Kinetic Theory and Gases

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Kinetic Theory and Gases
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Kinetic Theory

• Explains how temperature and pressure affect the
  motion of molecules

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Hydraulics
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KEKinetic Energy

• Energy of motion
• Depends on
• Mass
• Velocity

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PEPotential Energy

• Stored Energy
• Gravitational Potential Energy
• Energy due to height above earth
• 2) Chemical Potential Energy
• Energy stored in bonds of batteries, food,
  gasoline, etc.

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Ideal Gases

• Particles are point massesthey have no volume
• Particles have no mutual attraction to each other
• Behavior of ideal gases is a model for how real
  gases behave
• Ideal Gas calculations are simple and the results
  are close to those for real gases

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Three Assumptions of Kinetic Theory

• All matter is made of particles
• 2) Particles are in constant motion
• All collisions are perfectly elastic
• (molecules do not lose energy in collisions)

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Oxygen Gas

• At 25oC,
• average speed 443 m/s (1000 mph)
• Between collisions, an oxygen molecule travels
  314 times its diameter
• There are 4.5 billion collisions each second

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Pressure

• Air Pressure
• the weight of air over an area
• Standard Pressure
• average normal
• air pressure at sea level
• 760 mmHg 1 atm
• 14.7 lbs/in2 101.3 kPa

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What Causes Gas Pressure?

• number and intensity of collisions
• -- speed of particles (temperature)
• -- concentration of particles
• -- mass / size of particles

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Barometer

• Used to measure air pressure
• The weight of a column of mercury is balanced by
  the weight of the air

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Evangelista Torricelli
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How is Pressure related to Weather?
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How is Pressure related to Altitude?
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Boiling
Pvap Patm
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Boiling

• The boiling point of water in Oregon is usually
  about ____________
• Is Oregon above or below sea level?
• (974 feet above sea level)
• Record High 815 mmHg
• Record Low 656 mmHg

lt100oC
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Try These
101.3
760

• 1 atm ________ mmHg ________ kPa
• 2.1 atm _____mmHg 0.8 atm _____mmHg
• 798 mmHg _____atm 684 mmHg _____atm
• 750 mmHg _____kPa 790 mmHg _____kPa

1596
608
1.05
0.9
105.3
99.97
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Demonstrations

• Crush the can
• Vacuum pump (shaving cream, marshmallow, balloon)
• Tube with cap
• Flask with index card
• Gas can
• Air pressure mat, glass square, well plate,
  soda suction
• Mustard container
• Balloon in Flask
• Fire Syringe
• Syringe/Martian Popping Thing
• Bernoulli bag/ball in funnell
• Heros Fountain

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Temperature

• Average Kinetic Energy of particles in a
  substance (depends on the speed and mass of
  particles)

100 K
500 K
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Temperature Scales
Water Boils
Kelvin Absolute temperature scale Cannot have a
negative Kelvin temperature 0 K Absolute Zero
Water Freezes
oC 273 K

• http//www.rain.org/mkummel/stumpers/08oct99a.gif

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Practice Problems

• Convert to Kelvin
• 23oC _____ K
• -11oC _____ K
• 32 oF _____ K
• Convert to Celsius
• 315 K _____ oC
• 277 K _____ oC
• 212 oF _____ oC

296
262
273
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4
100
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STP

• Standard Temperature and Pressure
• 0oC
• 1 atm

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Diffusion

• What is diffusion
• The random movement of particles through a
  medium

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5 Factors that Affect the Diffusion Rate of Gases

• Mass of Particles
• ? mass, ? rate of diffusion
• Concentration of Particles
• ? conc, ? rate of diffusion
• Temperature
• ? temp, ? rate of diffusion
• Air Pressure
• ? Pair, ? rate of diffusion
• Presence of Another Gas
• Another gas, ? rate of diffusion

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Compare the relative rate of diffusion of H2 N2

H2 diffuses 3.74 times faster (further) than N2
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Lab 40

• What is the relative rate of diffusion of NH3 to
  HCl?

1 m
NH3
HCl
NH3(g) HCl (g) ? NH4Cl (s)
1.5 times faster/further
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Boyles Law

• The pressure of a gas is inversely proportional
  to its volume
• (when temperature is constant)
• P X V k (constant)
• P1 V1 P2 V2
• Initial Final
• USE COMMON UNITS FOR P AND V!!!
• (both atm, kPa or both L, ml, cm3)

Robert Boyle 1627-1691
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Try This

• You have 1000 ml of gas at 754 mmHg. Find the
  volume at standard pressure.
• P1 V1 P2 V2
• (754 mmHg)(1000ml) (760 mmHg)V2
• 760 mmHg 760 mmHg
• V2 992.1 ml

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Lab 37 Boyles Law
Measure this!
Calculate this!
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Not dot-to-dot draw a smooth curve Number your
axis so your graph takes up a lot of space
Pressure (mmHg)
Volume (ml)
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Daltons Law

• Total pressure sum of partial pressures
• Ptotal dPgas 1 dPgas 2 dPgas 3
• Pair dPN2 dPO2 dPH2O etc.

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Gases collected over water
over water

• Gases collected contain water vapor

H2O O2
lower bottle until water levels are equal
Ptotal dPH2O dPgas
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750 mmHg
Ptotal
PH2O dPgas
Pair
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Vapor Pressure Chart on PT

• dPH2O changes with water temp
• Ex A sample of H2 is collected
• at 25oC and the pressure is 775 mmHg. What is the
  pressure of the dry gas?

over water
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Example 2

• 80 ml of gas are collected
• at 22oC. The air pressure was 758 mmHg. Find the
  volume of dry gas at standard pressure.

over water
P2
P1
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Charles Law
The volume of a gas is directly proportional to
the absolute temperature (Kelvin) if the pressure
is held constant
V
T (K)
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Try This 1

• If you had 100 ml of a dry gas at 30oC, what
  volume would it occupy at 60oC?

V2 109.9 ml
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Try This 2

• 350 ml of gas at 0oC is compressed to 100 ml.
  What is the new temperature?

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Apparently, oil tank rail cars are cleaned by
scouring them with steam.
Unfortunately, someone shut the hatch too soon...
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Open vs Closed Containers

• Open Container
• Increase Temp?
• collisions?
• Pressure?
• Volume?

• Closed Container
• Increase Temp?
• collisions?
• Pressure?
• Volume?

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Guess the Gas Law

• An eqn with V and T
• An eqn with P and V
• find the pressure of the dry gas
• Uses vapor pressure of water
• PV k
• P
• V