Gases

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Gases
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GASES
manometers
pressure
Kinetic theory of gases
Units of pressure
Behavior of gases
Partial pressure of a gas
Pressure vs. volume
Pressure vs. temperature
Temperature vs. volume
Diffusion/effusion
Combined gas law
Ideal gas law
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Properties of Gases

• Very low density
• Low freezing points
• Low boiling points
• Can diffuse (rapidly and spontaneously spread out
  and mix)
• Flow
• Expand to fill container
• Compressible

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Kinetic Molecular Theory of Gases

• Particles move non-stop, in straight lines.
• Particles have negligible volume (treat as
  points)
• Particles have no attractions to each other (no
  repulsions, either).
• Collisions between particles are elastic (no
  gain or loss of energy)
• Particles exert pressure on the container by
  colliding with the container walls.

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Kinetic Energy

• Energy due to motion
• KE ½ mv2

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Temperature

• Temperature is a measure of average kinetic
  energy.
• Temperature measures how quickly the particles
  are moving. (Heat IS NOT the same as
  temperature!)
• If temperature increases, kinetic energy
  increases.
• Which has greater kinetic energy a 25 g sample
  of water at 25oC or a 25 g sample of water at
  -15oC?

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Why use the Kelvin scale?

• In the Kelvin scale, there is an absolute
  correlation between temperature and kinetic
  energy.
• As temperature in Kelvin increases, kinetic
  energy increases.
• Absolute zero All molecular motion ceases.
  There is no kinetic energy.
• 0 K

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Kelvin-Celsius Conversions

• K oC 273.15
• oC K 273.15

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Kelvin-Celsius conversions

• The temperature of liquid nitrogen is
  -196oC. What is this temperature in Kelvin?
• Convert 872 Kelvin to Celsius temperature.

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Pressure

• Pressure force/area
• Atmospheric pressure
• Because air molecules collide with objects
• More collisions ? greater pressure

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Pressure Units

• Atmosphere
• Pounds per square inch (psi)
• mm Hg
• Torr
• Pascal (Pa) or kilopascal (kPa)
• 1 atm 14.7 psi 760 mm Hg 760 torr 101.3
  kPa

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Barometer

• Torricelli-1643
• Air molecules collide with liquid mercury in open
  dish
• This holds the column up!
• Column height is an indirect measure of
  atmospheric pressure

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Manometer

• Two types open and closed
• Use to measure the pressure exerted by a confined
  gas

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Chapter 15 Wrapup (Honors)

• At the same temperature, smaller molecules (i.e.,
  molecules with lower gfm) have faster average
  velocity.
• Energy flows from warmer objects to cooler
  objects.
• Plasma
• High energy state consisting of cations and
  electrons
• Found in sun, fluorescent lights

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Boyles Law

• Pressure-volume relationships
• For a sample of a gas at constant temperature,
  pressure and volume are inversely related.
• Equation form
• P1V1 P2V2

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Charles Law

• Volume-temperature relationships
• For a sample of a gas at constant pressure,
  volume and temperature are directly related.
• Equation form

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Guy-Lussacs Law

• Pressure temperature relationships
• For a sample of a confined gas at constant
  volume, temperature and pressure are directly
  related.

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Combined Gas Law

• Sometimes, all three variables change
  simultaneously
• This single equation takes care of the other
  three gas laws!

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Daltons Law of Partial Pressures

• For a mixture of (nonreacting) gases, the total
  pressure exerted by the mixture is equal to the
  sum of the pressures exerted by the individual
  gases.

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Collecting a sample of gas over water

• Gas samples are sometimes collected by bubbling
  the gas through water

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• If a question asks about something relating to a
  dry gas, Daltons Law must be used to correct
  for the vapor pressure of water!

Table Vapor Pressure of Water
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Ideal Gas Law

• The number of moles of gas affects pressure and
  volume, also!
• n, number of moles
• n ? V
• n ? P
• P ? 1/V
• P ? T
• V ? T

Where R is the universal gas constant R 0.0821
L?atm/mol?K
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Ideal vs. Real Gases

• Ideal gas completely obeys all statements of
  kinetic molecular theory
• Real gas when one or more statements of KMT
  dont apply
• Real molecules do have volume, and there are
  attractions between molecules

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When to expect ideal behavior?

• Gases are most likely to exhibit ideal behavior
  at
• High temperatures
• Low pressures
• Gases are most likely to exhibit real (i.e.,
  non-ideal) behavior at
• Low temperatures
• High pressures

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Diffusion and Effusion

• Diffusion
• The gradual mixing of 2 gases due to random
  spontaneous motion
• Effusion
• When molecules of a confined gas escape through a
  tiny opening in a container

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Grahams Law

• Thomas Graham (1805-1869)
• Do all gases diffuse at the same rate?
• Grahams law discusses this quantitatively.
• Technically, this law only applies to gases
  effusing into a vacuum or into each other.

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Grahams Law

• Conceptual
• At the same temperature, molecules with a smaller
  gfm travel at a faster speed than molecules with
  a larger gfm.
• As gfm ?, v ?
• Consider H2 vs. Cl2
• Which would diffuse at the greater velocity?

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Grahams Law

• The relative rates of diffusion of two gases vary
  inversely with the square roots of the gram
  formula masses.
• Mathematically

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Grahams Law Problem

• A helium atom travels an average 1000. m/s at
  250oC. How fast would an atom of radon travel at
  the same temperature?
• Solution
• Let rate1 x rate2 1000. m/s
• Gfm1 radon 222 g/mol
• Gfm2 helium 4.00 g/mol

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Solution (cont.)

• Rearrange
• Substitute and evaluate

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Applications of Grahams Law

• Separation of uranium isotopes
• 235U
• Simple, inexpensive technique
• Used in Iraq in early 1990s as part of nuclear
  weapons development program
• Identifying unknowns
• Use relative rates to find gfm

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Problem 2

• An unknown gas effuses through an opening at a
  rate 3.16 times slower than that of helium gas.
  What is the gfm of this unknown gas?

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Solution

• Let gfm2 x rate2 1
• gfm1 4.00 rate1 3.16
• From Grahams Law,
• Rearrange

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Solution, cont.

• Substitute and evaluate