Kinetic Molecular Theory

1
Kinetic Molecular Theory

• Gas Laws

2
Kinetic Molecular Theory

• Gases consist of tiny particles (atoms or
  molecules)
• Gas molecules are in constant motion, pressure is
  the result of molecular collisions with the
  container walls.
• Molecular collisions are elastic ( there is no
  net gain or loss of energy)
• At a given temperature the average kinetic energy
  is constant and depends only on the temperature
• Kelvin Scale used to measure Kinetic energy of
  molecules
• Absolute Zero point at which all molecular
  motion stops

3
Characteristics and Behavior of Gases

• Avogadros law equal volumes of gases at the
  same temp and pressure contain the same number of
  molecules. 6.02 x 1023
• Pressure force applied to 1 unit of surface
  area
• Pressure can be measured with a barometer
• P Force ( neutons) measurement of force
• Area ( Pascals) Unit of force
• Pressure can also be measured in mm of Hg or
  inches of Hg
• 1 atm 1 atmosphere of pressure
• 1atm 101.3 kPa 760mm Hg 760 torr 14.7 psi

4
E. Pressure
Which shoes create the most pressure?
5
Barometers

• 760 mmHg
• atm
• pressure

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Characteristics of Gases cont.

• Compression and Expansion the ability of gases
  to move closer to each other or expand to fill
  the container
• Diffusion movement of gases through another
  (perfume)
• Effusion when a gas escapes through tiny
  openings.

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STP standard temp and pressure

• Temperature always use Kelvins for gases
  Kelvin C 273
• STP
• Temperature 0C 273 K
• Pressure 1 atm, 760 mmHg, 760 torr, 101kPa
• Molar volume volume 1 mole of a gas occupies at
  0C and 1atm 22.4L

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Temperature

• Always use absolute temperature (Kelvin) when
  working with gases.

9
The Gas Laws

• These will describe HOW gases behave.
• Can be predicted by the theory.
• Amount of change can be calculated with
  mathematical equations.

10
Volume of Gas

• In a smaller container, molecules have less room
  to move.
• Hit the sides of the container more often.
• As volume decreases, pressure increases. (think
  of a syringe)

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Boyles Law P1V1 P2V2

• At a constant temp, the product of the pressure
  and the volume of a gas sample is a constant
  value
• P1V1 original pressure and volume
• P2V2 new pressure and volume
• An inverse relationship exist
• If volume of gas decreses, pressure increases
• If volume of gas increases, pressure decreases

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E. Gas Law Problems

• A gas occupies 100. mL at 150. kPa. Find its
  volume at 200. kPa.

BOYLES LAW
GIVEN V1 100. mL P1 150. kPa V2 ? P2
200. kPa
WORK P1V1 P2V2
P?
V?
(150.kPa)(100.mL)(200.kPa)V2 V2 75.0 mL
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Examples

• A balloon is filled with 25 L of air at 1.0 atm
  pressure. If the pressure is changed to 1.5 atm
  what is the new volume?
• A balloon is filled with 73 L of air at 1.3 atm
  pressure. What pressure is needed to change the
  volume to 43 L?

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Temperature of Gas

• Raising the temperature of a gas increases the
  pressure, if the volume is held constant.
• The molecules hit the walls harder, and more
  frequently!
• The only way to increase the temperature at
  constant pressure is to increase the volume.

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Charles Law V1T2 V2T1

• At constant pressure, volume of a gas varies
  directly with the kelvin temperature
• A direct relationship
• If temperature of a gas increases, volume
  increases
• If temperature of a gas decrease, volume
  decreases

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E. Gas Law Problems

• A gas occupies 473 cm3 at 36C. Find its volume
  at 94C.

CHARLES LAW
GIVEN V1 473 cm3 T1 36C 309K V2 ? T2
94C 367K
WORK P1V1T2 P2V2T1
T?
V?
(473 cm3)(367 K)V2(309 K) V2 562 cm3
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Examples

• What is the temperature of a gas expanded from
  2.5 L at 25 ºC to 4.1L at constant pressure?
• What is the final volume of a gas that starts at
  8.3 L and 17 ºC, and is heated to 96 ºC?

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Ideal Gases

• Ideal gas a gas whose particles take up no
  space and have no intermolecular attractive
  forces. No gas is truly ideal however the
  formula can be used to get approximate actual
  experimental values

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PVnRT

• The number of moles is a 4th variable that can be
  added to pressure, volume, and temperature to
  describe a gas
• Increasing the number of particles present in a
  sample will raise the pressure if the volume and
  temperature are kept constant.
• Ideal Gas Law is used to explain how pressure,
  volume, temperature and number of moles are
  interrelated.

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PVnRT

• P pressure in kPa
• V volume in Liters
• N moles
• R gas law constant (check pressure to know
  which to use ) 8.31L kPa or .0821L atm
• Mol K mol K
• T Temperature in kelvins

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C. Ideal Gas Law Problems

• Calculate the pressure in atmospheres of 0.412
  mol of He at 16C occupying 3.25 L.

GIVEN P ? atm n 0.412 mol T 16C 289 K V
3.25 L R 0.0821L?atm/mol?K
WORK PV nRT P(3.25)(0.412)(0.0821)(289)
L mol L?atm/mol?K K P 3.01
atm
22
Combined Gas Law combination of Boyes,
Charles and Guy-Lussacs Law

• States the relationship between pressure, volume
  and temperature of a gas
• P1V1 P2V2
• T1 T2

23
E. Gas Law Problems

• A gas occupies 7.84 cm3 at 71.8 kPa 25C. Find
  its volume at STP.

COMBINED GAS LAW
GIVEN V1 7.84 cm3 P1 71.8 kPa T1 25C
298 K V2 ? P2 101.325 kPa T2 273 K
WORK P1V1T2 P2V2T1 (71.8 kPa)(7.84 cm3)(273
K) (101.325 kPa) V2 (298 K) V2 5.09 cm3
P? T?
V?