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Kinetic-Molecular Theory (Kinetic Theory)
A theory, developed by physicists, based on the assumption that a gas consists of molecules in constant, random motion.
The kinetic energy of an atom or molecule is related to the mass and speed:
speed=E m( )2K12
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Postulates of the Kinetic-Molecular Theory1. Gases are composed of molecules whose size is negligible
compared to the average distance between them
2. Molecules move randomly in straight lines in all directions and at various speeds.
3. The forces of attraction or repulsion between two molecules (intermolecular forces) in a gas are very weak or negligible, except when the molecules collide.
4. When molecules collide with each other, the collisions are elastic.
5. The average kinetic energy of a molecule is proportional to the absolute temperature.
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Elastic Collisions
• An elastic collision is one in which no kinetic energy is lost.• Kinetic-molecular theory assumes molecules collide without
loss of energy.
In The collision on the left causes the ball on the right to swing the same height as the ball on the left had initially, with essentially no loss of kinetic energy.
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• At 0 oC the molecules move over a low, narrow range of speeds.
• At 500 oC, molecular speeds covera broad range to high values
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mean speedmost probable speed
Molecular Speeds
According to kinetic-molecular theory, molecular speeds vary over a wide range of values.
The distribution of values depends on temperature – it spreads out as temperature increases.
Molecular Speeds - Simulation
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https://phet.colorado.edu/en/simulations/gas-properties/activities
Molecular SpeedsAccording to kinetic-molecular theory, molecular speeds vary over a wide range of values. The values depends on temperature, so it increases as the temperature increases.
Root-Mean Square (rms) Molecular Speed, uA type of average molecular speed, equal to the speed of a molecule that has the average molecular kinetic energy
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123 3RT
m m
RTuM M
æ ö= = ç ÷
è ø
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When applying the equation, consistent units are to be used.If SI units are used for R (= 8.31 kg·m2/s2·K·mol), T(K) and Mm (kg/mol), rmsspeed will be in meters per second.
Root-Mean Square (rms) Molecular Speed, u
Example: Determine the rms speed of O2 molecules in a cylinder at 21 oC and 15.7 atm.
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1/22 2
–33 8.31 kg m / (s K mol) 294K = = 479 m/s
32.0 10 kg/molu
æ ö´ × × × ´ç ÷´è ø
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Diffusion
Atoms, ions and molecules of separated substances use their thermal energy to move in all directions.
If in contact, the motions of the substances cause them to mix.
Atoms, ions and molecules diffuse in all states of matter.
Gases diffuse faster than liquids and liquids diffuse faster than solids.
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time
Diffusion - Simulation
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https://phet.colorado.edu/en/simulations/diffusion
Effusion
A process by which a gas flows through a small hole in a container.
Gas will diffuse through a microscopic hole in a balloon is one example in which effusion occurs.
Light atoms or molecules diffuse faster than heavyones.
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Effusion - Simulation
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https://phet.colorado.edu/en/simulations/gas-properties
Graham�s Law of Effusion
Light atoms or molecules diffuse faster than heavy ones.
The rate of effusion of gas molecules through a particular hole is inversely proportional to the square root of the molecular mass of the gas.
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µm
1Rateof effusionof moleculesM
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Graham�s Law of Effusion
How much faster does one molecule effuse than another?
Compare the rates of effusion:
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µm
1Rateof effusionof moleculesM
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22
2
2
2
2
1(CO )Rate of effusion of CO2 = 1Rate of effusion of SO(SO )
(SO ) = (CO )
64.1 g/mol =44.0 g/mol
m
m
m
m
M
M
MM
= 1.21
Practice: Calculate the ratio of effusion rates of molecules and CO2 and SO2 from the same container and at the same temperature and pressure.
Practice: Effusion
Each round flask contains 1 mole of gas. The long tube contains no gas - it is a vacuum.
a. If both valves are opened at the same time, which gas would you expect to reach the end of the long tube first?
b. If you wanted the Ar to reach the end of the long tube at the same time as the He, what experimental condition (that is, you cannot change the equipment) could you change to make this happen?
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Helium
Argon
