Chapter Five

1
Chapter Five

• Gases

2
Gases What Are They Like?

• Composed of widely separated particles in
  constant, random motion
• Flow readily and occupy the entire volume of
  their container
• Vapor is the term used to denote the gaseous
  state of a substance more commonly as a liquid.
• Many low molar mass molecular compounds are
  either gases or easily vaporizable liquids.

3
Visualizing Molecular Motion
4
Some Common Gases
5
Fundamental properties
Fundamental properties

• Amount of gas mass or moles
• Volume
• Temperature
• pressure

6
Gas Pressure

• Pressure is the force per unit area.
• In SI, force is expressed in newtons (N) and area
  in square meters (m2).
• The unit of pressure in SI is the pascal (Pa)
  with the units N/m2.
• Kilopascals (kPa) are often used instead since
  the pascal is such a small unit.

7
Standard Pressure Units
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Barometers

• Used to measure atmospheric pressure.
• The pressure exerted by a column of mercury
  exactly 760 mm high is called 1 atmosphere (atm).
• One millimeter of mercury is called a torr.
• 1 atm 760 mm Hg 760 Torr 101.325 kPa
• On the atmospheric level, gases do tend to settle
  under the effects of gravity this is why the
  pressure decreases as altitude increases.

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A Mercury Barometer
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Manometers

• Used to measure pressure of other gases.
• Pressure is measured as the difference in the
  heights of mercury in the two arms of the
  manometer.
• For open-ended manometers,
• pgas pbar Dh
• The pressure exerted by a liquid column is
• P g . d . h

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A Closed-End Manometer
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An Open-Ended Manometer
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Boyles LawPressure-Volume Relationship

• For a given amount of a gas at constant
  temperature, the volume of the gas varies
  inversely with its pressure.
• For a given amount of a gas at constant
  temperature, the product of the pressure and the
  volume is a constant.
• V a 1/P ? V a/P ? PV a
• P1V1 P2V2

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Graphical Representation of Boyles Law
15
Assignment 1

• Read p 158-164 p 193 3,4,20a,23,25,77

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Kinetic-Molecular Theory

• Provides a model for gases at the microscopic
  level.
• Molecules are in such rapid motion that they seem
  to resist the force of gravity.
• Movement of gases through three-dimensional space
  is called translational motion and is random.
• Helps to explain temperature and pressure of
  gases.

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Charless Law Temperature-Volume Relationship

• The volume of a fixed amount of a gas at constant
  pressure is directly proportional to its Kelvin
  temperature.
• Absolute zero is the temperature obtained by
  extrapolation to zero volume.
• Absolute zero on the Kelvin scale -273.15oC
• V a T ? V bT ? V/T b
• V1/T1 V2/T2

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Graphical Representation of Charless Law
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Avogadros LawMole-Volume Relationship

• At a fixed temperature and pressure, the volume
  of a gas is directly proportional to the amount
  of gas in moles (n) or to the number of molecules
  of gas.
• V a n ? V cn ? V/n c
• Standard temperature and pressure (STP) is equal
  to 0oC and 1 atm.
• The molar volume of a gas is the volume occupied
  by one mole of the gas at STP.

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The Combined Gas Law

• V a/P, V bT, and V cn
• V a (nT)/P
• (PV)/(nT) constant
• (P1V1)/(n1T1) (P2V2)/(n2T2)

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Effect of Temperature on a Gas
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The Ideal Gas Law

• (PV)/(nT) constant R
• R 0.082058 (L.atm)/(mol.K)
• R is called the ideal gas constant.
• PV nRT is the ideal gas equation
• P is in atmospheres
• V is in liters
• n is in moles
• T is in Kelvin

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Units for the Gas Constant, R
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Molecular Mass Determination

• M molar mass and m mass in grams
• n (PV)/(RT) and M m/n
• n m/M (PV)/(RT) ? mRT MPV
• M (mRT)/(PV)
• Useful for determining the molar mass of an
  unknown volatile liquid.

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Gas Densities

• Gases are much less dense than liquids and
  solids.
• Densities of gases are reported in g/L.
• At STP, d M/22.4L (M molar mass).
• Under other conditions
• d (MP)/(RT)
• From this equation, the density of a gas is
  directly proportional to its molar mass and
  pressure and, inversely proportional to its
  Kelvin temperature.

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The Law of Combining Volumes

• When gases measured at the same temperature and
  pressure are allowed to react, the volumes of
  gaseous reactants and products are in small
  whole-number ratios.
• Relates volumes of any two gaseous species in a
  reaction, even if some reactants or products are
  liquid or solid.
• A reaction need not be carried out at the
  particular temperature and/or pressure at which
  the gaseous species are compared.
• Dont need to know actual conditions as long as
  the same conditions were used to measure each
  species initially.

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Gay-Lussacs Law of Combining Volumes
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Avagadros Explanation ofGay-Lussacs Law
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Ideal Gas EquationIn Reaction Stoichiometry

• Ratios of gas volumes can be substituted for mole
  ratios only for gases and only if the gases are
  at the same temperature and pressure.
• Often the amount of a gaseous reactant or product
  needs to be related to that of a solid or liquid.
• The ideal gas equation allows us to relate mole
  of gas to other gas properties.

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Daltons Law Of Partial Pressure

• The total pressure exerted by a mixture of gases
  is equal to the sum of the partial pressures
  exerted by the separate gases.
• Ptotal P1 P2 P3
• P1 (n1RT)/V P2 (n2RT)/V and so on

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Partial Pressures Illustrated
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Mole Fraction

• The mole fraction is the fraction of all the
  molecules in a mixture that are of a given type.
• P1/Ptotal n1/ntotal x1
• P1 x1 . Ptotal
• The composition of gaseous mixtures are often
  given in percent by volume and this is equal to
  mole percent.

33
Collection of Gases Over Water

• As essentially insoluble gas is passed into a
  container of water, the gas rises because its
  density is much less than that of water and the
  water must be displaced.
• Assuming the gas is saturated with water vapor,
  the partial pressure of the water vapor is the
  vapor pressure of the water.
• Pgas Ptotal - PH2O(g) Pbar - PH2O(g)

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Collection of a Gas Over Water
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Vapor Pressure of Wateras a Function of
Temperature
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Some Quantitative Aspects ofthe
Kinetic-Molecular Theory

• A gas is made up of molecules that are in
  constant, random, straight-line motion.
• Molecules of a gas are far apart a gas is mostly
  empty space.
• There are no forces between molecules except
  during the instant of collision.
• Individual molecules may gain or lose energy as a
  result of collisions however, the total energy
  remains constant.

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The Kinetic-Molecular Theoryand Temperature

• RT 2/3 . NA . mu2 2/3 . NA . ek
• u2 is the average of the squares of the molecular
  speeds
• mu2 ek average translational kinetic energy
• ek 3/2 . R/NA . T
• Since ek , 3/2 , R , and NA are all fixed
  quantities,
• ek constant . T
• The average translational kinetic energy of the
  molecules of a gas is directly proportional to
  the Kelvin temperature.

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Molecular Speeds

• The root-mean-square speed, urms, is the square
  root of the average of the squares of the
  molecular speeds.
• urms (3RT)/M
• The units of urms are m/s.
• The molar mass, M, must be in units of kg/mole.
• R 8.3145 J/(mol . K).
• J joule (kg . m2)/s2

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Effects Of Molar MassAnd Temperature
At 273 K, the most probable speeds for O2 and H2
molecules are 377 and 1500 m/s, respectively.
Notice that the temperature must be greater than
1000 K before O2 molecules have the same most
probable sped as do H2 molecules at 273 K.
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Diffusion

• Diffusion is the process by which one substance
  mixes with one or more other substances as a
  result of the translational motion of molecules.
• Diffusion of gases is much slower than would be
  predicted by molecular speeds due to the frequent
  collisions of molecules.
• The average distance a molecule travels between
  collisions is called its mean free path.

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Diffusion of Gases
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Effusion

• Effusion is the process in which a gas escapes
  from its container through a tiny hole, or
  orifice.
• At a given temperature, the rates of effusion of
  gas molecules are inversely proportional to the
  square roots of their molar masses.
• effusion rate M2/M1
• effusion time a 1/(effusion rate)

43
Real Gases

• Under many conditions, real gases do not follow
  the ideal gas law.
• Intermolecular forces of attraction cause the
  measured pressure of a real gas to be less than
  expected.
• When molecules are close together, the volume of
  the molecules themselves becomes a significant
  fraction of the total volume of a gas.
• van der Waals equation
• (P (n2a)/V2)(V - nb) nRT

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Intermolecular Forces of Attraction
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van der Waals ConstantsFor Selected Gases
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Summary

• Gases consist of widely separated molecules that
  are moving constantly and randomly throughout the
  container.
• Molecular collisions with containers give rise to
  pressure.
• The SI unit of pressure is the pascal (Pa).
• Boyles Law at constant T, V a/P
• Charless Law at constant P, V bT
• Avogadros Law at constant T P, V cn
• Combined Gas Law (P1V1)/(n1T1) (P2V2)/(n2T2)
• Ideal Gas Law PV nRT, R 0.0821 L . atm .
  mol-1 . K-1

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Summary (continued)

• The ideal gas equation can be used in place of
  the simple or combined gas laws, especially in
  molecular mass and gas density determinations,
  and in stoichiometric calculations for reactions
  involving gases.
• The total pressure of a gaseous mixture is the
  sum of the partial pressures of each gas.
• The kinetic-molecular theory provides a basis for
  describing the diffusion and effusion of gases.
• Real gases are more likely to exhibit ideal
  behavior at high temperatures and low pressures.