John%20A.%20Schreifels

1
Chapter 5

• Gases

2
Overview

• Gas Laws
• Gas Pressure and its measurement
• Empirical gas laws
• Ideal gas laws
• Stoichiometry and gases
• Gas Mixtures Law of partial pressures
• Kinetic and Molecular Theory
• Kinetic theory of an Ideal gas
• Molecular speeds diffusion and effusion
• Real gases

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Gases and Gas Pressure

• They form homogeneous solutions. All gases
  dissolve in each other.
• Gases are compressible.
• Large molar volume.
• Barometer usually mercury column in tube mm Hg
  is a measure of pressure.
• Manometer tube of liquid connected to enclosed
  container makes it possible to measure pressure
  inside the container.
• Pressure
• One of the most important of the measured
  quantities for gases
• defined as the force/area P f/area.
• Pressure has traditionally been measured in units
  relating to the height of the Hg and is thus
  expressed as mm Hg 1 Torr.

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Gas Pressure

• Pressure is directly proportional to the height
  of the column in a barometer or manometer.
• Mercury often used but other low density liquids
  are used for low pressure changes
• P dHgghHg doilghoil or dHghHg doilhoil.
• E.g. Water is sometimes used to determine
  pressure determine the height of water if the
  barometer pressure was 750 mmHg. The density of
  Hg 13.596 g/cm3 and 1.00 g/cm3 respectively.
• Solution

5
The Gas Laws

• Boyle's Law For a fixed amount of gas and
  constant temperature, PV constant.
• Charles's Law at constant pressure the volume is
  linearly proportional to temperature. V/T
  constant
• Avagadros law for a fixed pressure and
  temperature, the volume of a gas is directly
  proportional to the number of moles of that gas.
  V/n k constant.
• E.g. 1 The volume of some amount of a gas was
  1.00 L when the pressure was 10.0 atm what would
  the volume be if the pressure decreased to 1.00
  atm?
• E.g. 2 A gas occupied a volume of 6.54 L at 25C
  what would its volume be at 100C?
• E.g. 3 The volume of 0.555 mol of some gas was
  100.0 L what would be the volume of 15.0 mol of
  the same gas at the same T and P?

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The Ideal Gas Equation

• Ideal gas law the functional relationship between
  the pressure, volume, temperature and moles of a
  gas. PV nRT all gases are ideal at low
  pressure.
• PV nRT. Each of the individual laws is
  contained in this equation.
• Boyle's Law PV k1 nRT.
• Charles's Law
• Avagadros law
• When any of the other three quantities in the
  ideal gas law have been determined the last one
  can be calculated.
• E.g. Calculate the pressure inside a TV picture
  tube, if it's volume is 5.00 liters, it's
  temperature is 23.0?C and it contains 0.0100 mg
  of nitrogen.

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Further Applications of Ideal-Gas Equation

• The density of a gas the density of a gas can be
  related to the pressure from the ideal gas law
  using the definition of density d mass/vol.
• E.g. Estimate the density of air at 20.0?C and
  1.00 atm by supposing that air is predominantly
  N2.
• E.g. From the results above determine the density
  of He.
• Rearrangement permits the determination of
  molecular mass of a gas from a measure of the
  density at a known temperature and pressure.
• E.g. A certain gas was found to have a density of
  0.480 g/L at 260?C and 103 Torr. Determine the
  FM of the compound.

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Stoichiometric Relationships with Gases

• When gases are involved in a reaction, das
  properties must be combined with stoichiometric
  relationships.
• E.g. Determine the volume of gas evolved at
  273.15 K and 1.00 atm if 1.00 kg of each reactant
  were used. Assume complete reaction (i.e. 100
  yield)
• CaO(s) 3C(s) ? CaC2(s) CO(g).
• Strategy
• Determine the number of moles of each reactant to
  which this mass corresponds.
• Use stoichiometry to tell us the corresponding
  number of moles of CO produced.
• Determine the volume of the gas from the ideal
  gas law.

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Partial Pressure and Daltons Law

• Dalton's Law the sum of the partial pressures
  of the gases in a mixture the total pressure or
  P PA PB PC ...where Pi the partial
  pressure of component i.
• Dalton found that gases obeying the ideal gas law
  in the pure form will continue to act ideally
  when mixed together with other ideal gases.
• The individual partial pressures are used to
  determine the amount of that gas in the mixture,
  not the total pressure, PA nART/V.
• Since they are in the same container T and V will
  be the same for all gases.
• E.g. 1.00 g of air consists of approximately
  0.76 g nitrogen and 0.24 g oxygen. Calculate the
  partial pressures and the total pressure when
  this sample occupies a 1.00 L vessel at 20.0?C.
• Solution
• Determine the number of moles of each gas.
• Using the ideal gas law determine the pressure of
  each and sum to determine the total pressure.

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Partial Pressure and Daltons Law2

• Mole fraction another quantity commonly
  determined for gas mixtures. It is defined the
  number of moles of one substance relative to the
  total number of moles in the mixture or
• X can be calculated from
• moles of each gas in the mixture or
• the pressures of each gas
• E.g. determine the mole fraction of N2 in the
  above example.
• Collection of a gaseous product over water is
  another example of Dalton's Law. Subtract the
  vapor pressure of water to find the pressure of
  the gaseous product.
• E.g. Suppose KClO3 was decomposed according to
• 2 KClO3(s) ? ? 2KCl(s) 3O2(g).
• PT 755.2 Torr and 370.0 mL of gas was
  collected over water at 20.0?C. Determine the
  number of moles of O2 if the vapor pressure of
  water is 17.5 torr at this temperature.

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The Behavior of Real Gases

• The molar volume is not constant as is expected
  for ideal gases.
• These deviations due to an attraction between
  some molecules.
• Finite molar molecular volume.
• For compounds that deviate from ideality the van
  der Waals equation is used
• where a and b are constants that are
  characteristic of the gas.
• Applicable at high pressures and low
  temperatures.

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The Kinetic Theory Molecular Theory of Gases

• Microscopic view of gases is called the kinetic
  theory of gases and assumes that
• Gas is collection of molecules (atoms) in
  continuous random motion.
• The molecules are infinitely small point-like
  particles that move in straight lines until they
  collide with something.
• Gas molecules do not influence each other except
  during collision.
• All collisions are elastic the total kinetic
  energy is constant at constant T.
• Average kinetic energy is proportional to T.

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The Kinetic Theory Molecular Theory of Gases

• Theory leads to a description of bulk properties
  i.e. observable properties.
• The average kinetic energy of the molecule is
• where NA Avagadros number.
• Average kinetic energy of moving particles can
  also be obtained from
• where u average velocity
• All speeds are possible giving really a
  distribution of speeds.
• Combine 1 2 to get a relationship between the
  velocity, temperature and molecular mass.
• Express M in kg/mol and R 8.3145 J/molK.
• E.g. determine average velocity of He at 300 K.
• E.g.2 predict the ratio of the speeds of some gas
  if the temperature increased from 300 K to 450 K.
  

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Grahams Law Diffusion and Effusion of Gases

• Diffusion the process whereby a gas spreads out
  through another gas to occupy the space with
  uniform partial pressure.
• Effusion the process in which a gas flows through
  a small hole in a container.
• Grahams law of Effusion the rate of effusion of
  gas molecules through a hole is inversely
  proportional to the square root of the molecular
  mass of the gas at constant temperature and
  pressure.
• E.g. determine the molecular mass of an unknown
  compound if it effused through a small orifice if
  it effused 3.55 times slower than CH4.
• E.g. A compound with a molecular mass of 32.0
  g/mol effused through a small opening in 35 s
  determine the effusion time for the same amount
  of a compound with a molecular mass of 16.0.