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‫خواص گازها‬
‫مجموعه ای از مولکولها هستند‬
‫به هر نسبتی قابل اختالط هستند‬
‫جرم مشخصی دارند‬
‫حجم قابل تغییر دارند‬
‫تغییر شکل می دهند‬
‫به سهولت پخش می شوند‬
Gases: Their Properties and Behavior
• Matter
– Solids, Liquids and …..
– Relatively few substances that are gaseous at
standard temperature.
– Importance to history of chemistry and to
basic concepts of reactions.
Gases and Gas Pressure
Gases and Gas Pressure
Column of air
1.0m2 through
Upper atmosphere
10,300kg of air
P=pgh
1 atm = 760mm Hg
101,325 Pa
Gases and Gas Pressure
Barometer
Gases and Gas Pressure
Manometer
Mercury Manometers
Gas Laws
• Boyle’s Law
– The volume of a gas varies inversely with
pressure.
• PV = k with the same amount of gas if there are
different amounts then  PV/n = k
• P = k/V
Gas Laws
• Boyle’s Law….
P=k/V
Gas Laws
• Charles’ Law
– The volume of a gas varies directly with
temperature. (at fixed pressure)
• V/T = k or
• V = kT
• Actually discovered by Joseph Louis GayLussac in 1802. He gave credit to
Jacques Charles’ work of 1787.
Gas Laws
• Charles’ Law
• Gay-Lussac's Law
Jacques Charles
Joseph Louis Gay-Lussac
V=kT
Gas Laws
• Avogadro’s Law
– The volume of a gas
depends on its molar
amount (at fixed
pressure and
temperature).
• V/n = k or
• V = kn
Gas Laws
• Avogadro’s Law
Ideal Gas Law
• Ideal Gas Law was
first written in 1834 by
Emil Clapeyron
• http://dbhs.wvusd.k12.ca.
us/GasLaw/GasIdeal.html
Ideal Gas Law
• Is the combination of Boyle’s, Charles’ and
Avogadro’s work.
• PV = nRT
• R = 8.3145 J/(K·mol)
• Standard Temperature and Pressure (STP)
• T = 0oC (273.15K)
• P = 1 atm.
• Note the changes to the standards (bottom of
page 348). We will use the old standards for
now.
Attention!
• R = 8.3145 J/(K·mol)
• When P is in Pascals and V is in m3.
• R = 0.08206 L·atm/K·mol
The Kinetic-Molecular Theory of Gases
• Ek = ½
• Ek = 3/2·RT/NA
mv2
Maxwell
Boltzmann
The kinetic theory of gases was
developed initially by James Clerk
Maxwell and Ludwig Boltzmann.
Maxwell's calculation (1859) of the
distribution law of molecular
velocities in thermal equilibrium can
be considered as the starting point of
statistical mechanics, the first time a
macroscopic, thermodynamic
concept such as temperature was
quantitatively related to the
microscopic dynamics. Boltzmann's
later work really laid down the
foundations for this discipline, with
the first microscopic analysis of
irreversibility and the approach to
equilibrium (1872).
The Kinetic-Molecular Theory of Gases
• Assumptions
• A gas consists of tiny particles in random motion.
• The volume of the particles is insignificant
compared to the volume of space occupied.
• There is no interaction between particles (neither
attractive nor repulsive forces exist).
• The kinetic energy of each particle remains
constant (all collisions are elastic).
• The kinetic energy of the particles is proportional to
the temperature (K). [All gases have the same
average translational energy at T(K)]
‫‪The Kinetic-Molecular Theory of Gases‬‬
‫• گازها از ذراتی به نام مولکول ساخته شده اند‬
‫• مولکولهای گازها در حال حرکت هستند و با یکدیگر و دیواره‬
‫ظرف برخورد می کنند‬
‫• میانگین انرژی جنبشی حرکتی گازها به دمای آن بستگی دارد‬
‫• نیروی جاذبه بین مولکولهای گازها ناچیز و قابل صرف نظر کردن‬
‫است‬
‫اثبات قانون گاز کامل براساس نظریه جنبش‬
‫مولکولی‬
‫؟‬
The Kinetic-Molecular Theory of Gases
• Comments concerning the individual gas
laws and the assumptions.
•
•
•
•
Boyle’s law
Charles’ law
Avogadro’s law
Dalton’s law
P=k/V
V = kT
V = kn
Pt = P1 + P2 + P3 ….
• Last assumption is probably the most accurate and
most meaningful here. We can use it to calculate
the kinetic energy of a gas at T(K) and then find
out how fast each particle is moving.
‫رفتار مخلوط گازها‬
‫• گازهایی که وقتی مخلوط شوند با یکدیگر واکنش شیمیایی‬
‫می دهند‪ .‬قانون ترکیب حجمی گیلوساک و آووگادرو‬
‫• گازهایی که وقتی مخلوط شوند با یکدیگر واکنش شیمیایی‬
‫نمی دهند‪ .‬قانون فشارهای جزئی دالتون‬
Stoichiometric Relationships with Gases
• Any chemical reaction involving a gas,
either reactant or product, will require a
stoichiometric calculation of the balanced
process.
• Moles of gas (n)
• Measurement of P and T.
• Determination of V and finally mass.
• The method in figure 9.11 is frequently
used in laboratory experimentation…..
11-10 ‫مثال‬
2C2 H 6 ( g )  7O2 ( g )  4CO2 ( g )  6H 2O( g )
2 LC2 H 6  7 LO2
 7 LO2 
  52.5LO2
? LO2  15.0 LC2 H 6 
 2 LC2 H 6 
2LC2 H 6  4LCO2
 4 LCO2 
  30.0 LCO2
? LCO2  15.0 LC2 H 6 
 2 LC2 H 6 
)‫الف‬
)‫ب‬
14-10 ‫مثال‬
2 NaN3 ( s)  2 Na( s)  3N 2 ( g )
2molNaN3  3molN 2
 1 mol NaN3  3 mol N 2 


? mol N 2  0.400 g NaN3 
 65.0 g NaN3  2 mol NaN3 
...............  0.00923 mol N 2
PV  nRT
V  0.230L
Partial Pressure and Dalton’s Law
• Ideal gas law can be applied to mixtures of gases
in the same way as a pure gas.
• Total PressurePt = P1 + P2 + P3……
– P1, P2, P3.. Represent the partial pressure of each individual
gas in the mixture (as if it were alone in the volume of space).
• Mole Fraction (X)
– Introduced as another way to find the value of n for
each individual gas in the mixture.
nA
XA 
n A  nB  ...  nZ
PA  X A Pt
The Kinetic-Molecular Theory of Gases
2000
1800
1600
1400
1200
1000
800
600
400
200
0
1960
1360
650
Hy
He
Wa
dro
liu
ter
m
ge
n
Average Speed
520
Nit
ro
490
415
Ox
Ca
y
rbo
ge
ge
nD
n
n
iox
id
e
3RT
Ek 
2N
Graham's Law of Effusion
Which gas has a lower molecular weight?
evacuated
chamber
mixed
gases
pinhole leak
Graham's Law of Effusion
• Uranium hexafluoride (UF6) is a gas that has
been used as a method to enrich the amount of
uranium-235 used in nuclear reactions.
• Uranium has two principle isotopes,
uranium235 and uranium-238.
Graham's Law of Effusion
If the effusion method is used to separate
235UF (MW = 349) from 238UF (MW = 352)
6
6
what will be the percentage enrichment per cycle?
How many enrichment cycles will be needed
to raise the uranium-235 content from
the natural abundance 0.3% to 5%?
Graham's Law of Effusion
If the effusion method is used to separate
35UF (MW = 349) from 238UF (MW = 352)
6
6
what will be the percentage enrichment per cycle?
Rate of effusion of 235UF6
Rate of effusion of
238UF
6
=
=
MW of
238UF
6
MW of
235UF
6
352
349
= 1.0043
Graham's Law of Effusion
each
enrichment
cycle
1.0043 increase
first cycle
1.0043 increase
second cycle
1.0043 x 1.0043 increase
nth cycle
(1.0043)n increase
Graham's Law of Effusion
0.3%
natural
abundance
of U-235
0.3% x (1.0043)n
(1.0043)n
n ln (1.0043)
5.0%
required purity
of U-235
for nuclear
applications
5.0%
5.0% / 0.3% = 16.7
ln (16.7)
n = 657 cycles
Ideal Gas Law
• What is an Ideal Gas anyway?
• Actually – none exist.
Gas
Ideal
Ammonia
Argon
Carbon Dioxide
Chlorine
Fluorine
Nitrogen
Hydrogen
Helium
Molar Volume (L)
22.414
22.40
22.09
22.40
22.06
22.38
22.40
22.43
22.41
Ideal Gas Law
Micheal Blader – Florida State U.
Ideal Gas Law
Micheal Blader – Florida State U.
Ideal Gas Law
• Non-Ideal gas adjustment - van der
Waals equation.
• (Pideal + a(n/V)2(Videal – bn) = nRT
Intermolecular forces Molecular volume
• a and b are constants for the specific gas.
van der Waals constants
Compound
a (L2-atm/mol2)
b (L/mol)
He
0.0341
0.02370
Ne
0.211
0.0171
Ar
1.34
0.0322
Kr
2.32
0.0398
Xe
4.19
0.0510
H2
0.244
0.0266
N2
1.39
0.0391
O2
1.36
0.0318
Cl2
6.49
0.0562
H2O
5.46
0.0305
CH4
2.25
0.0428
CO2
3.59
0.0427
CCl4
20.4
0.1383
Application of Ideal Gas Law
• Using the Ideal Gas Law,
estimate the reduction of
pressure in this tire if
there is a change of
temperature from 30oC to
-30oC. Assume the tire to
be mounted on a car with
an initial pressure of 32
pounds per square inch
(psi).
• University of Minnesota
Physics Dept.
The Earth’s Atmosphere
The Earth’s Atmosphere
Ozone
contribution from Mike Pluth Ozone Fact Bar
Cl + O3  ClO + O2
ClO + O  Cl + O2
O3 + O  2 O2
Web Sites
• A nice site for gas explanations with Flash
video.
• http://www.chemistry.ohiostate.edu/betha/nealGasLaw/
• Search the web for “Ideal Gas Law”
• 88,000 hits
• Or “Ideal Gas Law Calculator”
– 5000
‫تمرینهاي فصل ‪10‬‬
‫‪• 4-6-8-10-12-14-16-18-20-22-24-26-28-30‬‬‫‪32-34-36-38-40-50-52-54-58-60-62-64-66‬‬‫‪68‬‬
A Molecular Comparison of Liquids and
Solids
Intermolecular Forces
‫انواع نیروهای بین مولکولی‬
1.
2.
3.
4.
5.
Ion-Dipole
Dipole-dipole
Dipole-induced dipole
Instantaneous dipole -induced dipole
Hydrogen bonding
Intermolecular Forces
Intermolecular Forces
Intermolecular Forces
Intermolecular Forces
London Dispersion Forces
Intermolecular Forces
London Dispersion Forces
• Weakest of all intermolecular forces.
• It is possible for two adjacent neutral molecules to
affect each other.
• The nucleus of one molecule (or atom) attracts the
electrons of the adjacent molecule (or atom).
• For an instant, the electron clouds become
distorted.
• In that instant a dipole is formed (called an
instantaneous dipole).
Intermolecular Forces
London Dispersion Forces
Intermolecular Forces
London Dispersion Forces
• One instantaneous dipole can induce another
instantaneous dipole in an adjacent molecule
(or atom).
• The forces between instantaneous dipoles
are called London dispersion forces.
• Polarizability is the ease with which an
electron cloud can be deformed.
• The larger the molecule (the greater the
number of electrons) the more polarizable.
London Dispersion Forces
-Temporary Induced Dipole-Dipole interactions
–Very Weak always present in the condensed
phase
London Dispersion Forces
Intermolecular Forces
London Dispersion Forces
• London dispersion forces increase as molecular
weight increases.
• London dispersion forces exist between all
molecules.
• London dispersion forces depend on the shape of
the molecule.
• The greater the surface area available for contact,
the greater the dispersion forces.
• London dispersion forces between spherical
molecules are lower than between sausage-like
molecules.
London Forces in Hydrocarbons
Intermolecular Forces
London Dispersion Forces
Intermolecular Forces
Hydrogen Bonding
• Special case of dipole-dipole forces.
• By experiments: boiling points of compounds with
H-F, H-O, and H-N bonds are abnormally high.
• Intermolecular forces are abnormally strong.
• H-bonding requires H bonded to an electronegative
element (most important for compounds of F, O, and
N).
– Electrons in the H-X (X = electronegative element) lie
much closer to X than H.
– H has only one electron, so in the H-X bond, the + H
presents an almost bare proton to the - X.
– Therefore, H-bonds are strong.
H-Bonding
Occurs when Hydrogen is attached to a
highly electronegative atom.
+
N-H… N-
O-H… N-
F-H… N-
N-H… O-
O-H… O-
F-H… O-
N-H… F-
O-H… F-
F-H… F-
-
Requires Unshared Electron Pairs of Highly
Electronegative Elements
Hydrogen
Bonding
in Water
Molecules
Clasters of Water
Structure of Ice
Observe the orientation of the
Hydrogen Bonds
‫كريستالهاي منجمدشده آب‬
The messages from water
88
‫سالم‬
‫(كاواچي ) رقص سنتي ژاپني‬
‫“‪Goldberg Variations‬‬
‫آهنگ باخ‬
water can have highly organized
local structures when it interacts
with molecules capable of imposing
these structures on the water.
William Royer Jr.
U. of Mass. Medical school
Organized water
molecules
India, 2003
Stabilization by “bound water” molecules
a
b
Water binding in hemoglobin
The crystal structure of hemoglobin, shown
(a) with bound water molecules (red spheres) and
(b) without the water molecules
B-DNA with a spine
of water molecules
‘Bound water’ in biological
systems
• Intracellular water very close to any
membrane or organelle (sometimes called
vicinal water)
• Organized very differently from bulk water
• This structured water plays a significant
role in governing the shape (and thus
biological activity) of large folded
biopolymers.
Water chain in cytochrome f
Proton hopping
Water molecules form H-bonds with
polar solutes
95
Electrostatic interaction with
charged solutes
• When NaCl is mixed with water,
a shell of water surrounds each
Na+ and Cl- ion.
Ions change structure of liquid
water
• Ionic substances are soluble
because the net attraction of the
+ and – ions for water is greater
than the attraction of oppositely
charged ions for each other.
• Formation of the Hydration
shell.
97
Structured water
2(H2O)4
More dense water
(H2O)8

Less dense water
98
Types of ions
• Structure-breaking ion 'chaotrope'
(disorder-maker) (Na+)
• structure-forming ion 'kosmotrope'
(order-maker) (K+)
• Kosmotropes shift the local equilibrium to the right.
• Chaotropes shift it to the left.
more dense (condensed) water  less dense water
Water
preference
Ion
Surface charge
density
Intra-cellular
Extra-cellular
Ca2+
2.11
0.1 mM
2.5 mM
High density
Na+
1.00
10 mM
150 mM
High density
K+
0.56
159 mM
4 mM
Low density 99
Nonpolar gases
are poorly soluble in water
100
Hydrocarbons in water
•
Hydrocarbons and nonpolar molecules are
insoluble because water-water interactions
are stronger than water-hydrocarbon
interactions. So water molecules force
nonpolar molecules together and surround
them.
•
This phenomenon is called hydrophobic
effect or hydrophobic interaction.
101
102
Intermolecular Forces
Hydrogen Bonding
• Hydrogen bonds are responsible for:
– Ice Floating
•
•
•
•
•
•
•
•
•
Solids are usually more closely packed than liquids;
therefore, solids are more dense than liquids.
Ice is ordered with an open structure to optimize H-bonding.
Therefore, ice is less dense than water.
In water the H-O bond length is 1.0 Å.
The O…H hydrogen bond length is 1.8 Å.
Ice has waters arranged in an open, regular hexagon.
Each + H points towards a lone pair on O.
Ice floats, so it forms an insulating layer on top of lakes, rivers,
etc. Therefore, aquatic life can survive in winter.
Why Does Ice Float?
D2O(s)
H2O(s)
The Boiling Points of the Covalent Hydrides of the
Elements in Groups 4A, 5A, 6A, and 7A
Intermolecular Forces
Hydrogen Bonding
Intermolecular Forces
Hydrogen Bonding
• Hydrogen bonds are responsible for:
– Protein Structure
• Protein folding is a consequence of H-bonding.
• DNA Transport of Genetic Information
Protein Secondary Structure
Helix
Protein Secondary Structure
Pleated Sheet
Summary Intermolecular Forces
Proteins
Intermolecular Forces
Comparing Intermolecular Forces
Force-distance relationship
For the Fattraction proportional to 1/distance
molecules in contact with each other
Relative attractive force
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Force-distance relationship
Relative attractive force
1
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Force-distance relationship
Relative attractive force
1
2
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Force-distance relationship
Relative attractive force
1
3
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Force-distance relationship
Relative attractive force
1
4
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Force-distance relationship
Relative attractive force
1
5
0.8
0.6
Less than 20% the strength at
5 molecular distances
0.4
0.2
0
0
1
2
3
4
5
6
7
8
Relative molecular distance
9
10
Increasing strengths of IMF
The strength of IMF’s
•
•
•
•
•
•
•
H-bonding (fixed distance ~200 pm)
Ion-ion (1/r)
Ion-dipole (1/r2)
Inverse
3
Dipole-dipole (1/r )
functions of
distance to
Ion-induced dipole (1/r4)
various
6
Dipole-induced dipole (1/r )
powers
Induced dipole-induced dipole
(1/r6)
How do the other functions behave compared to 1/r?
Click here for an interactive Excel spreadsheet to explore
Base Pairs in DNA: H-bonding
AT pair
Why not
here?
GC pair
Lipid Bilayer: Induced Dipole – Induced Dipole
Interaction for Hydrocarbon Chains
phospholipid
Some Properties of Liquids
Viscosity
• Viscosity is the resistance of a liquid to flow.
• A liquid flows by sliding molecules over each
other.
• The stronger the intermolecular forces, the
higher the viscosity.
Surface Tension
• Bulk molecules (those in the liquid) are
equally attracted to their neighbors.
Viscosity
• Measure of a fluid’s
resistance to flow
•  viscosity,  flow
• As IM forces ,
–  viscosity
– Glycerol vs. H2O
example
Some Properties of Liquids
Surface Tension
• Surface molecules are only attracted inwards
towards the bulk molecules.
– Therefore, surface molecules are packed more
closely than bulk molecules.
• Surface tension is the amount of energy
required to increase the surface area of a
liquid.
• Cohesive forces bind molecules to each
other.
• Adhesive forces bind molecules to a surface.
Bulk and Surface Interactions in
Liquid
Some Properties of Liquids
Surface Tension
Some Properties of Liquids
Surface Tension
• Meniscus is the shape of the liquid surface.
– If adhesive forces are greater than cohesive
forces, the liquid surface is attracted to its
container more than the bulk molecules.
Therefore, the meniscus is U-shaped (e.g. water
in glass).
– If cohesive forces are greater than adhesive
forces, the meniscus is curved downwards.
• Capillary Action: When a narrow glass tube
is placed in water, the meniscus pulls the
water up the tube.
Meniscus of Water and of
Mercury
Adhesive and Cohesive Forces on
Surface
Capillary Action
Phase Changes
Energy Changes Accompanying Phase Changes
Phase Changes
Energy Changes Accompanying Phase Changes
– Sublimation: Hsub > 0 (endothermic).
– Vaporization: Hvap > 0 (endothermic).
– Melting or Fusion: Hfus > 0 (endothermic).
– Deposition: Hdep < 0 (exothermic).
– Condensation: Hcon < 0 (exothermic).
– Freezing: Hfre < 0 (exothermic).
Phase Changes
Heating Curves
Clausius-Clapeyron
log P  
H vap
C
2.303RT
H vap T2  T1
P1
log

P2 2.303R T1T2
Phase Diagrams
XRD
‫تمرینهای پایان فصل‬
‫• ‪،26 ،22 ،15 ،14 ،7 ،5 ،1‬‬
Solution
• Homogeneous mixtures
• Solute + Solvent  Solution
Types of Solutions
•
•
•
•
•
Gas-Gas
Liquid-Gas
Liquid-Liquid
Liquid-Solid
Solid-Solid
Solution Process
Solution Process
Solution Process
Solution Process
• Rate of Dissolving
– Solute + Solvent  Solution
• Saturation Point
– Solute + Solvent  Solution

Rate of Dissolving
•
•
•
•
Size of solute particles
Temperature
Concentration
Stirring
Saturated Solution
Dynamic Equilibrium
• Solute(s)  Solute(aq)

Solubility Factors
• Nature of solute & solvent
• Temperature
• Pressure
Energy Factors in Solubility
• Enthalpy
– Heat absorbed or evolved
• Entropy
– Measure of disorder
– Most important for gas-gas
Enthalpy in Solubility
• Bond breaking vs Bond making
+
Enthalpy in Ionic Solutions
• Relative strengths
– Lattice energy: ion-ion attraction
– Hydration: ion-dipole attraction
Enthalpy in Solubility
• Like dissolves like
– Like bonding, small H
– Entropy favors solution
Effect of Temperature
• Gas:
– Less soluble at higher temperature
• Liquid & Solid:
– if H positive then more soluble
– if H negative then less soluble
Effect of Pressure
• Gas:
– More soluble at higher pressure
• Liquid & Solid:
– Very little effect
Henry’s Law
William Henry 1775-1836
• Solubility of a gas increases with pressure
S = kH P
S2 P2

S1 P1
Concentration Units
• Mass Percent
• Molarity
• Mole fraction
• Molality
Mass Percent
mass solute
%mass 
 100%
mass solution
Molarity M
moles solute
Molarity 
Liters solution
Molality
moles solute
Molality 
kg solvent
Mole Fraction
moles of A
XA 
Total moles
Conversion of Mass% to mole
fraction
• Calculate the masses of solvent and
solute in 100g of solution.
• Calculate moles of each from masses.
• Calculate mole fraction
Vapor Pressure Lowering
Raoult’s Law
Francois-Marie Raoult 1830-1901
PA 
o
PA X A
PTotal 
o
PA X A
o
 PB XB
Colligative Properties of Ideal
Solutions
• Depend only on the concentration
• Ionic solutions
– Each ion can act as a separate particle.
– van’t Hoff factor: i
Colligative Properties
•
•
•
•
Vapor pressure lowering
Boiling point elevation
Freezing point depression
Osmotic pressure
Colligative Properties
• Boiling point elevation
tb = iKbCm
• Freezing point depression
tf = iKfCm
Calculations
Tb
molality 
Kb
Tb
moles 
 kgsolvent
Kb
masssolute
molar wt.
 Tb

 kgsolvent 

 Kb

Molar wt. of the unknown
masssolute
molar wt.
 Tb

 kgsolvent 

 Kb

Colligative Properties
• Osmotic pressure
• ‫ وانت هوف رابطه‬1887 ‫در سال‬
‫زیر را که شبیه به قانون گازها‬
‫باشد را کشف کرد‬
 V=nRT
•
 = MRT
 =iMRT
H2O
H2O
Na+
Cl-
H2O
H2O
H2O
‫تمرین ‪12-12‬‬
‫• محلولی شامل ‪ 0/30‬گرم از یک پروتئین در آب فشار‬
‫اسمزی معادل ‪ 0/0167‬اتمسفر در دمای ‪ 25/0‬درجه‬
‫دارد جرم مولکولی پروتئین را محاسبه کنید؟‬
‫‪n‬‬
‫‪    RT‬‬
‫‪V ‬‬
‫‪4‬‬
‫‪M  4.39 10‬‬
‫تمرینهای پایان فصل‬
‫• ‪،51 ،49 ،47 ،43 ،41 ،37 ،29 ،27 ،25 ،23 ،19‬‬
‫‪87 ،81 ،71،75 ،69 ،67 ،65، 63 ،55 ،53‬‬