Gases Chapter 5 Pg' 139179

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Gases Chapter 5 Pg. 139-179
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Goal

• To learn about the behavior of gases both on
  molecular and macroscopic levels.

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General Characteristics of Gases

• Uniformly fills any container.
• Gases are highly compressible.
• Mixes completely with any other gas.
• Gases form homogeneous mixtures with each other
  regardless of the identities or relative
  proportions of the component gases? Atmosphere.
• Exerts pressure on its surroundings.

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Force mass X acceleration

• To understand pressure, one has to understand
  force.
• Weight your mass X acceleration due to gravity
• Mr. Yoos force
• F 87 kg X 9.8 m/s2
• F 852.6 kg m /s2 850 N

Acceleration due to gravity
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Pressure Force / Area

• If Mr. Yoos weighs 850 N on earth, and I am
  standing on a scale that is 0.5m X 0.5m or 0.25m2
  , the pressure I exert is

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Lets Say Mr. Yoos is Wearing High Heels

• Total area for the heels 1X10-4m2. The force is
  850 N. What is the pressure?
• P F/A 850N/ 1X10-4m2 8.5 X 106 N/m2
• As the area decreases, the force increases.
• Thats gotta hurt!
• 1N/m2 1 Pascal or 1 Pa

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Air Exerts Pressure

• The standard atmosphere is equal to 101,325 Pa.
• 1 atm 101,325 Pa
• 1 atm 760 torr 760 mm Hg

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Questions Pressure Conversions

• Convert 0.357 atm to torr
• 271 torr
• Convert 6.6 X 10-2 torr to atm.
• 8.7 X 10-5 atm
• Convert 147.2 kPa to torr.
• 1104 torr

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Barometer
Evangelista Torricelli (1608-1647) pressure
experiments support the atmosphere has weight.
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Using a Manometer to Measure Gas Pressure

• On a certain dry day the barometer in a
  laboratory indicates that the atmospheric
  pressure is 764.7 torr. A sample of gas is
  placed in a flask attached to an open end mercury
  manometer. A meter stick is used to measure the
  height of the mercury above the bottom of the
  manometer. The level of the mercury in the
  open-end arm of the manometer has a height of
  136.4 mm, and the mercury in the arm that is in
  contact with the gas has a height of 103.8 mm.
  What is the pressure of the gas a. in
  atmospheres, b. in kPa
• Pgas 1.049 atm
• Pgas 16.3 kPa

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The Gas Laws

• Boyles Law- the pressure exerted by a gas is
  inversely proportional to the volume the gas
  occupies if the temperature remains constant.
• Pressure X Volume Constant
• PV K
• P1V1 P2V2 (at constant temperature)

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Boyles Law

• Example A gas which has a pressure of 1.3 atm
  occupies a volume of 27 L. What volume will the
  gas occupy if the pressure is increased to 3.9
  atm at constant temperature?

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Boyles Law
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Charless Law

• At constant pressure, the volume of a gas is
  directly proportional to the temperature (in
  Kelvin) of the gas.

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Charless Law
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• Example A gas at 30.00C and 1.00 atm occupies a
  volume of 0.842 L. What volume will the gas
  occupy at 60.00C and 1.00 atm?

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Avogadros Law

• For a gas at constant temperature and pressure
  the volume is directly proportional to the number
  of moles of gas.
• Volume Constant X number of moles (constant T,
  P)
• V an

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• (at constant T, P)
• If you triple the number of moles of gas (at
  constant temperature and pressure), the volume
  will also triple.

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• Example A 5.20 L sample at 18.00C and 2.00 atm
  pressure contains 0.436 moles of a gas. If we
  add an additional 1.27 moles of the gas at the
  same temperature and pressure, what will the
  total volume occupied by the gas be?

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The Ideal Gas Law

• PV nRT
• P in atm
• V in L
• n in moles
• T in Kelvins
• R 0.08206 L atm / K mol

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Keep in Mind

• This relationship assumes that the gas behaves
  ideally (conditions of low pressure and high
  temperature). Correction factors must be added
  under certain conditions.
• Keep track of dimensions! Many ideal gas law
  problems are best solved using DA.
• Always list what you are given. You may be able
  to simplify the problem.

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• Example A sample containing 0.614 moles of a gas
  at 12.00C occupies a volume of 12.9 L. What
  pressure does the gas exert?

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• Example A sample of methane gas (CH4) at 0.848
  atm and 4.0oC occupies a volume of 7.0 L. What
  volume will the gas occupy if the pressure is
  increased to 1.52 atm and the temperature is
  increased to 11.0oC?

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• Example How many moles of a gas at 104oC would
  occupy a volume of 6.8 L at a pressure of 270
  mmHg?

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Gas Stoichiometry

• Many gas law problems involve calculating the
  volume of a gas produced by the reaction of
  volume of other gases. The problem solving
  strategy that we have used throughout is still
  the same. That is, you want to relate moles of
  reactants to moles of products. The ideal gas law
  will allow you to use the following strategy

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Standard Temperature and PressureSTP

• P 1 atm
• T 00C
• The molar volume of an ideal gas is 22.4 L at STP

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• volume of reactants ?(apply the ideal gas law) ?
  moles of reactants? (apply stoichiometry)? moles
  of products (apply ideal gas law)? volume of
  products

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• Example A sample containing 15.0 g of dry ice
  (CO2(s)) is put into a balloon and allowed to
  sublime according to the following equation
• CO2 (s) ? CO2 (g)
• How big will the balloon be (ie, what is the
  volume of the balloon), at 22.0oC and 1.04 atm,
  after all of the dry ice has sublimed?

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• Example 0.500 L of H2 (g) are reacted with 0.600
  L of O2 (g) at STP according to the equation
• 2H2 (g) O2 (g) ? 2H2O (g)
• What volume will the H2O occupy at 1.00 atm and
  350.oC?

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Density and Molar Mass

• PV nRT
• P nRT/V
• P (m/MM)RT/V
• P m(RT)/V(MM)
• P dRT/MM
• MM dRT/P

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• Example A gas at 34.0oC and 1.75 atm has a
  density of 3.40 g/L. Calculate the molar mass
  (MM) of the gas.

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Daltons Law of Partial Pressures

• For a mixture of gases in a container, the total
  pressure is the sum of the pressures that each
  gas would exert if it were alone.
• Ptotal P1 P2 P3 Pn
• (n1 n2 nt) RT/V
• Because RT/V will be the same for each of the
  different gases in the same container.

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• Example A volume of 2.0 L of He at 46oC, and 1.2
  atm pressure, was added to a vessel that
  contained 4.5 L of N2 at STP. What is the total
  pressure and partial pressure of each gas at STP
  after the He is added?

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The Production of Oxygen by Thermal Decomposition
of KCIO3
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Vapor Pressure of Water
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Calculating the Amount of Gas Collected over Water

• A sample of KClO3 is partially decomposed
  producing O2 gas that is collected over water.
  The volume of gas collected is 0.250L at 26oC and
  765 torr total pressure. (a) How many moles of
  O2 are collected? (b) How many grams of KClO3
  were decomposed?

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Mole Fraction

• The ratio of the number of moles of a given
  component in a mixture to the total number of
  moles in the mixture.
• X1 n1 / ntotal
• The mole fraction of a particular component is a
  mixture of ideal gases is directly related to its
  partial pressure
• X1 P1 / Ptotal
• P1 X1 x Ptotal

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Kinetic Molecular Theory of Gases

• 1. The volume of the individual particles of a
  gas can be assumed to be negligible.
• 2. The particles are in constant motion. The
  collisions of the particles with the walls of the
  container are the cause of the pressure exerted
  by the gas.
• 3. The particles are assumed to exert no forces
  on each other
• 4. The average kinetic energy of a collection of
  gas particles is assumed to be directly
  proportional to the Kelvin temperature of the gas.

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Temperature is a Measure of the Average Kinetic
Energy of a Gas

• (KE)average 3/2 RT
• KE ½ mv2

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Root Mean Square Velocity

• The expression dealing with the average velocity
  of gas particles is called the root mean square
  velocity.
• Where R 8.3145 J/K mol 8.3145 kg m2/s2 / Kmol
• T temp in Kelvins
• M mass of a mole of the gas in Kilograms

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• Example Calculate the root mean square velocity
  for the atoms in a sample of oxygen gas at
• 0.0oC
• 300.oC

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Effusion or Diffusion?

• Diffusion- term used to describe the mixing of
  gases.
• Effusion- relates to the passage of a gas through
  an orifice into an evacuated chamber.

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Grahams Law of Effusion

• The higher the molar mass of the gas, the slower
  the rate of effusion through a small orifice.

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• Example How many times faster than He would NO2
  gas effuse?

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With Regard to Diffusion

• The important idea is that even though gases
  travel very rapidly (hundreds of meters per
  second), their motions are in all directions, so
  mixing is relatively slow. The basic structure
  of Grahams Law holds.

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Ideal Vs Real Gases

• No gas behaves in a truly ideal fashion.
• Ideal gas law fails under conditions of high
  pressure and low temperature.
• WHY? Gas molecules DO take up space and DO
  interact through attractive forces with one
  another.

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• For exactly one mole of an ideal gas
• The deviation from ideal behavior is large at
  high pressure and low temperature.

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The van der Waals Equation

• Accounts for the stickiness and size of
  molecules.
• The conditions for ideal gas law included
• Molecules are perfectly elastic in collisions (no
  stickiness)
• Molecules have no mass
• Molecules move at random

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• At low temperatures, all gases condense!
• The resulting liquid has a measurable volume!
• At high pressures, intermolecular distances
  become small, thereby allowing attractive forces
  to set up. These attractive forces reduce the
  momentum of molecules. As the momentum
  decreases, so does the pressure that is exerted
  on the containers walls.

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To Correct for Decrease in Pressure due to
Molecular Stickiness

• For stickiness to be a factor, two molecules must
  collide.
• Probability of first molecule proportional to
  the number density (n/V)
• Probability of second (n/V)
• Thus, reduction in pressure due to stickiness
  should be proportional to (n/V)2.
• Pideal Preal a (n2/V2)
• a proportionality constant that varies by
  substance

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To Correct for Volume

• As pressures and density increase, the
  significance due to the volume of the gas
  molecules themselves increases.

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• In the ideal gas law equation, the volume used is
  the free volume that the molecules find
  themselves in. The free volume is the container
  volume minus the volume that is taken up by the
  molecules of the gas itself.
• Videal Vreal nb
• Where b is a constant representing the volume of
  a mole of gas molecules at rest.

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van der Waals Equation

• The ideal gas equation corrected for molecular
  size and stickiness

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Rearranged
Correction for volume of molecules(decreases
volume as a function of the number of molecules
Correction for molecular attraction(decreases
pressure as volume decreases and the number of
molecules increases
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van der Waals Constants(vary with gas)
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• Example Calculate the pressure exerted by 0.3000
  mol of He in a 0.2000L container at 25.0oC.
• A. using the ideal gas law, and
• B. using van der Waals equation.

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Chemistry in the Atmosphere

• The atmosphere is composed of 78 N2, 21 O2,
  0.9 Ar, and 0.03 CO2 along with trace gases.
• The composition of the atmosphere varies as a
  function of distance from the earths surface.
  Heavier molecules tend to be near the surface due
  to gravity.
• Upper atmospheric chemistry is largely affected
  by UV, X-rays, and cosmic radiation emanating
  from space. The ozone layer is especially
  reactive to UV radiation.
• Manufacturing and other processes of our modern
  society affect the chemistry of our atmosphere.
  Air pollution is a direct result of such
  processes.

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Air Pollution

• Photochemical smog reactions
• N2 (g) O2 (g) heat ? 2NO (g)
• 2NO (g) O2 (g) ? 2NO2 (g)
• NO2 (g) radiant energy ? NO (g) O (g)
• O (g) O2 (g) ? O3 (g) Ozone
• Ozone causes lung and eye irritation and can be
  dangerous for people with asthma, emphysema, and
  other respiratory conditions.

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Photochemical Smog
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Ozone Layer
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A Schematic Diagram of the Process for Scrubbing
Sulfur Dioxide from Stack Gases in Power Plants
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Acid Rain

• 2NO2 (g) H2O (l) ? HNO2 (aq) HNO3 (aq)
• 2SO2 (g) O2(g) ? 2SO3 (g)
• SO3 (g) H2O (l) ? H2SO4 (aq)

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Acid Rain
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Acid Rain