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GAS AND
CONDENSED
MATTER
Bonding model for covalent
molecular substances


1.
2.

Bonding for covalent molecular substances falls into
two categories
The strong forces of attraction which holds atoms
together within molecules
The weak forces of attraction between molecules
Forces between molecules
(intermolecular forces)
will learn about the forces between molecules
or compounds are called intermolecular forces
 Inter means between or among
 Internet, interstate, international
 What would Interstellar travel be?
 we
Intermolecular Forces


Forces that occur between
molecules.
Intramolecular forces
 What

would intramolecular forces be?
 Forces within molecules e.g covalent, metallic or
ionic
 intra means within
 Intrastate, intranet, intracellular
 Most of the intermolecular forces we look at occur
between covalently bonded molecules or covalent
molecular substances
 Intramolecular bonds are stronger than
intermolecular forces.
Overview
 All

matter is held together by force.
 The force between atoms within a
molecule is a chemical or intramolecular
force.
 The force between molecules are a
physical or intermolecular force.
 These physical forces are what we
overcome when a chemical changes its
state (e.g. gas liquid).
What causes intermolecular forces?
 Molecules

are made up of charged particles: positive
nuclei and negative electrons.
 When one molecule approaches another there is a
multitude of forces between the particles in the two
molecules.
 Each electron in one molecule is attracted to the nuclei in
the other molecule but also repelled by the electrons
in the other molecule.
 The same applies for nuclei
Types of Intermolecular forces
 The

three main types of intermolecular
forces are:
1. Dipole-dipole attraction
occur only
btw polar molecules
2. H bonding – only with Hydrogen and
Oxygen, Fluorine and Nitrogen)
3. Dispersion forces (London Dispersion
Forces)
Intermolecular Forces


Forces that occur between
molecules.


Dipole–dipole forces




Hydrogen bonding

London dispersion forces
Dipole–Dipole Attraction
Dipole-Dipole Forces
 Dipole

moment – molecules with polar
bonds often behave in an electric field as if
they had a center of positive charge and a
center of negative charge.
 Molecules with dipole moments can attract
each other electrostatically. They line up so
that the positive and negative ends are
close to each other.
 Only about 1% as strong as covalent or ionic
bonds.
Hydrogen Bonding
Strong

dipole-dipole forces.
Hydrogen is bound to a highly
electronegative atom –
nitrogen, oxygen, or fluorine.
Hydrogen Bonding in Water


Blue dotted
lines are the
intermolecula
r forces
between the
water
molecules.
Hydrogen Bonding

Affects


physical properties

Boiling point
London Dispersion Forces






Instantaneous dipole that occurs
accidentally in a given atom induces a
similar dipole in a neighboring atom.
Significant in large atoms/molecules.
Occurs in all molecules, including
nonpolar ones.
London Dispersion Forces
Nonpolar Molecules
London Dispersion Forces


Become
stronger as the
sizes of atoms
or molecules
increase.
Melting and Boiling Points


In general, the stronger the
intermolecular forces, the higher
the melting and boiling points.
Strength of Intermolecular
Interactions
Hydrogen Bonding
↑
Dipole – Dipole
↑
London Dispersion Forces
Kinetic Molecular Theory

The kinetic theory of matter is based on the following
postulates:
1. Matter is composed of small particles called
molecules
2. The particles are in constant random motion
They possess kinetic energy due to their motion
3. There are repulsive and attractive forces between
particles.
They posses potential energy due to these
forces
4. Average particle speed increases with temperature
5. No energy is lost when the particles collide, called
elastic collision
Kinetic Molecular Theory
The kinetic energy of a particle is given by the equation:
1
KE = mv 2
Where:
2
m = particle mass in kg
v = particle velocity in m/s
KE = kg-m2/s2 = j (joule)
According to postulate 4 of our kinetic theory particle velocity
increases with temperature. This means as temperature
increases then kinetic energy increases.
Potential Energy
Potential energy is the sum of the attractive and
repulsive forces between particles.
Examples of these types of forces are the
gravitational attractive forces between objects and
the repulsive forces between the same poles of
magnets.
Alternatively we can say forces between particles may
be either cohesive or disruptive.
Interparticle Forces

Cohesive forces include dipole-dipole interactions,
dispersion forces, attraction between oppositely
charged ions.
Cohesive forces are largely temperature
independent.
e.g. magnets and gravity function the same way at
different temperature.
Interparticle Forces
Disruptive forces are those forces that make
particles move away from each other.
These forces result predominately from the particle
motion.
Disruptive forces increase with temperature in
agreement with postulate 4.
We can conclude that as we increase the
temperature particles will become further apart from
each other.
Tutorial 1
 State

and describe briefly three (3) main types of
intermolecular forces.
 State five (5) assumption in the kinetic molecular
theory
A Gas
 Has

neither a definite volume nor
shape.

 Uniformly

fills any container.

 Mixes

completely with any other gas

 Exerts

pressure on its surroundings.
Earth-like Atmosphere
Composition of Earth’s Atmosphere
Compound

%(Volume)

Mole Fractiona

Nitrogen
Oxygen
Argon
Carbon dioxide

78.08
20.95
0.934
0.033

0.7808
0.2095
0.00934
0.00033

Methane
Hydrogen

2 x 10-4
5 x 10-5

2 x 10-6
5 x 10-7

a. mole fraction = mol component/total mol in mixture.
A mercury barometer
The column height is proportional to the
atmospheric pressure.
Atmospheric pressure results
from the mass of the
atmosphere and gravitational
forces.
The pressure is the force per
unit area.
P = F/A
1 atm = 760 mmHg
1 atm = 1.01325 E5 Pa
1 mmHg = 1 torr
Units for Expressing Pressure
Unit
Atmosphere
Pascal (Pa)
Kilopascal (kPa)
mmHg
Torr
Bar
mbar
psi

Value
1 atm
1 atm = 1.01325 x 105 Pa
1 atm = 101.325 kPa
1 atm = 760 mmHg
1 atm = 760 torr
1 atm = 1.01325 bar
1 atm = 1013.25 mbar
1 atm = 14.7 psi
Pressure
is equal to force/unit area
 SI units = Newton/meter2 = 1 Pascal (Pa)
 1 standard atmosphere = 101,325 Pa
(100,000 Pa = 1 bar)
 1 standard atmosphere = 1 atm =


760 mm Hg = 760 torr = 1013.25 hPa
= 14.695 psi
Meteorologists often report pressure in
millibar; 1 mbar =0.001bar =0.1 kPa =
1hPa
Variables Affecting Gases
 Pressure

(P)

 Volume

(V)

 Temperature
 Number

(T)

of Moles (n)
Elevation and Atmospheric
Pressure
Manometer
Manometers are
used to measure
gas pressure in
closed systems.
For instance in a
reaction vessel.
The Gas Laws and Absolute Temperature

The relationship between the volume, pressure, temperature, and mass of a gas is
called an equation of state.
We will deal here with gases that are not too dense.

Boyle’s Law: the volume of a given amount of gas is
inversely proportional to the pressure as long as the
temperature is constant.
Boyle Law…pressure is inversely
proportional to volume (at constant
T and moles, n).
The Gas Laws and Absolute Temperature
The volume is linearly proportional to the temperature, as long as the
temperature is somewhat above the condensation point and the
pressure is constant:
Extrapolating, the volume becomes zero at −273.15°C; this temperature
is called absolute zero.
Avogadro’s Law


For a gas at
constant
temperature and
pressure, the volume
is directly
proportional to the
number of moles of
gas (at low
pressures).
V α n
V1 = V2
n1
n2
The Gas Laws and Absolute Temperature
The concept of absolute zero allows us to define a third temperature scale –
the absolute, or Kelvin, scale.
This scale starts with 0 K at absolute zero, but otherwise is the same as the
Celsius scale.
Therefore, the freezing point of water is 273.15 K, and the boiling point is
373.15 K.
Finally, when the volume is constant, the pressure is directly proportional to
the temperature:
Combined Gas Law
 Combining

the gas laws the relationship
P α T(n/V) can be obtained.

 If

n (number of moles) is held constant,
then PV/T = constant.

P1
V
P2
V
1
2
=
T
T
1
2
Ideal Gas Law
PV = nRT
R = universal gas constant
= 0.08206 L atm K-1 mol-1

P = pressure in atm
V = volume in liters
n = moles
T = temperature in Kelvin
Standard Temperature
and Pressure (for gases)
“STP”






P = 1 atmosphere
T = 0°C
The molar volume of an ideal gas is 22.42 liters at STP
(put 1 mole, 1 atm, R, and 273 K in the ideal gas law
and calculate V)
Note STP is different for other phases, e.g. solutions or
enthalpies of formation.
The Ideal Gas Law
A mole (mol) is defined as the number of grams of a substance that is numerically
equal to the molecular mass of the substance:
1 mol H2 has a mass of 2 g
1 mol Ne has a mass of 20 g
1 mol CO2 has a mass of 44 g
The number of moles in a certain mass of material:
The Ideal Gas
Equation

• Charles’s Law:

1
V ∝ (constant n, T )
P
V ∝ T (constant n, P )

• Avogadro’s Law:

V ∝ n (constant P, T )

• Boyle’s Law:

• We can combine these into a general gas law:
nT
V∝
P
The Ideal Gas
Equation
• R = gas constant, then
 nT 
V = R

 P 

• The ideal gas equation is:

PV = nRT
• R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K
• J = kPa·L = kPa·dm3 = Pa·m3
• Real Gases behave ideally at low P and high T.
Ideal Gas Law in Terms of Molecules:
Avogadro’s Number
Since the gas constant is universal, the number of molecules in one mole is the
same for all gases. That number is called Avogadro’s number:

The number of molecules in a gas is the number of moles times Avogadro’s
number:
Ideal Gas Law in Terms of Molecules:
Avogadro’s Number
Therefore we can write:

where k is called Boltzmann’s constant.

(13-4)
The Ideal Gas
Equation
 Calculate

the pressure exerted by 84.0 g of ammonia,
NH3, in a 5.00 L container at 200. oC using the ideal gas
law.
PV = nRT
P = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273
P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K)
(5 L)
P = 38.3 atm
Tutorial 2.
 The

pressure on a sample of an ideal gas was
increased from 715 torr to 3.55 atm at constant
temperature. If the initial volume of the gas was 485.
mL, what would be the final volume?

A

7.9 L sample of gas was cooled from 79°C to a
temperature at which the volume of the gas was
4.3 L. Assuming the pressure remains constant,
calculate the final temperature.
 Calculate the pressure in atmospheres and pascals
of a 1.2 mol sample of methane gas in a 3.3 L
container at 25°C.
Real Gases:
Deviations from Ideality




Real gases behave ideally at ordinary
temperatures and pressures.
At low temperatures and high pressures real
gases do not behave ideally.
The reasons for the deviations from ideality
are:
1.
The molecules are very close to one
another, thus their volume is important.
2.
The molecular interactions also become
important.
J. van der Waals, 1837-1923,
Professor of Physics,
Amsterdam. Nobel Prize 1910.
Real Gases:
Deviations from Ideality
 van

der Waals’ equation accounts for the
behavior of real gases at low temperatures
and high pressures.


n 2a 
V − nb) = nRT
P +
2 (
V 


•

The van der Waals constants a and b take into account two things:

1. a accounts for intermolecular attraction
a.
b.

For nonpolar gases the attractive forces are London Forces
For polar gases the attractive forces are dipole-dipole attractions
or hydrogen bonds.

2. b accounts for volume of gas molecules
At large volumes a and b are relatively small and van der Waal’s
equation reduces to ideal gas law at high temperatures and low
pressures.
Real Gases: Deviations from Ideal
Behavior
The van der Waals Equation
nRT
n 2a
P=
− 2
V − nb V
Corrects for
Corrects for
molecular
molecular
volume
attraction
• General form of the van der Waals equation:

n 2a 
P +
( V − nb ) = nRT

V2 


Example
Condensed matter : the three
states of matter.
Some Characteristics of Gases, Liquids and Solids and the Microscopic
Explanation for the Behavior
gas

liquid

solid

assumes the shape and
volume of its container
particles can move past
one another

assumes the shape of
the part of the container
which it occupies
particles can move/slide
past one another

retains a fixed volume
and shape
rigid - particles locked
into place

compressible
lots of free space
between particles

not easily compressible
little free space between
particles

not easily compressible
little free space between
particles

flows easily
particles can move past
one another

flows easily
particles can move/slide
past one another

does not flow easily
rigid - particles cannot
move/slide past one
another
Clearly, a theory used to describe
the condensed states of matter
must include an attraction between
the particles in the substance
 Condensed

of Matter:

.
 Liquids

 Solids

States
Kinetic Theory Description of the
Liquid State.
 Like

gases, the
condensed states of
matter can consist of
atoms, ions, or
molecules.
 What separates the
three states of matter is
the proximity of the
particles in the
substance.
 For the condensed
states of matter the
particles are close
enough to interact.
Phase Changes
Triple Point Diagram of Water
 Regions:

Each region corresponds
to one phase which is stable for
any combination of P and T within
its region
 Lines Between Region: Lines
separating the regions
representing phase-transition
curves
 Triple Point: The triple point
represents the P and T at which all
3 phases coexist in equilibrium
 Critical Point: At the critical point
the vapor pressure cannot be
condensed to liquid no matter
what pressure is applied.
Tutorial 3
 Van

der Waals, realized that two of the assumptions
mentioned above were questionable. He then
developed the Van der Waals equation of state
which predicted the formation of liquid phase. Write
the equation and state two corrections that he
made.
 (a) Calculate the pressure exerted by 1.00 mol of
CO2 in a 1.00 L vessel at 300 K, assuming that the
gas behaves ideally. (b) Repeat the calculation by
using the van der Waals equation.
 Sketch and label the liquid region, gas region solid
region and triple point in water phase diagram

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Gas and condensed matter

  • 2. Bonding model for covalent molecular substances  1. 2. Bonding for covalent molecular substances falls into two categories The strong forces of attraction which holds atoms together within molecules The weak forces of attraction between molecules
  • 3. Forces between molecules (intermolecular forces) will learn about the forces between molecules or compounds are called intermolecular forces  Inter means between or among  Internet, interstate, international  What would Interstellar travel be?  we
  • 4. Intermolecular Forces  Forces that occur between molecules.
  • 5. Intramolecular forces  What would intramolecular forces be?  Forces within molecules e.g covalent, metallic or ionic  intra means within  Intrastate, intranet, intracellular  Most of the intermolecular forces we look at occur between covalently bonded molecules or covalent molecular substances  Intramolecular bonds are stronger than intermolecular forces.
  • 6. Overview  All matter is held together by force.  The force between atoms within a molecule is a chemical or intramolecular force.  The force between molecules are a physical or intermolecular force.  These physical forces are what we overcome when a chemical changes its state (e.g. gas liquid).
  • 7. What causes intermolecular forces?  Molecules are made up of charged particles: positive nuclei and negative electrons.  When one molecule approaches another there is a multitude of forces between the particles in the two molecules.  Each electron in one molecule is attracted to the nuclei in the other molecule but also repelled by the electrons in the other molecule.  The same applies for nuclei
  • 8. Types of Intermolecular forces  The three main types of intermolecular forces are: 1. Dipole-dipole attraction occur only btw polar molecules 2. H bonding – only with Hydrogen and Oxygen, Fluorine and Nitrogen) 3. Dispersion forces (London Dispersion Forces)
  • 9. Intermolecular Forces  Forces that occur between molecules.  Dipole–dipole forces   Hydrogen bonding London dispersion forces
  • 11. Dipole-Dipole Forces  Dipole moment – molecules with polar bonds often behave in an electric field as if they had a center of positive charge and a center of negative charge.  Molecules with dipole moments can attract each other electrostatically. They line up so that the positive and negative ends are close to each other.  Only about 1% as strong as covalent or ionic bonds.
  • 12. Hydrogen Bonding Strong dipole-dipole forces. Hydrogen is bound to a highly electronegative atom – nitrogen, oxygen, or fluorine.
  • 13. Hydrogen Bonding in Water  Blue dotted lines are the intermolecula r forces between the water molecules.
  • 15. London Dispersion Forces    Instantaneous dipole that occurs accidentally in a given atom induces a similar dipole in a neighboring atom. Significant in large atoms/molecules. Occurs in all molecules, including nonpolar ones.
  • 17. London Dispersion Forces  Become stronger as the sizes of atoms or molecules increase.
  • 18. Melting and Boiling Points  In general, the stronger the intermolecular forces, the higher the melting and boiling points.
  • 19. Strength of Intermolecular Interactions Hydrogen Bonding ↑ Dipole – Dipole ↑ London Dispersion Forces
  • 20. Kinetic Molecular Theory The kinetic theory of matter is based on the following postulates: 1. Matter is composed of small particles called molecules 2. The particles are in constant random motion They possess kinetic energy due to their motion 3. There are repulsive and attractive forces between particles. They posses potential energy due to these forces 4. Average particle speed increases with temperature 5. No energy is lost when the particles collide, called elastic collision
  • 21. Kinetic Molecular Theory The kinetic energy of a particle is given by the equation: 1 KE = mv 2 Where: 2 m = particle mass in kg v = particle velocity in m/s KE = kg-m2/s2 = j (joule) According to postulate 4 of our kinetic theory particle velocity increases with temperature. This means as temperature increases then kinetic energy increases.
  • 22. Potential Energy Potential energy is the sum of the attractive and repulsive forces between particles. Examples of these types of forces are the gravitational attractive forces between objects and the repulsive forces between the same poles of magnets. Alternatively we can say forces between particles may be either cohesive or disruptive.
  • 23. Interparticle Forces Cohesive forces include dipole-dipole interactions, dispersion forces, attraction between oppositely charged ions. Cohesive forces are largely temperature independent. e.g. magnets and gravity function the same way at different temperature.
  • 24. Interparticle Forces Disruptive forces are those forces that make particles move away from each other. These forces result predominately from the particle motion. Disruptive forces increase with temperature in agreement with postulate 4. We can conclude that as we increase the temperature particles will become further apart from each other.
  • 25. Tutorial 1  State and describe briefly three (3) main types of intermolecular forces.  State five (5) assumption in the kinetic molecular theory
  • 26. A Gas  Has neither a definite volume nor shape.  Uniformly fills any container.  Mixes completely with any other gas  Exerts pressure on its surroundings.
  • 27. Earth-like Atmosphere Composition of Earth’s Atmosphere Compound %(Volume) Mole Fractiona Nitrogen Oxygen Argon Carbon dioxide 78.08 20.95 0.934 0.033 0.7808 0.2095 0.00934 0.00033 Methane Hydrogen 2 x 10-4 5 x 10-5 2 x 10-6 5 x 10-7 a. mole fraction = mol component/total mol in mixture.
  • 28. A mercury barometer The column height is proportional to the atmospheric pressure. Atmospheric pressure results from the mass of the atmosphere and gravitational forces. The pressure is the force per unit area. P = F/A 1 atm = 760 mmHg 1 atm = 1.01325 E5 Pa 1 mmHg = 1 torr
  • 29. Units for Expressing Pressure Unit Atmosphere Pascal (Pa) Kilopascal (kPa) mmHg Torr Bar mbar psi Value 1 atm 1 atm = 1.01325 x 105 Pa 1 atm = 101.325 kPa 1 atm = 760 mmHg 1 atm = 760 torr 1 atm = 1.01325 bar 1 atm = 1013.25 mbar 1 atm = 14.7 psi
  • 30. Pressure is equal to force/unit area  SI units = Newton/meter2 = 1 Pascal (Pa)  1 standard atmosphere = 101,325 Pa (100,000 Pa = 1 bar)  1 standard atmosphere = 1 atm =  760 mm Hg = 760 torr = 1013.25 hPa = 14.695 psi Meteorologists often report pressure in millibar; 1 mbar =0.001bar =0.1 kPa = 1hPa
  • 31. Variables Affecting Gases  Pressure (P)  Volume (V)  Temperature  Number (T) of Moles (n)
  • 33. Manometer Manometers are used to measure gas pressure in closed systems. For instance in a reaction vessel.
  • 34. The Gas Laws and Absolute Temperature The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state. We will deal here with gases that are not too dense. Boyle’s Law: the volume of a given amount of gas is inversely proportional to the pressure as long as the temperature is constant.
  • 35. Boyle Law…pressure is inversely proportional to volume (at constant T and moles, n).
  • 36. The Gas Laws and Absolute Temperature The volume is linearly proportional to the temperature, as long as the temperature is somewhat above the condensation point and the pressure is constant: Extrapolating, the volume becomes zero at −273.15°C; this temperature is called absolute zero.
  • 37. Avogadro’s Law  For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V α n V1 = V2 n1 n2
  • 38. The Gas Laws and Absolute Temperature The concept of absolute zero allows us to define a third temperature scale – the absolute, or Kelvin, scale. This scale starts with 0 K at absolute zero, but otherwise is the same as the Celsius scale. Therefore, the freezing point of water is 273.15 K, and the boiling point is 373.15 K. Finally, when the volume is constant, the pressure is directly proportional to the temperature:
  • 39. Combined Gas Law  Combining the gas laws the relationship P α T(n/V) can be obtained.  If n (number of moles) is held constant, then PV/T = constant. P1 V P2 V 1 2 = T T 1 2
  • 40. Ideal Gas Law PV = nRT R = universal gas constant = 0.08206 L atm K-1 mol-1 P = pressure in atm V = volume in liters n = moles T = temperature in Kelvin
  • 41. Standard Temperature and Pressure (for gases) “STP”     P = 1 atmosphere T = 0°C The molar volume of an ideal gas is 22.42 liters at STP (put 1 mole, 1 atm, R, and 273 K in the ideal gas law and calculate V) Note STP is different for other phases, e.g. solutions or enthalpies of formation.
  • 42. The Ideal Gas Law A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular mass of the substance: 1 mol H2 has a mass of 2 g 1 mol Ne has a mass of 20 g 1 mol CO2 has a mass of 44 g The number of moles in a certain mass of material:
  • 43. The Ideal Gas Equation • Charles’s Law: 1 V ∝ (constant n, T ) P V ∝ T (constant n, P ) • Avogadro’s Law: V ∝ n (constant P, T ) • Boyle’s Law: • We can combine these into a general gas law: nT V∝ P
  • 44. The Ideal Gas Equation • R = gas constant, then  nT  V = R   P  • The ideal gas equation is: PV = nRT • R = 0.08206 L·atm/mol·K = 8.3145 J/mol·K • J = kPa·L = kPa·dm3 = Pa·m3 • Real Gases behave ideally at low P and high T.
  • 45. Ideal Gas Law in Terms of Molecules: Avogadro’s Number Since the gas constant is universal, the number of molecules in one mole is the same for all gases. That number is called Avogadro’s number: The number of molecules in a gas is the number of moles times Avogadro’s number:
  • 46. Ideal Gas Law in Terms of Molecules: Avogadro’s Number Therefore we can write: where k is called Boltzmann’s constant. (13-4)
  • 47. The Ideal Gas Equation  Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law. PV = nRT P = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K) (5 L) P = 38.3 atm
  • 48. Tutorial 2.  The pressure on a sample of an ideal gas was increased from 715 torr to 3.55 atm at constant temperature. If the initial volume of the gas was 485. mL, what would be the final volume? A 7.9 L sample of gas was cooled from 79°C to a temperature at which the volume of the gas was 4.3 L. Assuming the pressure remains constant, calculate the final temperature.  Calculate the pressure in atmospheres and pascals of a 1.2 mol sample of methane gas in a 3.3 L container at 25°C.
  • 49. Real Gases: Deviations from Ideality    Real gases behave ideally at ordinary temperatures and pressures. At low temperatures and high pressures real gases do not behave ideally. The reasons for the deviations from ideality are: 1. The molecules are very close to one another, thus their volume is important. 2. The molecular interactions also become important. J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910.
  • 50. Real Gases: Deviations from Ideality  van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures.  n 2a  V − nb) = nRT P + 2 ( V   • The van der Waals constants a and b take into account two things: 1. a accounts for intermolecular attraction a. b. For nonpolar gases the attractive forces are London Forces For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds. 2. b accounts for volume of gas molecules At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.
  • 51. Real Gases: Deviations from Ideal Behavior The van der Waals Equation nRT n 2a P= − 2 V − nb V Corrects for Corrects for molecular molecular volume attraction • General form of the van der Waals equation:  n 2a  P + ( V − nb ) = nRT  V2   
  • 53. Condensed matter : the three states of matter.
  • 54. Some Characteristics of Gases, Liquids and Solids and the Microscopic Explanation for the Behavior gas liquid solid assumes the shape and volume of its container particles can move past one another assumes the shape of the part of the container which it occupies particles can move/slide past one another retains a fixed volume and shape rigid - particles locked into place compressible lots of free space between particles not easily compressible little free space between particles not easily compressible little free space between particles flows easily particles can move past one another flows easily particles can move/slide past one another does not flow easily rigid - particles cannot move/slide past one another
  • 55. Clearly, a theory used to describe the condensed states of matter must include an attraction between the particles in the substance  Condensed of Matter: .  Liquids  Solids States
  • 56. Kinetic Theory Description of the Liquid State.  Like gases, the condensed states of matter can consist of atoms, ions, or molecules.  What separates the three states of matter is the proximity of the particles in the substance.  For the condensed states of matter the particles are close enough to interact.
  • 58. Triple Point Diagram of Water  Regions: Each region corresponds to one phase which is stable for any combination of P and T within its region  Lines Between Region: Lines separating the regions representing phase-transition curves  Triple Point: The triple point represents the P and T at which all 3 phases coexist in equilibrium  Critical Point: At the critical point the vapor pressure cannot be condensed to liquid no matter what pressure is applied.
  • 59. Tutorial 3  Van der Waals, realized that two of the assumptions mentioned above were questionable. He then developed the Van der Waals equation of state which predicted the formation of liquid phase. Write the equation and state two corrections that he made.  (a) Calculate the pressure exerted by 1.00 mol of CO2 in a 1.00 L vessel at 300 K, assuming that the gas behaves ideally. (b) Repeat the calculation by using the van der Waals equation.  Sketch and label the liquid region, gas region solid region and triple point in water phase diagram