Gases

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Gases

• Chapter 13

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13.1 Pressure

• Objective to learn about atmospheric pressure
  and the way in which barometers work.
• To learn the various units of pressure.
• Pressure total force applied to a certain
  areaF/S
• larger force larger pressure
• smaller area larger pressure
• Pressure is caused by gas molecules colliding
  with container or surface.
• More forceful collisions or more frequent
  collisions mean higher gas pressure.

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Properties of Gases

• Expand to completely fill their container
• Take the Shape of their container
• Low Density
• much less than solid or liquid state
• Compressible
• Mixtures of gases are always homogeneous
• Fluid

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Units of Gas Pressure

• atmosphere (atm)
• height of a column of mercury (mm Hg, in Hg)
• torr
• Pascal (Pa)
• pounds per square inch (psi, lbs./in2)
• 1.000 atm 760.0 mm Hg 29.92 in Hg 760.0
  torr 101,325 Pa 101.325 kPa 14.69 psi

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1 atmosphere 760 mm Hg
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13.2 Pressure and Volume Boyles Law

• Objective To understand the law that relates the
  pressure and volume of a gas.
• To do calculations involving this law.

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A.5 Boyles LawP-V Relationships

• Robert Boyle (1627-1691) noted that the volume of
  a gas decreased as the pressure was increased.
  Doubling the pressure caused the gas to decrease
  to one-half its original volume.
• Boyle's Law (T constant)
• The volume of a fixed quantity of gas maintained
  at constant temperature is inversely proportional
  to the pressure.

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• The relationship of pressure and volume can be
  written as an equation by using a proportionality
  constant (k) at specific temperature, therefore
  PV k
• P1V1 P2V2, where P1 and V1 indicates the
  initial pressure and volume of a sample, and P2 ,
  V2 indicate the final pressure and volume of a
  sample.
• Example A 1.50-L sample of methane gas exerts a
  pressure of 1650 mm Hg. Calculate the new
  pressure if the volume changes to 7.00 L. Assume
  temperature remains constant.

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• graph P vs V is curve
• graph V vs 1/P is straight line

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13.3 The Temperature-Volume Relationship
Charles' Law

• The relationship between gas volume and
  temperature was discovered in 1787 by Jacques
  Charles (1746-1823). The law states The volume
  of a fixed amount of gas maintained at constant
  pressure is directly proportional to its absolute
  temperature. Doubling the absolute temperature
  causes the gas volume to double.
• V ? T (P constant). V kT, therefore
• and The value of constant
  k depends
• on the pressure and amount of gas.

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• Example A 275-L helium balloon is heated from
  20 to 40 C. Calculate the new volume assuming
  the pressure remains constant.

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13.4 Volume and Moles Avogadros Law

• Objective to understand the law relating the
  volume and the number of moles of a sample of gas
  at constant temperature and pressure, and to do
  calculations involving this law.
• Avogadros Law States that equal volumes of
  gases at the same temperature and pressure
  contain the same number of molecules.

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• We can represent Avogadros Law as
• Practice Suppose we have a 12.2 L sample
  containing 0.5 mol of oxygen gas, O2, at a
  pressure of 1 atm and temperature of 25 C. If
  all of this O2 is converted to ozone, O3 , at the
  same temperature and pressure, what will be the
  volume of the ozone formed?

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13.5 The Ideal Gas

• Objective to understand the ideal gas law and
  use it in calculations.
• By combing the proportionality constants from the
  gas laws we can write a general equation
• R is called the gas constant
• The value of R depends on the units of P and V
• Generally use R 0.08206 L.atm/K.mol
• The gas law defines the behavior of an ideal gas
  when pressure is low (at or below 1 atm) and
  temperature is high (above 0C).

PV nRT
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• Values for the gas constant R
• Units Value
• L atm/mol K 0.08206
• cal/mol K 1.987
• J/mol K 8.314
• m3 Pa/mol K 8.314
• L torr/mol K 62.36
• .

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Combined Gas Law
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• Practice
• A sample of hydrogen gas, H2, has a volume of
  8.56 L at a temperature of 0 C and a pressure of
  1.5 atm. Calculate the number of moles of H2
  present in this gas sample. (Assume that the gas
  behaves ideally).
• Suppose we have a 0.240 mol sample of ammonia gas
  at 25 C with a volume of 3.5 L at a pressure of
  1.68 atm. The gas is compressed to a volume of
  1.35 L at 25 C. Use the ideal gas law to
  calculate the final pressure.

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13.6 Daltons Law of Partial Pressures

• Objective to understand the relationship between
  the partial and total pressures of a gas mixture,
  and to use this relationship in calculations.
• The total pressure of a mixture of gases equals
  the sum of the pressures each gas would exert
  independently
• Partial pressures is the pressure a gas in a
  mixture would exert if it were alone in the
  container
• Ptotal Pgas A Pgas B
• For determining the pressure a dry gas would have
  after it is collected over water
• Pwet gas Pdry gas Pwater vapor
• Pwater vapor depends on the temperature, look up
  in table 13.2 on page 424.

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Calculating Total Pressure

• The partial pressure of each gas in a mixture
• can be calculated using the Ideal Gas Law

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• Practice
• Mixtures of helium and oxygen are used in the air
  tanks of underwater divers for deep dives. For a
  particular dive, 12 L of O2 at 25 C and 1.0 atm
  and 46 L of He at 25 C and 1.0 atom were both
  pumped into a 5 L tank. Calculate the partial
  pressure of each gas and the total pressure in
  the tank at 25 C.

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13.8 The Kinetic Molecular Theory of Gases

• Objective To understand the basic postulates of
  the kinetic molecular theory.
• It is a model that attempts to explain the
  behavior of an ideal gas.
• In solids, the molecules have no translational
  freedom, they are held in place by strong
  attractive forces
• May only vibrate
• In liquids, the molecules have some translational
  freedom, but not enough to escape their
  attraction for neighboring molecules
• They can slide past one another, rotate as well
  as vibrate

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• In gases, the molecules have complete freedom
  from each other, they have enough energy to
  overcome all attractive forces.

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• Postulates of the Kinetic Molecular Theory of
  Gases
• Gases consist of tiny particles (atoms or
  molecules).
• These particles are so small, compared with the
  distances between them, that the volume (size) of
  the individual particles can be assumed to be
  negligible (zero).
• The particles are in constant random motion,
  colliding with the walls of the container. These
  collisions with the walls cause the pressure
  exerted by the gas.
• The particles are assumed not to attract or to
  repel each other.
• The average kinetic energy of the gas particles
  is directly proportional to the Kelvin
  temperature of the gas.

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13.11 Gas Stoichiometry

• Objectives To understand the molar volume of an
  ideal gas.
• To learn the definition of STP.
• To use these concepts and the ideal gas equation.
• Molar Volume (22.4 L) is the volume occupied by
  one mole of a substance at STP.
• STP (standard temperature and pressure) are the
  conditions at 0 C and 1 atm.
• At 0 C and 1 atm, 22.4L of gas, contains one
  mole.

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Practice

• A sample of nitrogen gas has a volume of 1.75 L
  at STP. How many moles of N2 are present?
• Quicklime, CaO, is produced by heating calcium
  carbonate, CaCO3. Calculate the volume of CO2
  produced at STP from the decomposition of 152 g
  of CaCO3 according to the reaction
• CaCO3(s)? CaO(s) CO2 (g)

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Grahams Law of Effusion

• Effusion is the passage of a gas through a small
  opening.
• At constant pressure and temperature, the rate of
  effusion, ? of a gas is inversely proportional to
  the square root of its molar mass, M.
• Lighter molecules travel faster than heavy
  molecules.
• Practice compare the speed of effusion of H2
  with that of O2.

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• Diffusion is the process by which particles mix
  by dispersing from regions of higher
  concentration to regions of lower concentration.
  The mixture becomes homogeneous at the end.
• Practice Hydrogen sulfide, H2S has a very strong
  rotten-egg odor. Methyl salicylate, C8H10O3, has
  a wintergreen odor. Benzaldehyde, C7H6O, has an
  almond odor. If vapors for these three
  substances were released at the same time from
  across the room, which would you smell first? Why?