GASES AND KINETIC-MOLECULAR THEORY

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CHAPTER 3

• GASES AND KINETIC-MOLECULAR THEORY

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CHAPTER GOALS

1. Comparison of Solids, Liquids, and Gases
2. Composition of the Atmosphere and Some Common
   Properties of Gases
3. Pressure
4. Boyles Law The Volume-Pressure Relationship
5. Charles Law The Volume-Temperature
   Relationship The Absolute Temperature Scale
6. Standard Temperature and Pressure
7. The Combined Gas Law Equation

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CHAPTER GOALS

• Mass-Volume Relationships in Reactions Involving
  Gases
• The Kinetic-Molecular Theory
• Diffusion and Effusion of Gases
• Real Gases Deviations from Ideality

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Comparison of Solids, Liquids, and Gases

• The density of gases is much less than that of
  solids or liquids.

Densities (g/mL) Solid Liquid Gas
H2O 0.917 0.998 0.000588
CCl4 1.70 1.59 0.00503

• Gas molecules must be very far apart compared to
  liquids and solids.

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Composition of the Atmosphere and Some Common
Properties of Gases
Composition of Dry Air
Gas by Volume
N2 78.09
O2 20.94
Ar 0.93
CO2 0.03
He, Ne, Kr, Xe 0.002
CH4 0.00015
H2 0.00005
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Pressure

• Pressure is force per unit area.
• lb/in2
• N/m2
• Gas pressure as most people think of it.

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Pressure

• Atmospheric pressure is measured using a
  barometer.
• Definitions of standard pressure
• 76 cm Hg
• 760 mm Hg
• 760 torr
• 1 atmosphere
• 101.3 kPa

Hg density 13.6 g/mL
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Boyles Law The Volume-Pressure Relationship

• V ? 1/P or
• V k (1/P) or PV k
• P1V1 k1 for one sample of a gas.
• P2V2 k2 for a second sample of a gas.
• k1 k2 for the same sample of a gas at the same
  T.
• Thus we can write Boyles Law mathematically as
  P1V1 P2V2

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Boyles Law The Volume-Pressure Relationship

• Example 3-1 At 25oC a sample of He has a volume
  of 4.00 x 102 mL under a pressure of 7.60 x 102
  torr. What volume would it occupy under a
  pressure of 2.00 atm at the same T?

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Boyles Law The Volume-Pressure Relationship

• Notice that in Boyles law we can use any
  pressure or volume units as long as we
  consistently use the same units for both P1 and
  P2 or V1 and V2.
• Use your intuition to help you decide if the
  volume will go up or down as the pressure is
  changed and vice versa.

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Charles Law The Volume-Temperature
Relationship The Absolute Temperature Scale
absolute zero -273.15 0C
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Charles Law The Volume-Temperature
Relationship The Absolute Temperature Scale

• Charless law states that the volume of a gas is
  directly proportional to the absolute temperature
  at constant pressure.
• Gas laws must use the Kelvin scale to be correct.
• Relationship between Kelvin and centigrade.

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Charles Law The Volume-Temperature
Relationship The Absolute Temperature Scale

• Mathematical form of Charles law.

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Charles Law The Volume-Temperature
Relationship The Absolute Temperature Scale

• Example 3-2 A sample of hydrogen, H2, occupies
  1.00 x 102 mL at 25.0oC and 1.00 atm. What
  volume would it occupy at 50.0oC under the same
  pressure?
• T1 25 273 298
• T2 50 273 323

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Standard Temperature and Pressure

• Standard temperature and pressure is given the
  symbol STP.
• It is a reference point for some gas
  calculations.
• Standard P ? 1.00 atm or 101.3 kPa
• Standard T ? 273.15 K or 0.00oC

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The Combined Gas Law Equation

• Boyles and Charles Laws combined into one
  statement is called the combined gas law
  equation.
• Useful when the V, T, and P of a gas are changing.

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The Combined Gas Law Equation

• Example 3-3 A sample of nitrogen gas, N2,
  occupies 7.50 x 102 mL at 75.00C under a pressure
  of 8.10 x 102 torr. What volume would it occupy
  at STP?

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The Combined Gas Law Equation

• Example 3-4 A sample of methane, CH4, occupies
  2.60 x 102 mL at 32oC under a pressure of 0.500
  atm. At what temperature would it occupy 5.00 x
  102 mL under a pressure of 1.20 x 103 torr?
• You do it!

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The Combined Gas Law Equation
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Summary of Gas LawsThe Ideal Gas Law

• Boyles Law - V ? 1/P (at constant T n)
• Charles Law V ? T (at constant P n)
• Combine these three laws into one statement
• V ? nT/P

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Daltons Law of Partial Pressures

• Daltons law states that the pressure exerted by
  a mixture of gases is the sum of the partial
  pressures of the individual gases.
• Ptotal PA PB PC .....

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Daltons Law of Partial Pressure
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Daltons Law of Partial Pressures

• Example 3-5 If 1.00 x 102 mL of hydrogen,
  measured at 25.0 oC and 3.00 atm pressure, and
  1.00 x 102 mL of oxygen, measured at 25.0 oC and
  2.00 atm pressure, were forced into one of the
  containers at 25.0 oC, what would be the pressure
  of the mixture of gases?

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Daltons Law of Partial Pressures

• Vapor Pressure is the pressure exerted by a
  substances vapor over the substances liquid at
  equilibrium.

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Daltons Law of Partial Pressures

• Example 3-6 A sample of hydrogen was collected
  by displacement of water at 25.0 oC. The
  atmospheric pressure was 748 torr. What pressure
  would the dry hydrogen exert in the same
  container?

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Daltons Law of Partial Pressures

• Example 3-7 A sample of oxygen was collected by
  displacement of water. The oxygen occupied 742
  mL at 27.0 oC. The barometric pressure was 753
  torr. What volume would the dry oxygen occupy at
  STP?
• You do it!

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The Kinetic-Molecular Theory

• The basic assumptions of kinetic-molecular theory
  are
• Postulate 1
• Gases consist of discrete molecules that are
  relatively far apart.
• Gases have few intermolecular attractions.
• The volume of individual molecules is very small
  compared to the gass volume.
• Proof - Gases are easily compressible.

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The Kinetic-Molecular Theory

• Postulate 2
• Gas molecules are in constant, random, straight
  line motion with varying velocities.
• Proof - Brownian motion displays molecular motion.

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The Kinetic-Molecular Theory

• Postulate 3
• Gas molecules have elastic collisions with
  themselves and the container.
• Total energy is conserved during a collision.
• Proof - A sealed, confined gas exhibits no
  pressure drop over time.

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The Kinetic-Molecular Theory

• Postulate 4
• The kinetic energy of the molecules is
  proportional to the absolute temperature.
• The average kinetic energies of molecules of
  different gases are equal at a given temperature.
• Proof - Brownian motion increases as temperature
  increases.

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The Kinetic-Molecular Theory

• The kinetic energy of the molecules is
  proportional to the absolute temperature. The
  kinetic energy of the molecules is proportional
  to the absolute temperature.
• Displayed in a Maxwellian distribution.

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The Kinetic-Molecular Theory

• The gas laws that we have looked at earlier in
  this chapter are proofs that kinetic-molecular
  theory is the basis of gaseous behavior.
• Boyles Law
• P ? 1/V
• As the V increases the molecular collisions with
  container walls decrease and the P decreases.
• Daltons Law
• Ptotal PA PB PC .....
• Because gases have few intermolecular
  attractions, their pressures are independent of
  other gases in the container.
• Charles Law
• V ? T
• An increase in temperature raises the molecular
  velocities, thus the V increases to keep the P
  constant.

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The Kinetic-Molecular Theory
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Diffusion and Effusion of Gases

• Diffusion is the intermingling of gases.
• Effusion is the escape of gases through tiny
  holes.

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Diffusion and Effusion of Gases

• This is a demonstration of diffusion.

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Diffusion and Effusion of Gases

• The rate of effusion is inversely proportional to
  the square roots of the molecular weights or
  densities.

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Diffusion and Effusion of Gases

• Example 3-8 Calculate the ratio of the rate of
  effusion of He to that of sulfur dioxide, SO2, at
  the same temperature and pressure.

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Diffusion and Effusion of Gases

• Example 3-9 A sample of hydrogen, H2, was found
  to effuse through a pinhole 5.2 times as rapidly
  as the same volume of unknown gas (at the same
  temperature and pressure). What is the molecular
  weight of the unknown gas?
• You do it!

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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
• The molecules are very close to one another, thus
  their volume is important.
• The molecular interactions also become important.

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Real GasesDeviations from Ideality

• What are the intermolecular forces in gases that
  cause them to deviate from ideality?
• For nonpolar gases the attractive forces are
  London Forces
• For polar gases the attractive forces are
  dipole-dipole attractions or hydrogen bonds.