jednadžba idealnog plina i kinetička teorija...unutrašnja energija pitanja za ponavljanje. title:...
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
Jednadžba idealnog plinai kinetička teorija
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
To facilitate comparison of the mass of one atom with another, a mass scaleknow as the atomic mass scale has been established.
The unit is called the atomic mass unit (symbol u). The reference element ischosen to be the most abundant isotope of carbon, which is called carbon-12.
kg106605.1u 1 27
The atomic mass is given in atomicmass units. For example, a Li atom has a mass of 6.941u.
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
One mole of a substance contains as manyparticles as there are atoms in 12 grams ofthe isotope carbon-12.
The number of atoms per mole is known asAvogadro’s number, NA.
123 mol10022.6 AN
ANNn
number ofmoles
number ofatoms
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
moleper Massparticleparticle m
NmNm
nA
The mass per mole (in g/mol) of a substancehas the same numerical value as the atomic or molecular mass of the substance (in atomicmass units).
For example Hydrogen has an atomic massof 1.00794 g/mol, while the mass of a single hydrogen atom is 1.00794 u.
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
Example 1 The Hope Diamond and the Rosser Reeves Ruby
The Hope diamond (44.5 carats) is almost pure carbon. The RosserReeves ruby (138 carats) is primarily aluminum oxide (Al2O3). Onecarat is equivalent to a mass of 0.200 g. Determine (a) the number ofcarbon atoms in the Hope diamond and (b) the number of Al2O3 molecules in the ruby.
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
mol 741.0molg011.12
carat 1g 200.0carats 5.44moleper Mass
mn(a)
(b)
molecules 271.0molg96.101
carat 1g 200.0carats 138moleper Mass
99.15398.262
mn
atoms1046.4mol10022.6mol 741.0 23123 AnNN
atoms1063.1mol10022.6mol 271.0 23123 AnNN
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14.2 The Ideal Gas Law
An ideal gas is an idealized model for real gases that have sufficiently low densities.
The condition of low density means that the molecules are so far apart that they do not interact except during collisions, which are effectively elastic.
TP
At constant volume the pressureis proportional to the temperature.
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.2 The Ideal Gas Law
At constant temperature, the pressure is inversely proportional to the volume.
VP 1
The pressure is also proportionalto the amount of gas.
nP
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14.2 The Ideal Gas Law
THE IDEAL GAS LAW
The absolute pressure of an ideal gas is directly proportional to the Kelvintemperature and the number of moles of the gas and is inversely proportionalto the volume of the gas.
VnRTP
nRTPV
KmolJ31.8 R
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14.2 The Ideal Gas Law
NkTTNRNnRTPVA
ANNn
KJ1038.1mol106.022
KmolJ31.8 23123
ANRk
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14.2 The Ideal Gas Law
Example 2 Oxygen in the Lungs
In the lungs, the respiratory membrane separates tiny sacs of air(pressure 1.00x105Pa) from the blood in the capillaries. These sacsare called alveoli. The average radius of the alveoli is 0.125 mm, andthe air inside contains 14% oxygen. Assuming that the air behaves asan ideal gas at 310K, find the number of oxygen molecules in one ofthese sacs.
NkTPV
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14.2 The Ideal Gas Law
air of molecules109.1
K 310KJ1038.1m10125.0Pa1000.1
14
23
33345
kTPVN
molecules107.214.0109.1 sac onein oxygen of molecules ofNumber
1314
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14.2 The Ideal Gas Law
Conceptual Example 3 Beer Bubbles on the Rise
Watch the bubbles rise in a glass of beer. If you look carefully, you’llsee them grow in size as they move upward, often doubling in volumeby the time they reach the surface. Why does the bubble grow as itascends?
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Copyright © 2015 John Wiley & Sons, Inc. All rights reserved.
14.2 The Ideal Gas Law
Consider a sample of an ideal gas that is taken from an initial to a finalstate, with the amount of the gas remaining constant.
nRTPV
i
ii
f
ff
TVP
TVP
constant nRTPV
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14.2 The Ideal Gas Law
i
ii
f
ff
TVP
TVP
Constant T, constant n: iiff VPVP Boyle’s law
Constant P, constant n:i
i
f
f
TV
TV
Charles’ law
+ Gay-Lussac’s law
Gay-Lussac's
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14.3 Kinetic Theory of Gases
The particles are in constant, randommotion, colliding with each otherand with the walls of the container.
Each collision changes the particle’s speed.
As a result, the atoms and molecules have different speeds.
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14.3 Kinetic Theory of Gases
THE DISTRIBUTION OF MOLECULAR SPEEDS
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14.3 Kinetic Theory of Gases
KINETIC THEORY
Lmv
vLmvmv 2
2
collisions successivebetween Timemomentum Initial-momentum Final force Average
tmv
tvmmaF
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14.3 Kinetic Theory of Gases
LmvF
2
For a single molecule, the average force is:
For N molecules, the average force is:
LvmNF
2
3 root-mean-squarespeed
3
2
2 3 LvmN
LF
AFP
volume
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14.3 Kinetic Theory of Gases
VvmNP
2
3
22132231 rmsrms mvNmvNPV
NkT KE
kTmvrms 232
21KE
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14.3 Kinetic Theory of Gases
Conceptual Example 5 Does a Single Particle Have a Temperature?
Each particle in a gas has kinetic energy. On the previous page, we haveestablished the relationship between the average kinetic energy per particleand the temperature of an ideal gas.
Is it valid, then, to conclude that a single particle has a temperature?
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14.3 Kinetic Theory of Gases
Example 6 The Speed of Molecules in Air
Air is primarily a mixture of nitrogen N2 molecules (molecular mass 28.0u) and oxygen O2 molecules (molecular mass 32.0u). Assumethat each behaves as an ideal gas and determine the rms speedsof the nitrogen and oxygen molecules when the temperature of the airis 293K.
kTmvrms 232
21
mkTvrms
3
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14.3 Kinetic Theory of Gases
sm511kg1065.4
K293KJ1038.13326
23
mkTvrms
For nitrogen…
kg1065.4g1065.4mol106.022
molg0.28 2623123
m
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14.3 Kinetic Theory of Gases
kTmvrms 232
21KE
THE INTERNAL ENERGY OF A MONATOMIC IDEAL GAS
nRTkTNU 2323
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14.4 Diffusion
The process in which molecules move from a region of higher concentrationto one of lower concentration is called diffusion.
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14.4 Diffusion
Conceptual Example 7 Why Diffusion is Relatively Slow
A gas molecule has a translational rms speed of hundreds of metersper second at room temperature. At such speed, a molecule could travel across an ordinary room in just a fraction of a second. Yet, it often takes several seconds, and sometimes minutes, for the fragrance of a perfume to reach the other side of the room. Why does it take solong?
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14.4 Diffusion
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14.4 Diffusion
L
tCDAm
FICK’S LAW OF DIFFUSION
The mass m of solute that diffuses in a time t through a solvent containedin a channel of length L and cross sectional area A is
concentration gradientbetween ends
diffusion constant
SI Units for the Diffusion Constant: m2/s
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14.4 Diffusion
Example 8 Water Given Off by Plant Leaves
Large amounts of water can be given off byplants. Inside the leaf, water passes from theliquid phase to the vapor phase at the wallsof the mesophyll cells.
The diffusion constant for water is 2.4x10-5m2/s.A stomatal pore has a cross sectional area of about 8.0x10-11m2 and a length of about 2.5x10-5m. The concentration on the interiorside of the pore is roughly 0.022 kg/m3, whilethat on the outside is approximately 0.011 kg/m3.
Determine the mass of water that passes throughthe stomatal pore in one hour.
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14.4 Diffusion
kg100.3
m102.5s 3600mkg011.0mkg022.0m100.8sm104.2
9
5-
3321125
LtCDAm
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PITANJA ZA PONAVLJANJE
1. Idealni plin
2. Atomska jedinica mase
3. Količina tvari
4. Avogadrova konstanta
5. Boyle-Mariotteov zakon
6. Charlesov zakon
7. Gay-Lussacov zakon
8. Jednadžba idealnog plina
9. Boltzmannova konstanta
10. Unutrašnja energija
PITANJA ZA PONAVLJANJE
Slide 114.1 Molecular Mass, the Mole, and Avogadro’s Number14.1 Molecular Mass, the Mole, and Avogadro’s Number14.1 Molecular Mass, the Mole, and Avogadro’s Number14.1 Molecular Mass, the Mole, and Avogadro’s Number14.1 Molecular Mass, the Mole, and Avogadro’s Number14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.2 The Ideal Gas Law14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.3 Kinetic Theory of Gases14.4 Diffusion14.4 Diffusion14.4 Diffusion14.4 Diffusion14.4 Diffusion14.4 DiffusionSlide 31