Gases: Mixtures and Movements

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Gases Mixtures and Movements

• Prentice-Hall Chapter 14.4
• Dr. Yager

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Objectives

• Relate the total pressure of a mixture of gases
  to the partial pressures of the component gases
• Explain how the molar mass of a gas affects the
  rate at which the gas diffuses and effuses

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Daltons Law

• In a mixture of gases, the total pressure is the
  sum of the partial pressures of the gases.

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Partial Pressure
The contribution each gas in a mixture makes to
the total pressure is called the partial pressure
exerted by that gas.
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Daltons Law of Partial Pressures

• Daltons Law of Partial Pressures
• states that, at constant volume and temperature,
  the total pressure exerted by a mixture of gases
  is equal to the sum of the partial pressures of
  the component gases.

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Three gases are combined in Container T.



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The partial pressure of oxygen must be 10.67 kPa
or higher to support respiration in humans. The
Mt. Everest climber below needs an oxygen mask
and a cylinder of compressed oxygen to survive.
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A gas mixture containing oxygen, nitrogen, and
carbon dioxide has a total pressure of 32.9 kPa.
If PO2 6.6 kPa, and PN2
23.0 kPa, what is the pressure of the carbon
dioxide? Ptotal sum of all the partial
pressures 32.9 kPa 6.6 kPa 23.0 kPa
pressure of CO2 3.3 kPa pressure of CO2
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Diffusion vs Effusion

• Diffusion is the tendency of molecules to move
  towards areas of lower concentration.
• Effusion is the movement of a gas through a tiny
  hole in a container.

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• Key Idea
• Gases of lower molar mass diffuse and effuse
  faster than gases of higher molar mass.

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Diffusion is the tendency of molecules to move
toward areas of lower concentration until the
concentration is uniform throughout.
After several hours, the bromine has diffused
almost to the top of the cylinder.
Bromine vapor is diffusing upward through the air
in a graduated cylinder
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Grahams Law of Effusion

• Grahams Law states that the rate of effusion of
  a gas is inversely proportional to the square
  root of the gas molar mass.
• This law can also be applied to the diffusion of
  gases.

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A helium filled balloon will deflate sooner than
an air-filled balloon.
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• Helium and air molecules pass freely through
  pores in the balloon. Helium atoms are less
  massive than oxygen or nitrogen molecules.
• At the same temperature (same kinetic energy)
• KE ½ mv2 m mass, v
  velocity
• For constant KE, an increase in mass must be
  balanced by a decrease in velocity. So air
  molecules (oxygen, nitrogen) move more slowly
  than helium atoms with the same kinetic energy.

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Because the rate of effusion is related only to a
particles speed, Grahams law can be written as
follows for two gases, A and B.
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Helium effuses (and diffuses) nearly three times
faster than nitrogen at the same temperature.
Molar mass of N2 28 g Molar
mass of He 4 g
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• 1. What is the partial pressure of oxygen in a
  diving tank containing oxygen and helium if the
  total pressure is 800 kPa and the partial
  pressure of helium is 600 kPa?
• 200 kPa
• 0.75 kPa
• 1.40 x 104 kPa
• 1.33 kPa

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• 1. What is the partial pressure of oxygen in a
  diving tank containing oxygen and helium if the
  total pressure is 800 kPa and the partial
  pressure of helium is 600 kPa?
• 200 kPa
• 0.75 kPa
• 1.40 x 104 kPa
• 1.33 kPa

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• 2. A mixture of three gases exerts a pressure of
  448 kPa, and the gases are present in the mole
  ratio 1 2 5. What are the individual gas
  pressures?
• 44 kPa, 88 kPa, and 316 kPa
• 52 kPa, 104 kPa, and 292 kPa
• 56 kPa, 112 kPa, and 280 kPa
• 84 kPa, 168 kPa, and 196 kPa

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• 2. A mixture of three gases exerts a pressure of
  448 kPa, and the gases are present in the mole
  ratio 1 2 5. What are the individual gas
  pressures?
• 44 kPa, 88 kPa, and 316 kPa
• 52 kPa, 104 kPa, and 292 kPa
• 56 kPa, 112 kPa, and 280 kPa
• 84 kPa, 168 kPa, and 196 kPa

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• 3. Choose the correct words for the spaces.
  Graham's Law says that the rate of diffusion of a
  gas is __________ proportional to the square root
  of its _________ mass.
• directly, atomic
• inversely, atomic
• inversely, molar
• directly, molar

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• 3. Choose the correct words for the spaces.
  Graham's Law says that the rate of diffusion of a
  gas is __________ proportional to the square root
  of its _________ mass.
• directly, atomic
• inversely, atomic
• inversely, molar
• directly, molar