Kinetic-Molecular Theory and Gas Laws

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Kinetic-Molecular Theory and Gas Laws
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Properties of Gases

• highly compressible and low density due to the
  large spaces between gas particles
• indefinite shape will take shape of its
  container
• indefinite volume will occupy the entire volume
  of its container
• high fluidity the particles easily glide by one
  another, allow the gas to flow

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Kinetic-Molecular Theory and Gases

• Gas is composed of particles
• either molecules or atoms
• (Ex O2 or Ar)
• Gas particles do not attract or repel one
  another.
• Like billiards balls, they bounce off of one
  anther after a collision

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Kinetic-Molecular Theory and Gases

• Gas particles are in constant, random motion
• they move in straight line paths
• only changing direction when they collide with
  one another or walls of container
• All gas particle collisions are elastic
  collisions
• energy transferred from one particle to another
  without a loss of kinetic energy.

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• 5. The amount of kinetic energy, how fast the
  particles move, depends on temperature.
• Higher temperature, move faster
• Lower temperature, move slower
• At absolute zero (0 K lowest possible
  temperature) NO movement

Effusion gradual movement of a gas through a
small opening
Diffusion gradual mixing of gases due to
constant random motion
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Standard Temperature and Pressure

• Temperature
• 0oC 273 K
• Temperature conversion examples What is 25oC in
  Kelvin? What is 345 K in Celsius?
• Pressure units are
• 101.3 kPa 760 mm Hg 760 torr 1 atm
• Pressure conversion example If a barometer at
  you home reads 768.2 mmHg, what is the
  atmospheric pressure in kPa?

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Daltons Law of Partial Pressures

• Total pressure (Ptotal) of a mixture of gases is
  equal to the sum of the pressures of each of the
  gases
• Equation
• Ptotal Pgas 1 Pgas 2 Pgas 3 .....
• If a gas is collected over water, as the gas is
  collected some of the water is evaporated and
  joins the gas.
• Thus the pressure in the collection container is
  the sum of the gas and the water.
• To find the pressure of just the gas, the
  pressure of the water needs to be subtracted.
• Pgas Ptotal - Pwater vapor

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Examples

• A scuba tank contains a mixture of gases
  including 0.42 atm N2, 205 torr O2 and 35.5 kPa
  CO2. What is the total pressure inside the tank
  in atmospheres?
• Oxygen gas was collected over water at 16oC.
  Total volume of gas is 188 mL at pressure of 92.3
  kPa. What is the pressure of the O2? (at 16oC,
  vapor pressure 1.82 kPa)

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Boyles Law

• the volume of a gas is inversely proportional to
  pressure , at constant temperature
• - if volume increases, then
• pressure decreases
• - if volume decreases, then
• pressure increases
• Equation
• P1 V1 P2 V2
• Example A sample of neon gas occupies a volume
  of 2.8 L at 1.8 atm. What would its volume be at
  1.2 atm?

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Charles Law

• volume of a gas is directly proportional to
  temperature (in Kelvin), at constant pressure
• if temperature doubles, then
• volume also doubles
• Equation
• V1 V2
• T1 T2
• Example A sample of nitrogen occupies a volume
  of 250 mL at 25 C. What volume will it occupy
  at 95 C?

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Gay-Lussacs Law

• the pressure of a gas is directly proportional to
  absolute temperature (Kelvin), at constant volume
• if temperature doubles, then
• pressure also doubles
• Equation
• P1 P2
• T1 T2
• Example If a gas is cooled from 323.0 K to
  273.15 K and the volume is kept constant, what
  final pressure would result if the original
  pressure was 750.00 mmHg?

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Combined Gas Law

• relationship of pressure, volume, and temperature
  (in Kelvin) of a sample of gas with constant
  mass
• Equation P1V1 P2V2
• T1 T2
• Example An unopened, cold 2.00 L bottle of soda
  contains 46.0 mL of gas confined at a pressure of
  131.96 kPa at a temperature of 5.0C. If the
  bottle is dropped into a lake and sinks to a
  depth at which the pressure is 154 kPa and a
  temperature of 2.1C, what will be the new volume
  of the gas?

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Ideal Gas Law

• Equation P V n R T
• P pressure
• V volume (in liters)
• n number of moles
• T temperature (in Kelvin)
• R ideal gas constant (pick which one based on
  the unit of pressure)
• R 0.0821 atmL R 62.4 mmHgL
• molK molK
• R 8.314 kPaL
• molK
• Example Calculate the number of moles of gas
  contained in a 3.0L vessel at 33C and a pressure
  of 1.50 atm.

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Avogadros Principle

• equal volumes of gases at the same temperature
  pressure contain equal numbers of particles
• At STP, one mole of any gas
• 1 mol 6.022 x 1023 particles Molar Mass in
  grams 22.4 L
• Examples
• Determine the volume occupied by 2.5 mol of a gas
  at STP.
• What volume will 0.416 g of krypton occupy at STP?

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Gas Stoichiometry

• coefficients in balanced chemical equations
  represent number of
• moles of each substance
• liters of gases, assuming pressure and temp.
  remain constant
• Example
• C3H8 (g) 5 O2 (g) 3 CO2 (g) 4 H2O (g)
• 1 mol 5 mol 3 mol 4
  mol
• 1 L 5 L 3 L 4 L

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VolumeVolume Problems

• use the balanced equation to find volume ratio
• Example If 1.78 L of oxygen reacts, what volume
  of nitrogen will be produced?
• NH3 (g) O2 (g) N2 (g) H2O (l)
• 1.78 L O2 2 N2 1.19 L N2
• 3 O2