1 Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73; Recommended #5, 16, 22, 60, 61, 83

1Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73;

Recommended #5, 16, 22, 60, 61, 83

Particles in a gas are very far apart, and have almost no interaction.› Ex: In a sample of air, only 0.1% of the

total volume actually consists of matter.

Gases expand spontaneously to fill their container (have indefinite volume and shape.)

http://chemconnections.org/Java/molecules/index.html

http://zonalandeducation.com/mstm/physics/mechanics/energy/heatAndTemperature/gasMoleculeMotion/gasMoleculeMotion.html

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A force that acts on a given area

3

A

FP

Atmospheric pressure: the result of the bombardment of air molecules upon all surfaces 1 atm = 760 mm Hg

= 760 torr= 101.3 kPa= 14.7 PSI

100 km

Barometer: measures atmospheric P compared to a vacuum

* Invented by Torricelli in 1643 Liquid Hg is pushed up the closed glass tube by air

pressure

4

Evangelista Torricelli(1608-1647)

1. Closed-end: difference in Hg levels (h) shows P of gas in container compared to a vacuum

http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html

5

closed

Difference in Hg levels (h) shows P of gas in container compared to Patm

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7

Amadeo Avogadro(1776 - 1856)

Robert Boyle(1627-1691)

Jacques Charles(1746-1823)

John Dalton(1766-1844)

Joseph Louis Gay-Lussac(1778-1850)

Thomas Graham(1805-1869)

Boyle’s law: the volume (V) of a fixed quantity (n) of a gas is inversely proportional to the pressure at constant temperature (T).

8

2211 VPVP P

1constantV

P

V

1/P

V

Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html

Ex: A sample of gas is sealed in a chamber with a movable piston. If the piston applies twice the pressure on the sample, the volume of the gas will be

. If the volume of the sample is tripled, the pressure of the gas will be

halved

reduced to 1/3

V of a fixed quantity of a gas is directly proportional to its absolute T at constant P.

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T

V

Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

2

2

1

1

T

V

T

V

TconstantV

Extrapolation to V = 0 is the basis for absolute zero. 

V = 11.5 L

2730.1002730.50

0.10 2

VL

Ex: A 10.0 L sample of gas is sealed in a chamber with a movable piston. If the temperature of the gas increases from 50.0 ºC to 100.0 ºC, what will be the new volume of the sample?

Seen as derivative of C’s and B’s laws P of a fixed quantity of a gas is directly

proportional to its absolute T at constant V.

10

T

P

2

2

1

1

T

P

T

P

TconstantP

http://www.youtube.com/watch?v=Mytvt0wlZK8&feature=related

Equal volumes of gases at the same T & P contain equal numbers of molecules

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n

V

nconstantV

› Ex: A 10.0 L sample of gas at 100.0ºC and 2.0 atm is sealed in a chamber. If the temperature of the gas increases to 300.0ºC and the pressure decreases to 0.25 atm, what will be the new volume of the sample?

12

2

22

1

11

T

VP

T

VPconstant

PV

T

V2 =120 L

)2730.300(

)25.0(

)2730.100(

)00.10)(0.2( 2

VatmLatm

Used for calculations for an ideal (hypothetical) gas whose P, V and T behavior are completely predictable.

R = 0.0821 L•atm/mol•K= 8.31 J/mol•K

› Ex: How many moles of an ideal gas have a volume of 200.0 mL at 200.0ºC and 450 mm Hg?

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nRTPV

n = 3.0 x 10-3 mol

)2730.200)(0821.0(1000

0.200

760

450

n

What is the V of 1.000 mol of an ideal gas at standard temperature and pressure (STP, 0.00°C and 1.000 atm)

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nRTPV

V = 22.4 L (called the molar volume)

22.4 L of an ideal gas at STP contains 6.022 x 1023 particles (Avogadro’s number)

)273)(0821.0)(000.1()000.1( KmolVatm

http://www.chm.davidson.edu/vce/GasLaws/GasConstant.html

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Gas density (d):

Molar mass (M):

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RT

PM

V

md

RTPV

mM

nRTPV M

massn

V

md RT

M

mPV

RTM

mPV

Partial pressure: P exerted by a particular component in a mixture of gases

Dalton’s law of partial pressures: the total P of a mixture of gases is the sum of the partial pressures of each gas

PTOTAL = PA + PB + PC + …

(also, nTOTAL = nA + nB + nC + …)17

=

nRTPV PH2 =(0.60)(0.0821)(293) / 5.0 = 2.9 atm

PHe =(1.50)(0.0821)(293) / 5.0 = 7.2 atm

PT = 2.9 + 7.2 = 10.1 atm

+

Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %)

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RTVP

RTVP

T

A

Ex: What are the mole fractions of H2 and He in the previous example?

TOTAL

AA n

nX TA PP

T

A

n

n

T

A

P

P ∴

TAA PP X

29.02.10

0.60X

2H 714.02.10

1.50XHe

When a gas is bubbled through water, the vapor pressure of the water (partial pressure of the water) must be subtracted from the pressure of the collected gas:

PT = Pgas + PH2O

∴ Pgas = PT – PH2O

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See Appendix B for vapor pressures of water at different temperatures.

* Formulated by Bernoulli in 1738

Assumptions:1. Gases consist of particles (atoms

or molecules) that are point masses. No volume - just a mass.

2. Gas particles travel linearly until colliding ‘elastically’ (do not stick together).

3. Gas particles do not experience intermolecular forces.

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Daniel Bernoulli (1700-1782)

4. Two gases at the same T have the same kinetic energy

› KE is proportional to absolute T

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2

2

1 rmsave muKE kTKEave 2

3

urms = root-mean-square speedm = mass of gas particle

(NOTE: in kg)k = Boltzmann’s constant,

1.38 x 10-23 J/K

http://www.epa.gov/apti/bces/module1/kinetics/kinetics.htm#animate1

Ludwig Boltzmann(1844-1906)

23

James Clerk Maxwell(1831-1879)

http://intro.chem.okstate.edu/1314f00/laboratory/glp.htm

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kTKEave 2

3

O2 at 273K

O2 at 1000K

H2 at 273K2

2

1 rmsave muKE

Nu

mb

er

at

speed

, u

Speed, u

Since the average KE of a gas has a specific value at a given absolute T, then a gas composed of lighter particles will have a higher urms.

25

m

kTurms

3

m = mass (kg)M = molar mass (kg/mol)R = ideal gas law constant, 8.31 J/mol·K

kTmuKE rmsave 2

3

2

1 2

kTmurms 32

M

RT3

Effusion: escape of gas molecules through a tiny hole into an evacuated space

http://www.rkm.com.au/animations/GAS-effusion.html

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Diffusion: spread of one substance throughout a space or throughout a second substance

http://sci-culture.com/advancedpoll/GCSE/diffusion%20simulator.html

The effusion rate of a gas is inversely proportional to the square root of its molar mass

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B

A

B

A

u

u

r

r

r = u = rate (speed) of effusiont = time of effusion

B

B

A

A

MRT

MRT

3

3

A

B

t

t

A

B

M

M

a = correction for dec in P from intermolecular attractions (significant at high P, low T)

b = correction for available free space from V of atoms (significant at high concentrations)

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nRTnbVV

anP

2

2

Particles of a real gas:1. Have measurable volumes2. Interact with each other (experience

intermolecular forces) Van der Waal’s equation:

2

2

V

an

nbV

nRTP

or

Johannes van der Waals(1837-1923)

A gas deviates from ideal:› As the particles get larger (van der Waal’s “b”)› As the e- become more widely spread out (van

der Waal’s “a”)

The most nearly ideal gas is He.

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