmosphere) = 1.01325 105 Pa (Pascal)- 1 atm (atmosphere) = 101.325 kPa (Kilopascal)

Chapter 12 5

The Gas LawsThe Gas Laws- There are four variables required to describe a gas:

- Amount of substance: moles- Volume of substance: liters- Pressures of substance: atmospheres (atm)- Temperature of substance: kelvin

- The gas laws will hold two of the quantities constant and see how the other two vary.

Chapter 12 6

The Gas LawsThe Gas LawsThe Pressures-Volume Relationship: Boyle’s LawThe Pressures-Volume Relationship: Boyle’s LawBoyle’s Law - The volume of a fixed quantity of gas is

inversely proportional to its pressure at constant temperature.

) and (constant 1

TnV

P

Chapter 12 7

The Gas LawsThe Gas LawsThe Pressures-Volume Relationship: Boyle’s LawThe Pressures-Volume Relationship: Boyle’s LawBoyle’s Law - The volume of a fixed quantity of gas is

inversely proportional to its pressure at constant temperature.

2211

) and (constant 1

VPVP

TnV

P

Chapter 12 8

The Gas LawsThe Gas LawsThe Temperature-Volume Relationship: The Temperature-Volume Relationship:

Charles’s LawCharles’s LawCharles’s Law - The volume of a fixed quantity of gas at

constant pressure is directly proportional to the substances temperature in Kelvin.

)and(constant PnTV

Chapter 12 9

The Gas LawsThe Gas LawsThe Temperature-Volume Relationship: The Temperature-Volume Relationship:

Charles’s LawCharles’s LawCharles’s Law - The volume of a fixed quantity of gas at

constant pressure is directly proportional to the substances temperature in Kelvin.

2

2

1

1

)and(constant

T

V

T

V

PnTV

Chapter 12 10

The Gas LawsThe Gas LawsThe General Gas LawThe General Gas Law- This is a combination of Boyle’s and Charles’s gas law.

constantisn2

22

1

11

T

VP

T

VP

Chapter 12 11

The Gas LawsThe Gas LawsThe Quantity-Volume Relationship: Avogadro’s The Quantity-Volume Relationship: Avogadro’s

LawLawAvogadro’s Law - The volume of gas at a given

temperature and pressure is directly proportional to the number of moles of gas.

) and (constant TPnV

Chapter 12 12

The Ideal Gas EquationThe Ideal Gas Equation- Combine the gas laws (Boyle, Charles, Avogadro)

yields a new law or equation.

Ideal gas equation:

PV = nRT

R = gas constant = 0.08206 L(atm)/mol(K)

P = pressure (atm) V = volume (L)

n = moles T = temperature (K)

Chapter 12 13

The Ideal Gas EquationThe Ideal Gas Equation- We define STP (standard temperature and pressure)

as 0C (273.15 K), 1 atm.- Volume of 1 mol of gas at STP is 22.4 L (molar vol.).

Chapter 12 14

Gas Densities and Molar MassGas Densities and Molar Mass- Rearranging the ideal-gas equation with M as molar

mass yields

Applications of The Ideal-Gas EquationApplications of The Ideal-Gas Equation

RT

Pd

M

Chapter 12 15

Gas Mixtures and Partial PressuresGas Mixtures and Partial PressuresDalton’s Law - In a gas mixture the total pressure is

given by the sum of partial pressures of each component:

Ptotal = P1 + P2 + P3 + …

- The pressure due to an individual gas is called a partial pressure.

Chapter 12 16

Gas Mixtures and Partial PressuresGas Mixtures and Partial PressuresPartial Pressures and Mole FractionsPartial Pressures and Mole Fractions- The partial pressure of a gas can determined if you

know the mole fraction of the gas of interest and the total pressure of the system.

i is the mole fraction of gas i (ni/ntotal).

Pi = iPtotal

Chapter 12 17

Kinetic-Molecular TheoryKinetic-Molecular Theory- Theory developed to explain gas behavior- To describe the behavior of a gas, we must first

describe what a gas is:– Gases consist of a large number of molecules in constant

random motion.

– Volume of individual molecules negligible compared to volume of container.

– Intermolecular forces (forces between gas molecules) negligible.

– Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.

– Average kinetic energy of molecules is proportional to temperature.

Chapter 12 18

Molecular Effusion and DiffusionMolecular Effusion and DiffusionGraham’s Law of EffusionGraham’s Law of EffusionGraham’s Law of Effusion - The rate of effusion of a gas

is inversely proportional to the square root of its molecular weight.- Effusion is the escape of a gas through a tiny hole (a balloon

will deflate over time due to effusion).

1

2

2

1MM

rr

Chapter 12 19

Real Gases: Deviations from Ideal Real Gases: Deviations from Ideal BehaviorBehavior- The assumptions in kinetic molecular theory show

where ideal gas behavior breaks down– When the volume of the gas becomes very small (the volume

of the gas molecules become significant)

– When the pressure become very large (gas molecules start to attract each other).

Chapter 12 20

Real Gases: Deviations from Ideal Real Gases: Deviations from Ideal BehaviorBehavior

Chapter 12 21

Real Gases: Deviations from Ideal Real Gases: Deviations from Ideal BehaviorBehaviorThe van der Waals EquationThe van der Waals Equation• We add two terms to the ideal gas equation one to

correct for volume of molecules and the other to correct for intermolecular attractions

• The correction terms generate the van der Waals equation:

where a and b are empirical constants.

2

2

V

annbV

nRTP

Chapter 12 22

2, 14, 20, 28, 36, 38, 48, 56

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