gases. highly compressible. occupy the full volume of their containers. when gas is subjected to...

GasesGases

P V T nEm pirical Gas Law sIdeal G as LawM ixtures

M athem atical Descriptions

Kinetic EnergyM olecular SpeedReal GasesApplications

KM - M odel of Gases

Behavior & Properties

• Highly compressible.• Occupy the full volume of their containers.• When gas is subjected to pressure, its volume decreases.• Gases always form homogeneous mixtures with other

gases.• Gases only occupy about 0.1 % of the volume of their

containers.

General Characteristics of GasesGeneral Characteristics of Gases

Four Physical Quantities for GasesFour Physical Quantities for Gases

Phys. Qty. Symbol SI unit Other common units

pressure PPascal (Pa)

atm, mm Hg, torr, psi

volume V m3 dm3, L, mL, cm3

temp. T K °C, °F

moles n mol

Atmosphere Pressure and the Barometer

Figure 10.2: PressureFigure 10.2: Pressure

A

FP

•Standard atmospheric pressure = 760 mm of Hg

•1 atm = 760 mmHg = 760 torr = 101.325 kPa.

Units: Force and PressureUnits: Force and Pressure

Units: Force and Pressure – F12Units: Force and Pressure – F12

• Closed Systems => manometers

Figure 10.3: PressureFigure 10.3: Pressure

Figure 10.7: The Pressure-Volume Relationship: Boyle’s Law

The Empirical Gas LawsThe Empirical Gas Laws

The Pressure-Volume Relationship: Boyle’s Law

• Mathematically:

• A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

PV

1constant constantPV

2211 VPVP


•A sample of gas contained in a flask with a volume of 1.53 L and kept at a pressure of 5.6x103 Pa. If the pressure is changed to 1.5x104 Pa at constant temperature, what will be the new volume?

2211 VPVP

The Temperature-Volume Relationship: Charles’s Law• Charles’s Law: the volume of a fixed quantity of gas at constant

pressure increases as the temperature increases.• Mathematically:

• A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?

TV constant2

2

1

1

T

V constant

T

V

T

V


Example CalculationExample Calculation

•A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will be the new volume if temp. is increased to 38°C at constant pressure?

2

2

1

1

T

V

T

V

Figure 10.9

The Quantity-Volume Relationship: Avogadro’s Law

• Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas.

• Mathematically:

nV constant

2

2

1

1

n

V

n

V

2

2

1

1

n

V

n

V


• We can combine these into a general gas law:

The Ideal Gas EquationThe Ideal Gas Equation

), (constant 1

TnP

V

), (constant PnTV

),(constant TPnV

• Boyle’s Law:

• Charles’s Law:

• Avogadro’s Law:

PnT

V

• R = gas constant, then

• The ideal gas equation is:

• R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K• J = kPa·L = kPa·dm3 = Pa·m3

• Real Gases behave ideally at low P and high T.

The Ideal Gas EquationThe Ideal Gas Equation

P

nTRV

nRTPV

Gas ExamplesGas Examples

• A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.

• At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?

• A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?

• What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]

• A sample of H2 gas has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the moles of H2 present.

nRTPV

At a constant temperature of 25°C and a pressure of 1 atm, a 12.2 L sample containing 0.50 moles of O2 gas was converted to ozone ( O3 ). What would be the volume of ozone?

nRTPV 2

2

1

1

n

V

n

V

2

2

1

1

n

V

n

V

• A sample of diborane gas ( B2H6 ), a substance that bursts into flames when exposed to air, has a pressure of 345 torr at a temperature of -15°C and a volume of 3.48 L. If temp. and pressure are changed to 36°C and 468 torr; what will be the new volume of the gas?

nRTPV

V2 = 3.07 L

n = 0.07457 mol

What is the molar volume of an ideal gas at STP? [STP stands for Standard Temperature and Pressure: 0°C and 1 atm. STP is only applied to gases.]

nRTPV

Key – F14

Gas Densities and Molar Mass• The molar mass of a gas can be determined as follows:

• The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?

Density of an Ideal-GasDensity of an Ideal-Gas

PdRTM

Density of an Ideal-GasDensity of an Ideal-Gas

nRTPV PdRTM

PdRTMnRTPV

Density of an Ideal-Gas – F12Density of an Ideal-Gas – F12

Density CalculationDensity Calculation

•The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molecular weight of the gas? If the gas is a homonuclear diatomic, what is this gas?

PdRTM

HW 11-9-11 - Key

• Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component:

• Each gas obeys the ideal gas equation:

Gas Mixtures and Partial PressuresGas Mixtures and Partial Pressures

321total PPPP

VRT

nP ii

• Partial Pressures and Mole Fractions

• Let ni be the number of moles of gas i exerting a partial pressure Pi, then

where i is the mole fraction (ni/nt).

Gas Mixtures and Partial PressuresGas Mixtures and Partial Pressures

totalPP ii

CyberChem Diving video

Assumptions:– 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.

Kinetic Molecular TheoryKinetic Molecular Theory

MTR

u

3

TR2

3Energy Kinetic

How fast can gas molecules move?How fast can gas molecules move?


Graham’s Law of Effusion• Effusion is the escape of a gas

through a tiny hole (a balloon will deflate over time due to effusion).

Figure 10.20

Diffusion• Diffusion of a gas is the spread of the gas through space

and the mixing through other gases.

• Diffusion is faster for light gas molecules.

• Diffusion is slowed by gas molecules colliding with each other.


Graham’s Law of Effusion

• Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by:


1

2

2

1

2

1

2

13

3

MM

M

M RT

RT

uu

rr

Also works for Comparison of Diffusion rates

Figure 10.19: Molecular Effusion and Diffusion• The lower the molar mass, M, the higher the rms.


Figure 10.23

Why Low Pressure?...Ideal


Figure 10.24

Why High Temperature?...Ideal


The van der Waals Equation

• General form of the van der Waals equation:

Real Gases: Deviations from Ideal BehaviorReal Gases: Deviations from Ideal Behavior

2

2

V

annbV

nRTP

nRTnbVV

anP

2

2

Corrects for molecular volume

Corrects for molecular attraction

GasesGases

P V T nEm pirical Gas Law sIdeal G as LawM ixtures

M athem atical Descriptions

Kinetic EnergyM olecular SpeedReal GasesApplications

KM - M odel of Gases

Behavior & PropertiesTRnVP M

TRspeed

3

gases. highly compressible. occupy the full volume of their containers. when gas is subjected to...

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