The Behavior Of Gases

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CHAPTER 11
The Behavior Of Gases
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Characteristics of Gases

• Substances that are normally liquids or solids
  can have a gaseous phase as well, where they are
  referred to as VAPORS
• A gas expands spontaneously to fill its container
• Gases are easily compressed
• They form homogeneous mixtures with each other

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More Characteristics..

• Their individual molecules are relatively far
  apart
• In the air we breathe, the molecules only take up
  about 0.1 of the total volume, the rest being
  empty space
• Gas molecules are not very attracted to each
  other
• Molecules for solids and liquids are close
  together and attracted to one another

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Adding or Removing Gas

• Gas molecules are constantly colliding with each
  other and with the sides of their container.
• As you add gas (pumping up a tire), you increase
  the number of gas particles.
• This makes the particles collide even more !
• Increase in pressure (force that acts on a given
  area)

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If you keep adding air to a tire

• The pressure becomes greater than the strength of
  the container
• The tire will explode!

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Letting air out of a tire, or container

• Decreases the pressure
• There are less particles left to collide
• There is a lot more empty space

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Three Variables in Gas Laws

• Pressure
• Volume
• Temperature
• In testing the behavior of gases, one variable
  must be held constant.

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Boyles Law

• At a constant temperature, a volume of gas varies
  inversely with pressure

P1
P2
V2
V1
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The Formula

• P1 x V1 P2 x V2

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Try One

• A sample of oxygen gas occupies a volume of 6.3 L
  at 0.98 atm. What volume will it occupy at 1.2
  atm.?
• Answer 5.1 L

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Charles Law

• Held pressure constant
• Studied the effects of temperature on volume
• The volume of a gas is directly proportional to
  its Kelvin temperature if pressure is kept
  constant

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Its a direct relationship
100 kPa
100 kPa
V2
V1
T1
T2
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The Formula

• V1 V2
• T1 T2
• ____

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Try One..

• A sample of nitrogen occupies a volume of 1.6 L
  at 275 K. What volume will it occupy at 295 K?
• Answer 1.7 L

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Gay-Lussacs Lawdont laugh, thats his name

• Volume held constant
• The pressure of a gas is directly proportional to
  the Kelvin temperature

P2
P1
T1
T2
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The Formula

• P1 P2
• T1 T2

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Example

• If a sample of Helium at 220K exerts a pressure
  of 98.2 kPa, what would its temperature be at
  101.3 kPa?
• Answer 226.9K

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So if they proved that all this stuff is true

• Then we can combine the three gas laws into a
  single one called

The Combined Gas Law
P1 x V1 P2 x V2 T1 T2
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The Ideal Gas Law

• The previous gas laws havent dealt with amounts
  of gas.
• If you want to throw moles into the mix, then you
  use the Ideal Gas Law
• PV nRT
• n is equal to the number of moles

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So, where did the R come from?

• R is the ideal gas constant
• You know that one mole of every gas occupies 22.4
  Liters at STP

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Rearrange the equation to solve for R

• P x V R
• T x n
• 101.3 kPa x 22.4 L
• 273 K x 1 mol
• 8.31 (L x kPa)/(K x mol)

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R can also be expressed in different units,

• R 0.0821 L atm/(mol K)

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Dalton's Law of Partial Pressures

• At constant volume and temperature, the total
  pressure exerted by a mixture of gases is equal
  to the sum of its parts
• Ptotal P1 P2 P3

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EXAMPLE

• The air we breathe contains O2, N2, CO2, and
  trace gases
• Calculate the partial pressure of oxygen (PO2) at
  101.3 kPa if PN2 79.10 kPa, PCO2 0.040 kPa,
  and Ptrace 0.94 kPa
• Ptotal PO2 PN2 PCO2 Ptrace
• Rearrange to solve for PO2

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The formula becomes

• PO2 Ptotal (PN2 PCO2 Ptrace)
• 101.3 kPa (79.10 kPa 0.040 kPa
• 0.94 kPa)
• 21.22 kPa

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Real gases deviate from ideal behavior

• Because, at lower temperatures, gas particles are
  attracted to one another
• And, gas particles have a finite volume (ideal
  gases have no molecular attractions, and the
  particles have no volume)
• The ideal gas law works well for gases with large
  volumes and at low pressures