Kinetic Theory of Matter

Kinetic Theory of Matter

Why Johnny can’t sit still (Johnny is a gas particle)

Kinetic model of gases • Ideal gas particles are point masses • Particles travel in a straight line until

they run into something – around 100 -1000 m/s– Collisions with walls of container cause

pressure– Diffusion – dispersion of a gas by random

motion – heavier gases diffuse more slowly

Kinetic model of gases• Collisions are perfectly elastic – no

other interactions between gas particles – like air hockey pucks

• Temperature is related to the average kinetic energy of the gas molecules – higher temp = faster speed

Kinetic model of gasesPlot of speed vs. # molecules

Kinetic model of gases• Brownian motion – Random motion

of suspended particles in liquid or gas

• Due to collisions between particles and atoms of gas or liquid

• Used by Einstein to prove atomic theory of matter

Brownian motion

Brownian motion animation

Properties of gases• Gases can flow• Gases take the shape of the

container• Gases have no definite volume• Gases and liquids are fluids

(anything that can flow)

Kinetic model of liquids • Particles are much closer together than

gases• Interparticle interactions are significant• Particles slide past each other like

magnetized marbles – Flow– Take shape of container– Have a definite volume

Kinetic model of liquids• Particles cannot move in a straight

line• Particles vibrate along random

paths • Higher temp means more vibration

and faster speed

Kinetic model of solids • Particles vibrate in place• Higher temp means faster/wider

vibrations• Crystalline solids – regular arrangement

of particles (salt, diamond)• Amorphous solid – random

arrangement (wax, rubber, glass)

Liquid crystals• Substances that lose organization

in only one dimension as they melt• Used in electronic displays

because their characteristics change with electric charge

Plasmas• Most like

gases• Composed of

ions and subatomic particles at high energy – candle flame, fluorescent lights

Kinetic energy and temperature

• Temperature scales– Celsius – based on melting point

(0ºC) and boiling point (100ºC) of water

– Kelvin – based on absolute zero (temperature at which all atomic movement ceases)

Kinetic energy and temperature

• Kelvins are the same size as ºC• Absolute zero is the same as –

273ºC• K=C+273• Find the Kelvin equivalent of room

temperature (25ºC)K = 25 + 273 = 298K (no “º”)

Kinetic energy and temperature

• Kelvins are directly proportional to kinetic energy– Molecules at 400K have twice as

much energy as molecules at 200K• Degrees Celsius are not directly

proportional to kinetic energy

Mass and energy • Kinetic energy depends on mass

and speed• At the same temperature, heavier

molecules move more slowly• Heavier molecules diffuse more

slowly than light ones

Mass and energy• Consider the following gasesHe at 300K Rn at 300KH2 at 100K Br2 at 100K• In which gas are the molecules

moving the fastest?• In which gas are particles moving

the slowest?

Specific heat capacity• Heat it takes to raise the

temperature of one gram of stuff 1ºC

• Unit is J/gºC; symbol is CP

• Metals have low heat capacity• Water has a very high heat

capacity (4.184J/gºC, or 1cal/gºC)

Specific heat capacity• q = mCPT• Find the heat necessary to raise

the temperature of a 5g slug of lead from 22-100ºC. CP for lead = 0.13J/gºC

• H = mCPT = 5(0.13)(100-22) = 50.7J

Changing state • Gas – liquid• Evaporation – some molecules of a

liquid have enough energy to escape – happens at RT

• Boiling point – temperature at which the vapor pressure of a liquid equals the atmospheric pressure

Liquid state to gas state

• Vapor pressure – pressure exerted by molecules trying to leave the surface of a liquid – increases with increasing temperature

• Boiling point depends on:– Molar mass - higher MM, higher BP– Polarity – high polarity, high BP – Atmospheric pressure – high AP, high BP

Liquid state to gas state

• Heat of vaporization – heat necessary to vaporize one gram of a liquid at its boiling point

• Hv = 2260 J/g for water• J = Joule• 1 calorie is the heat necessary to raise

the temperature of 1g of water 1ºC. 1 cal = 4.184 J

Liquid state to gas state

• Heat transfer – when a liquid boils or evaporates, heat goes from surroundings to the liquid (sweating)

• When a gas condenses, heat is transferred from the gas to the surroundings (steam burns)

Liquid state to gas state

• Heat = mHv

• Find the heat necessary to boil 230g water.

• Heat = 230gx2260J/g = 519,800 Joules

Solid state to liquid state

• Melting – molecules get enough energy to acquire linear motion

• Freezing – molecules slow down enough so they get trapped in place

• Heat of fusion – heat released when one gram of a substance freezes – Hf = 334J/g for water

Solid state to liquid state

• Math is the same as for boiling• Find the heat released when 10.0g

water freezes to form ice.• q = Hfxm = 10.0gx334J/g = 3340J• Heat transfer happens without

temperature changes during phase change

Heating curves

Sublimation• Solid – gas – sublimation –

happens when pressure is low• Dry ice and iodine sublime readily

at standard atmospheric pressure• Below freezing, ice will sublime

slowly• Many substances can be made to

sublime under a vacuum

Sublimation• Sublimation involves heat transfer

from the surroundings to the substance

• Opposite process is deposition (heat goes from substance to surroundings)