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!"#$%&'(%)#*%((&%

!"+,-#.%/%0%1+2#2%

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The Concept of Pressure

!The pressure exertedby a solid.

Both cylinders have thesame mass

They have differentareas of contact

P (Pa) =Area (m2)Force (N)

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Liquid Pressure

!The pressure exerted bya liquid depends on:

The height of thecolumn of liquid.

The density of thecolumn of liquid.

P = g !h !d

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Barometric Pressure

Standard Atmospheric Pressure

1.00 atm, 760 mm Hg, 760 torr, 101.325 kPa, 1.01325 bar

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Manometers

hh

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6-2 Simple Gas Laws

!Boyle 1662 P" 1V

PV = constant

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Charless Law

Charles 1787

Gay-Lussac 1802

V " T V = b T

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Standard Temperature and Pressure

!Gas properties depend on conditions.!Define standard conditions of temperature

and pressure (STP).

P = 1 atm = 760 mm Hg

T = 0C = 273.15 K

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Prentice-Hall 2007General Chemistry: Chapter 6

Avogadros Law

!Gay-Lussac 1808 Small volumes of gases react in the ratio of

small whole numbers.

!Avogadro 1811 Equal volumes of gases have equal numbers of

molecules and

Gas molecules may break up when they react.

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Avogadros Law

V" n or V = c n

At STP

1 mol gas = 22.4 L gas

At an a fixed temperature and pressure:

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Prentice-Hall 2007General Chemistry: Chapter 6

6-3 Combining the Gas Laws: The Ideal

Gas Equation and the General GasEquation

!Boyles law V" 1/P!Charless law V" T!Avogadros law V" n

PV = nRT

V "nTP

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Prentice-Hall 2007General Chemistry: Chapter 6

The Gas Constant

R=

PVnT

= 0.082057 L atm mol-1 K-1

= 8.3145 m3

Pa mol-1

K-1

PV = nRT

= 8.3145 J mol-1 K-1= 8.3145 m

3

Pa mol-1

K-1

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Prentice-Hall 2007General Chemistry: Chapter 6

Using the Gas Law

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Prentice-Hall 2007General Chemistry: Chapter 6

The General Gas Equation

R= =P2V2n2T2

P1V1n1T1

=

P2

T2

P1

T1

If we hold the amount and volume constant:

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Prentice-Hall 2007General Chemistry: Chapter 6

6-4 Applications of the Ideal Gas Equation

PV = nRT and n =mM

PV =mM

RT

M =m

PV

RT

Molar Mass Determination

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Gas Densities

PV = nRT and d =mV

PV =m

M RT

MP

RTV

m= d =

, n =mM

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Prentice-Hall 2007General Chemistry: Chapter 6

6-5 Gases in Chemical Reactions

!Stoichiometric factors relate gas quantities toquantities of other reactants or products.

!Ideal gas equation relates the amount of a gasto volume, temperature and pressure.

!Law of combining volumes can be developedusing the gas law.

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Prentice-Hall 2007General Chemistry: Chapter 6

6-6 Mixtures of Gases

!Partial pressure Each component of a gas mixture exerts a

pressure that it would exert if it were in thecontainer alone.

!Gas laws apply to mixtures of gases.!Simplest approach is to use ntotal, but....

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Prentice-Hall 2007General Chemistry: Chapter 6

Daltons Law of Partial Pressure

The total pressure of a mixture of gases is the sum of

the partial pressures of the components of the mixture.

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Prentice-Hall 2007General Chemistry: Chapter 6

Partial Pressure

Ptot = Pa + Pb +

Va = naRT/Ptot and Vtot = Va + Vb+

Va

Vtot

naRT/PtotntotRT/Ptot

= =na

ntot

Pa

Ptot

naRT/VtotntotRT/Vtot

= =na

ntot

na

ntot= #aRecall

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Prentice-Hall 2007General Chemistry: Chapter 6

6-7 Kinetic Molecular Theory

! Particles are point masses in constant,random, straight line motion.

! Particles are separated by greatdistances.

! Collisions are rapid and elastic.!No force between particles.! Total energy remains constant.

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Prentice-Hall 2007General Chemistry: Chapter 6

Pressure Assessing Collision Forces

! Translational kinetic energy,! Frequency of collisions,! Impulse or momentum transfer,! Pressure proportional to

impulse times frequency

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Prentice-Hall 2007General Chemistry: Chapter 6

Pressure and Molecular Speed

! Three dimensional systems lead to:

um is the modal speed

uavis the simple average

urms

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Prentice-Hall 2007General Chemistry: Chapter 6

Pressure

Assume one mole:

PV=RT so:

NAm = M:

Rearrange:

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Distribution of Molecular Speeds

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Prentice-Hall 2007General Chemistry: Chapter 6

Determining Molecular Speed

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Temperature

Modify:

PV=RT so:

Solve for ek:

Average kinetic energy is directly proportional to temperature!

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6-8 Gas Properties Relating to the

Kinetic-Molecular Theory

!DiffusionNet rate is proportional to

molecular speed.

!Effusion A related phenomenon.

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Prentice-Hall 2007General Chemistry: Chapter 6

Grahams Law

! Only for gases at low pressure (natural escape, not a jet).! Tiny orifice (no collisions)! Does not apply to diffusion.

=

(urms)A

(urms)B=

3RT/MA

3RT/MB=

MB

MA

! Ratio used can be: Rate of effusion (as above) Molecular speeds Effusion times

Distances traveled by molecules Amounts of gas effused.

Rate of effusion of A

Rate of effusion of B

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Prentice-Hall 2007General Chemistry: Chapter 6

6-9 Nonideal (Real) Gases

!Compressibility factor PV/nRT = 1!Deviations occur for real gases.

PV/nRT > 1 - molecular volume is significant. PV/nRT < 1 intermolecular forces of attraction.

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Prentice-Hall 2007General Chemistry: Chapter 6

Real Gases

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van der Waals Equation

P +n2a

V2

V nb = nRT