ch104 chapter 8 gases gases & kinetic theory pressure gas laws

CH104 Chapter 8

Gases

Gases & Kinetic Theory

Pressure

Gas Laws

Elemental states at 25oC

He

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLsBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

AcRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

Gd

Cm

Tb

Bk

Sm

Pu

Eu

Am

Nd

U

Pm

Np

Ce

Th

Pr

Pa

Yb

No

Lu

Lr

Er

Fm

Tm

Md

Dy

Cf

Ho

Es

At

Te

As

Si

B

6 - 2

SolidLiquid

Gas

Changes of State

Melting Pt = Freezing Pt

Boiling Pt

Solid

Liquid

Vapor

CondenseCondense

FreezeFreezeMeltMelt

VaporizeVaporize

Slow, close,Fixed

arrangement

Moderate, close,Random

arrangement

Fast, far apart,Random

Solid

Liquid

Vapor

Changes of State

FrostDepositDeposit

SublimeSublimeFreeze Dry

We live at the bottom of an ocean of air

Atmospheric Pressure

Atmosphere:A sea of colorless, odorless gases surrounding the earth

(in mole %)78.08 % N2

20.95 % O2

0.033 % CO2

0.934 % Ar

(in mole %)78.08 % N2

20.95 % O2

0.033 % CO2

0.934 % Ar

Atmosphere:Atmosphere:

Properties of matterSolids, liquids and gases can easily be recognized by their different properties.

DensityThe mass of matter divided by it’s volume.

ShapeIs it fixed or take the shape of the container?

CompressibilityIf we apply pressure, does the volume decrease?

Thermal expansionHow much does the volume change when heated?

Solid

Liquid

Vapor

Slow moving, dense,Fixed shape

Moderate movement,Dense,Takes shape of container

Fast moving, Low density,Expands to fill container

Density Shape Compressibility

Small compressibility,

Very small heat expansion

Large compressibility,

Expands w/ heat

Smallcompressibility,

Small heat expansion

1. All gases are made up of tiny particles moving in • straight lines • in all directions • at various speeds.

Kinetic molecular theory of Gases

Model to explain behavior of gases

Vapor

3. V of a gas = V of container

V of a gas is mostly empty space.

2. Particles far apart have no effect on each other. (Don’t attract or repel)

Kinetic molecular theory

Kinetic molecular theory

4. The ave KE as the T

• The average KE is the same for all gases at the same T.

TKE

(K.E. a T)

E is conservedwhen colliding with each other or container walls.

For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

E is conservedwhen colliding with each other or container walls.

For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

5. Gas molecules exert pressure as they collide with container walls

The > the # of collisions (per unit time), the > the pressure

Kinetic molecular theory

Pressure= Force per unit of Area. Force

AreaP = Force

Area

In the atmosphere, molecules of air (N2, O2, Ar, H2O, etc..) are constantly bouncing

off us.

We live at the bottom of an ocean of air

Atmospheric Pressure

Atmosphere:A sea of colorless, odorless gases surrounding the earth

PressureAt higher elevations, there is less air so the P is less.

Boiling Point = Temp where molecules

overcome atmospheric Pressure

Sea Level

760 torrDenver (5280’)

630 torrMt. Evans,CO(14,000’)

Mt. Everest(20,000’)

467 torr

270 torr H2O

= 100 oC

= 95 oC

= 87 oC

= 73 oC

Measuring PressureAttempts to

pump water out of flooded

mines often failed because

H2O can’t be

lifted more than 34 feet.

Measuring PressureTorricelli believed reason was that P of atmosphere could not hold anything heavier than a 34’ column of water.

Like drinking from a straw.

What causes the liquid to move up the straw to your mouth ?

Atmospheric Pressure

34’ columnof water

1 Atm

The atmosphere

would support a column of

H2O> 34 feet high.

Measuring Pressure

Torricelli BarometerPressure of the atmosphere supports acolumn of Hg 760 mm high.

1 atm

1 atm =760 mm Hg760 torr29.92 in Hg14.7 lb/in2

101,325 Pa

vacuum

Mercury used because it’s so dense.

Blood pressure (systolic over diastolic):most often in mm Hg. (ex. 120/80)

Meteorologists refer to pressure systems in mm or inches of Hg. ex. 30.01 in

STPStandard Temperature & Pressure

1 atm

1 atm =760 mm Hg760 torr29.92 in Hg14.7 lb/in2

101,325 Pa

0oC

273K

Gas lawsLaws that show relationships between volume and properties of gasesBoyle’s LawCharles’ LawGay-Lussac’s Law

Avogadro’s LawIdeal Gas LawDalton’s Law

CombinedGas Law

V is inversely proportional to P when T is constant.

Boyle’s law

V 1

Por V = k

1

Por PV = k

If P goes down V goes upP

V

P V

V

P

P1 = 1 Atm

1 LV1 =

P2 = 0.5 Atm

2 LP1V1 = P2V2 V2 =

P1V1 = V2

P2

1atm (1L) =

0.5 atm

2 L

Boyle’s law: V vs P

1 L

Boyle’s law: V vs P2 L

Drive to top of mountain - ears start popping.

Breathing at high altitudes is more difficult because the pressure of O2 is less.

It all “Boyle’s” down to Breathing in and out.

Boyle’s law

Charles’s law: V vs TThe volume of a gas is directly proportional to the absolute temperature (K).

T V

P

If T goes up V goes up

V1 = 125 mL

T1 = 273 K

Charles’s law: V vs T V1 = V2

T1 T2

V1 = V2

T1 T2

V2 =

T2 = 546 K

250 mL

(546K)125 mL = 273 K

T2V1 = V2

T1

A balloon indoors, where the temp is at 27oC, has a volume of 2.0 liters. What will its volume be outside where the temperature is -23oC ? (Assume no change in pressure.)

Using Charles’ Law

V1 = V2

T1 T2

V1 = V2

T1 T2

= (250K)2.0 L = 300 K

T2V1 = V2

T1

Convert all temps to the Kelvin.

T1 = 27 + 273 = 300 K

T2 = -23 + 273 = 250 K

1.7 L

Gay-Lussac’s Law (PT)Pressure of a gas is directly proportional to

Absolute Temp (K) when Volume is constant

P1 = P2

T1 T2

P1 = P2

T1 T2

P T

V

If P goes up T goes up

Example: an auto tire was inflated to a pressure of 32 psi when the temperature was -20ºC. After driving all day in a hot desert, the temperature of the tire has climbed to 60ºC. What is the pressure inside the tire?

Gay-Lussac’s Law

Assume the tire’s volume is fixed.

P2 = ??P1 = 32 psiT1 = -20 + 273 = 253K T2 = 60 + 273 = 333K

P1 = P2

T1 T2

= (333K)32 psi = 253 K

T2P1 = P2

T1

42 psi

Boyle’s

Gay-Lussac’s

Charles’

PT

VV

T VP

TP

VGas LawsP1V1 = P2V2

V1 = V2

T1 T2

P1 = P2

T1 T2

Boyle’s

Gay-Lussac’s

Charles’

CombinedGas Law

PT

VV

T VP

TP

VGas Laws

P1V1

T1

= P2V2

T2

A 10 m3 balloon contains helium on the ground where the temperature is 27ºC and the pressure is 740 torr. Find the volume at an altitude of 5300 m if pressure is 370 mm Hg and temperature is -33 ºC.

P1 = 740 mm

T1 = 27 + 273 = 300 K

V1 = 10 m3

P2 = 370 mm

T2 = -33 + 273 = 240 K

V2 = ?

= 16 m3V2 = (240 K)(740 mm)(10 m3 )

(370 mm) (300 K)

P1V1

T1

= P2V2

T2

T2P1V1

P2 T1

= V2

Combined Gas Law

Boiling Point = Temp where Vapor Pressure (Pvap) of molecules overcome

atmospheric Pressure

Sea Level = 100 oC

760 torrDenver (5280’) = 95 oC

630 torrMt. Evans,CO(14,000’) = 87 oC

Mt. Everest(20,000’) = 73 oC467 torr

270 torr H2O

Avogadro’s lawThe volume of a gas is directly

proportional to the number of molecules

V1 = V2

n1 n2

V1 = V2

n1 n2

More moles of a gas, takes up more space.

At Standard Temperature & Pressure (STP)

V of 1 mole of gas = 22.4 liters

Equal volumes of gas (at same T and P)

contain equal numbers of molecules.

Avogadro’s law

At T = 273 K (0ºC) P = 1 atm (760 mm)

1 mol He

4 g He

22.4 L

1 mol He

4 g He

22.4 L

1 mol N2

28 g N2

22.4 L

1 mol N2

28 g N2

22.4 L

1 mol CO2

44 g CO2

22.4 L

1 mol CO2

44 g CO2

22.4 L

Standard conditions (STP)When 36.0 g of liquid H2O is vaporized,

what will be the volume of the gas?

1 mole H2O

18.0 g H2O

22.4 liters

1 mole H2O= 44.8 36.0 g H2O

L

66 g CO2

Example: What volume (in Liters)

will 66 grams of CO2 occupy at STP?

1 mole CO2

44 g CO2

22.4 liters

1 mole CO2

= 33.6

STP

L

The Ideal gas lawA combination of • Boyle’s, • Charles’ , • Gay-Lussac’s and • Avogadro’s Laws

PV = nRT

V nT

P

V = RnT/P where R is a constant

V nT

P

V = RnT/P where R is a constant

AtmL

K

mol L atmmol K

( 1 atm ) ( 22.4 L)( 1 mol ) ( 273 K)

PVnT

R =

= 0.0821 atm-L mol-1 K-1

R =

R (the gas constant) can easily be determined from standard conditions.

= 0.0821 atm-L

mol-K

The Ideal gas law

What is the volume of 2.00 moles of gas at3.50 atm and 310.0 K?

PV = nRT V = nRT P

= (2.00 mol)(0.0821 L• atm)(310. K) K . mol

(3.50 atm)

= 14.5 liters

The Ideal gas law

PV = nRT

The Ideal gas law

moles n = grams = g_

molecular weight MW

So: we can substitute for n.

PV = g R T MW

MW = g R T PV

What is the molecular weight of a gas if 25.0 g

of the gas occupies a volume of 15.0 liters at a pressure of .950 atm and a temperature of 50.0 ºC?

(25.0g)(0.0821 L atm )(323 K)mol K

(0 .950 atm)(15.0 L)

= 46.5 __g_

mol

The Ideal gas law

MW = g R T = PV

Remember

density =

The Ideal gas law• can also be used with density of a gas

g

V

MW = d R T P

If the density of a gas

is 1.75 _g_

L

at 740 torr and 300 K,

what is its MW?

MW = g R T P V

740 torr ( 1 atm ) (760 torr)

The Ideal gas law

MW = d R T P

If density of a gas = 1.75 g_

L

at 740 torr and 300 K,

What is its MW?

MW = 1.75 g (.0821 L atm)( 300 K) L mol K = 44.3 g_

mol

The Ideal gas law• can solve for density of a gas if needed

MW = d R T P

d = P MW RT

Dalton’s law of Partial Pressures

The total pressure of a gas mix = sum of the partial pressures of each gas.

Pair = PN2 + PO2 + PAr + PCO2 + PH2O

PT = P1 + P2 + P3 + .....

Each gas acts independently of the others.

Example: Air

Pair = PN2 + PO2 + PCO2 + PH2O

Typical values for Atmospheric air at 0 ºC (excluding argon):

PN2 = 594.7 mm PO2 = 160 mm

PH2O = 5.0 mmPCO2 = 0.3 mm

Pair = 594.7 mm + 160 mm + 0.3 mm + 5.0 mm

As T of air increases, more H2O is found in the mix.example: at 20 ºC, the PH2O = 18 mm

Since total pressure (760 mm) can’t change,

the other gases are diluted

to make room for the water.

Pair = 594.7 mm + 160 mm + 0.3 mm + 5.0 mm

Pair = PN2 + PO2 + PCO2 + PH2O

Air moving over warm water

has more water in it.

Low pressure

is often associated with this air.

Typhoons and hurricanes

are associated with very warm, moist air.

Pair = PN2 + PO2 + PCO2 + PH2O = 760 mm

Values are for 97% oxygen saturation at pH = 7.4.

Blood Gases

PCO2 ~ 40 mm Hg

Normal PO2 in the air =160 mm.

If drops

< 100 mm,

can’t diffuse into the blood.

Arterial Blood Gases (ABGs)

PBG = PO2 + PCO2

PO2 ~ 100 mm Hg

PCO2 ~ 46 mm Hg

Venous Blood Gases (VBGs)

PO2 ~ 40 mm Hg

We only use about 25% of the Oxygen we inhale.

The rest is exhaled along with the Nitrogen and some carbon dioxide.

THIS IS WHY CPR WORKS !!!

Bernoulli's Principle

Faster moving gases exert less pressure than slow moving gases.

Fast moving Gases Low P

Slow moving Gases

High P

Bernoulli's PrincipleSlow moving

Gases

Fast moving Gases

High P

Low P

Graham’s Law

lightweight gases move faster than heavy gases

KE=0.5 mv2

Diffusion (gasses intermingling when together)

Graham’s Law

AMW

BMW

B rateeffusion

A rateeffusion

Effusion (gas escaping through small hole;

ie balloon going flat)

UF6-235 needed for nuclear reactor

UF6-238

Gas Centrifuge: heavy spins to outside

Porous membrane: lighters go through faster