Merlin's  

   The Kinetic Theory

1.)  All matter is composed of small particles such as ions, atoms, or molecules.

2.)  The particles of matter are in constant motion.

Solid-vibrate in a fixed position

Liquid-rolls over each other 

Gas-travels in straight lines

3.)  All collisions are perfectly elastic

elastic collision- no loss of energy

kinetic energy is transferred

- mean free path- is the average distance a particle travels between collisions with another particle

Oxygen gas  at 25 degrees Celsius travels at 443 meters per second or 1700 kilometers per hour---the mean free path is 106 nanometers--this will cause 1/4 to 1/2 a billion collisions per second

-Pressure- a measure of the force of moving particles hitting the walls of a container- unit (force per unit area)

Standard pressure (average air pressure at sea level)

1.013 * 10⁵ pa - Pascal

101.3 KPa- Kilopascal

14.7 psi - pounds per square inch

76.0 cm of Hg- centimeters of Mercury

760 Torr- Torr

1.00 atm- Atmospheres

760 mm of Hg- millimeters of Mercury

29.9 in of Hg- inches of Mercury

1013.25 mb --millibars

Manometer- an instrument used to measure gas pressure open or closed tube

Barometer- a closed arm manometer used to measure atmospheric pressure

Temperature- a measure of the average kinetic energy of the particles of an object

Kinetic energy = 1/2 mv² 

Kelvin Temperature scale (The SI unit of temperature)

Zero Kelvin= absolute zero- the coldest possible all molecular motion will cease at Zero Kelvin

Kelvin= Degrees Celsius + 273

The Four States of Matter

Solid-Liquid-Gas-Plasma

Gas

- High kinetic energy

-travels independently in straight line path

-No definite shape or volume

-Low density (g/L unit form gas)

Liquid

-Less kinetic energy than a gas

-Vibrates and rolls around each other

- No definite shape, but has a definite volume

-Higher density than a gas (g/ml or g/cm³  units)

Solid

-Less kinetic energy than a liquid

-Vibrates in a fixed position

-Particles arranged in definite patterns

-Definite shape and volume 

Plasma- when matter is heated to very high temp. (over 5000 degrees Celsius) collisions between particles are so violent that electrons are knocked away from the atom.  Plasmas are composed of electrons and positive ions.  Most of the universe is made of plasma; example stars and outer space (thin plasma).  The van Allen radiation belt around the earth is a type of plasma.  Electric and magnetic fields effects plasma because of the ions.  Magneto hydrodynamics- the study of plasma.

Solid

Kinetic theory description of the solid state

The particles of solids may be ions, atoms, or molecules.

They have less kinetic energy than gases or liquids (more ordered).

Solid particles are more closely packed than liquids or gases.

This makes their intermolecular forces stronger

(dipole-dipole attraction, London forces, and Hydrogen bonding)

Types of Solids

1.)  Crystalline solids- crystal- a substance in which the particles are arranged in orderly, geometric repeating pattern.

2.)  Amorphous solids- particles are arranged randomly. ex: glass, plastics

Properties of Solids

1.)  Definite shape

2.)  Definite volume (volume may change a little with temperature)

3.)  Nonfluidity (amorphous solids flow at very slow rates)

4.)  Definite melting point- temp at which a solid becomes a liquid (amorphous solids do not have a definite melting point- they are called super cooled liquids)

5.)  High density units g/cm³ 

6.)   Incompressibility

7.)  Slow rate of diffusion (millions of times slower than liquid)

Shapes of Crystals- 1.) isometeric or cubic    2.)  Tetragonal    3.)diclinic

4.) Trigonal    5.) orthorhombic    6.) monoclinic    7.)triclinic

Crystal lattice- pattern of points that describe the arrangement of a crystal's particles.

Liquids

    A state of matter that has a definite volume but an indefinite shape

    Liquids are the least common state of matter in the universe

Kinetic Theory description of the liquid state

-the particles may be ions, atoms or molecules

-these particles have less kinetic energy(more ordered) than a gas and more kinetic energy than a solid

-particles of a liquid roll around each other

Properties of liquids

1)definite volume

2)fluidity (fluid-a substance that can flow and therefore conform to the shape of the container)

3)relatively high density- units g/cm³ or g/mL

4)relative incompressibility (noncompressibility) under a high pressure there is little change in volume; at 1000 atm, volume decreases by about 4%

5)dissolving ability- when one substance is added to another so that after mixing only one physical state is observed

6)ability to diffuse- only liquid will diffuse through another liquid in which it can be dissolved

7)surface tension- a force that tends to pull adjacent parts of a liquid's surface together, thus making the surface less penetrable by solid bodies.  surface tension is the result of attractive forces between particles                   ex. capillary action, meniscus forces

8)Tendency to evaporate and boil

1. -vaporization: the process by which a liquid or solid changes to a gas

2. -evaporation: the process by which particles escape from the surface of a non-boiling liquid and enter the gaseous state

3. -boiling: the change of a liquid to bubbles of vapor that appear throughout the liquid when the equilibrium vapor pressure of the liquid equals the atmospheric pressure

4. -boiling point: the temperature at which a liquid boils at a certain pressure

9)Tendency to solidify

1. -freezing: the physical change of a liquid to a solid

2. -equilibrium: a dynamic condition in which two opposing physical or chemical changes occur at equal rates in the same closed system

       closed system- sample of matter being studied

       phase- any part of a system that has uniform properties

       condensation- the process by which a gas changes to a liquid

       concentration- the number of particles per unit volume

dynamic equilibrium

evaporation=liquid + heat energy à vapor

condensation=vaporàliquid+heat energy

Henri Louis Le Chatelier(1850-1936) French chemist

-Le Chatelier’s principle: if any of the factors determining an equilibrium are changed, the system will adjust itself in a way that tends to minimize the change and bring it back to equilibrium

Phase diagram- a graph of temperature versus pressure that indicates the conditions under which gaseous, liquids, and solid phase of a particular substance exist

A. Triple point-indicates the temperature and pressure conditions at which the solid, liquid, and vapor of the substance can coexist at equilibrium              0.0060 atm and 0.01 °C

B. Normal freezing point 0°C at 1atm

C. Critical point

-Critical temperature Tc- the temperature above which the substance cannot exist in the liquid state.   374.1 °C

-Critical pressure Pc- the lowest pressure required for the substance to exist as a liquid at the critical temperature.  218.3 atm

D. Normal boiling point 100°C at 1atm

Gases

The Kinetic Theory description of a gas

1.    Matter is composed of very tiny particles

2.    The particles of matter are in continual motion

3.     The total kinetic energy of colliding particles remains constant

Properties of gases

1.    Expansion- a gas does not have a definite shape or volume.  It will fill or take on the shape of the container

2.    Pressure- force per unit area- the pressure of a gas is produced by the impact of the gas molecules on the wall of the container

3.    Low Density – Gases have low density and is usually measured in g/L. The density of a gas is about 1/1000 of the density of the same substance in the liquid or solid phase.

4.    Diffusion- mixability- two of more different gases will mix completely and uniformly when placed in the contact with each other.

Ideal gases vs. Real gases

Ideal gas- a gas which follows all of the assumptions of the kinetic theory at any temperature or pressure (there is no such gas.

Real Gas- under moderate conditions of temperature and pressure it behaves as an ideal gas, but if the temperature is very low or the pressure very high they deviate from ideal gas predictions

Standard temperature and pressure- STP

Standard temperature- ST= 0^oC and 273 K

Standard pressure- SP= 760 mm of Hg

This is the pressure exerted by a column of mercury exactly 760mm high.

The Gas Laws

·        Boyle’s Law- The volume of a gas varies inversely with the pressure if the temperature is constant. (Robert Boyle 17^th century scientist)

V_n=V_oP_o/P_n

§         As the pressure on a gas increases the volume decreases

·        Charles’s Law- (Jacques Charles 1787 French scientist)  The volume of a gas varies directly with the temperature if the pressure is constant.

V_n=V_oT_n/T_o    

§         As the temperature of a gas increases the volume will increase.  Temperature must be in Kelvin so no negative numbers are used in the problem.

·        Dalton’s Law of Partial Pressure- (John Dalton- English channel 1766-1844)  The total amount of a mixture of gases is equal to the sum of the partial pressure of the component gases.

Ptotal= P₁+P₂+P₃….

·        Dalton’s Law is used when a gas is collected by water displacement.  (also collecting a gas over water)

P_gas= P_total - P_{water vapor}

(water vapor pressure depends on the temperature)

·        Combined Gas Laws

Used when the pressure and the temperature changes at the same time.

V_n= V_oP_oT_n/P_nT_o

·        Graham’s Law- (Thomas Graham- Scottish Chemist)  The rates at  which two gases under identical conditions (same temperature and pressure) will diffuse varies inversely as the square roots of their molecular masses.

diffusion- the process whereby gases (or liquids) intermingle freely of their own by kinetic energy.

V₁/V₂=ÖM₂/ÖM₁

§         Example: what is the diffusion rate between H₂ and O₂        V1=H₂     V2=O₂

§         V₁ = ÖM₂ = Ö32 amu = Ö16 =4

V₂   ÖM₁    Ö2  amu    Ö1   1

§         V= velocity, m= atomic mass or molecular mass

§                     H₂ diffuses four times as fast as O₂

·        Ideal Gas Laws- shows the relationship between pressure, volume, temperature, and the number of moles of a gas

§                     R= constant  0.0821  L atm

                             Mol K

§                     N= number of moles of the gas

§                     PV=nRT

From PowerPoint 

 The States of Matter

u Gases indefinite volume and shape, low density.

u Liquids definite volume, indefinite shape, and high density.

u Solids definite volume and shape, high density

u Solids and liquids have high densities because their molecules are close together.

Kinetic Theory

l

l

are evidence of this.

The Kinetic Theory

u   

u  1.)  All matter is composed of small particles such as ions, atoms, or molecules.

u  2.)  The particles of matter are in constant motion.

u  Solid-vibrate in a fixed position

u  Liquid-rolls over each other

u  Gas-travels in straight lines

u  3.)  All collisions are perfectly elastic

u elastic collision- no loss of energy

u kinetic energy is transferred

u - mean free path- is the average distance a particle travels between collisions with another particle

u Oxygen gas  at 25 degrees Celsius travels at 443 meters per second or 1700 kilometers per hour---the mean free path is 106 nanometers--this will cause 1/4 to 1/2 a billion collisions per second

u -Pressure- a measure of the force of moving particles hitting the walls of a container- unit (force per unit area)

u  Standard pressure (average air pressure at sea level)

u  1.013 * 105 pa - Pascal

u  101.3 KPa- Kilopascal

u  14.7 psi - pounds per square inch

u  76.0 cm of Hg- centimeters of Mercury

u  760 Torr- Torr

u  1.00 atm- Atmospheres

u  760 mm of Hg- millimeters of Mercury

u  29.9 in of Hg- inches of Mercury

The Kinetic Theory of Gases
Makes three assumptions about gases

Ê A Gas is composed of particles

H      usually molecules or atoms

H      Considered to be hard spheres far enough apart that we can ignore their volume.

H      Between the molecules is empty space.

Ë The particles are in constant random motion.

H     Move in straight lines until they bounce off each other or the walls.

Ì All collisions are perfectly elastic

u The Average speed of an oxygen molecule is 1656 km/hr at 20ºC

u The molecules don’t travel very far without hitting each other so they move in random directions.

u Kinetic energy = 1/2 mv²

u Kelvin Temperature scale (The SI unit of temperature)

u Zero Kelvin= absolute zero- the coldest possible all molecular motion will cease at Zero Kelvin

u Kelvin= Degrees Celsius + 273

Temperature

u The  average kinetic energy is directly proportional to the temperature in Kelvin

u If you double the temperature (in Kelvin) you double the average kinetic energy.

u If you change the temperature from 300 K to 600 K the kinetic energy doubles.

Temperature

u If you change the temperature from 300ºC to 600ºC the Kinetic energy doesn’t double.

u 873 K is not twice 573 K

u Manometer- an instrument used to measure gas pressure open or closed tube

u Barometer- a closed arm manometer used to measure atmospheric pressure

Pressure

u Pressure is the result of collisions of the molecules with the sides of a container.

u A vacuum is completely empty space - it has no pressure.

u Pressure is measured in units of atmospheres (atm).

u It is measured with a device called a barometer.

Barometer

uAt one atmosphere pressure a column of mercury 760 mm high.

Barometer

uAt one atmosphere pressure a column of mercury 760 mm high.

uA second unit of  pressure is mm Hg

u1 atm = 760 mm Hg

u The Four States of Matter

u Solid-Liquid-Gas-Plasma

u Gas

u - High kinetic energy

u -travels independently in straight line path

u -No definite shape or volume

u -Low density (g/L unit form gas)

u Liquid

u -Less kinetic energy than a gas

u -Vibrates and rolls around each other

u - No definite shape, but has a definite volume

u -Higher density than a gas (g/ml or g/cm3  units)

u Solid

u -Less kinetic energy than a liquid

u -Vibrates in a fixed position

u -Particles arranged in definite patterns

u -Definite shape and volume

u  Plasma- when matter is heated to very high temp. (over 5000 degrees Celsius) collisions between particles are so violent that electrons are knocked away from the atom.  Plasmas are composed of electrons and positive ions.  Most of the universe is made of plasma; example stars and outer space (thin plasma).  The van Allen radiation belt around the earth is a type of plasma.  Electric and magnetic fields effects plasma because of the ions.  Magneto hydrodynamics- the study of plasma.

u   Solid

u   Kinetic theory description of the solid state

u   The particles of solids may be ions, atoms, or molecules.

u   They have less kinetic energy than gases or liquids (more ordered).

u   Solid particles are more closely packed than liquids or gases.

u   This makes their intermolecular forces stronger

u   (dipole-dipole attraction, London forces, and Hydrogen bonding

u Types of Solids

u 1.)  Crystalline solids- crystal- a substance in which the particles are arranged in orderly, geometric repeating pattern.

u 2.)  Amorphous solids- particles are arranged randomly. ex: glass, plastics

Properties of Solids

u 1.)  Definite shape

u 2.)  Definite volume (volume may change a little with temperature)

u 3.)  Nonfluidity (amorphous solids flow at very slow rates)

u 4.)  Definite melting point- temp at which a solid becomes a liquid (amorphous solids do not have a definite melting point- they are called super cooled liquids)

u   5.)  High density units g/cm3

u   6.)   Incompressibility

u   7.)  Slow rate of diffusion (millions of times slower than liquid)

u   Shapes of Crystals- 1.) isometeric or cubic    2.)  Tetragonal    3.)diclinic

u   4.) Trigonal    5.) orthorhombic    6.) monoclinic    7.)triclinic

u   Crystal lattice- pattern of points that describe the arrangement of a crystal's particles.

u   Unit Cell- the simplest unit of repetition in a crystal.

u  Types of crystals

u  1.)Ionic Crystals- a crystal consisting of ions arranged in a pattern.

u  2.)Covalent Network Crystal- single atom or molecule covalently bonded.

u  3.)Metallic Crystals- metallic bonding between metal atoms

u  4.)Covalent Molecular Crystals- covalent molecules held together by Van der Waal forces (London dispersion forces, polar             ex. sugar, ice

u  Hydrated Crystals- ions chemically bonded to water ex. CaSO4 X 2H2O

u  Hydroscopic- a substance that will attract water from the air

u  Deliquescent- a substance that will take up enough water from the air to turn into a liquid

u  Liquid Crystals- they lose their crystalline order in only 1 or 2 dimensions as they change to a liquid state

Liquids

u  A state of matter that has a definite volume but an indefinite shape

u      Liquids are the least common state of matter in the universe

u  Kinetic Theory description of the liquid state

u  -the particles may be ions, atoms or molecules

u  -these particles have less kinetic energy(more ordered) than a gas and more kinetic energy than a solid

u  -particles of a liquid roll around each other

Properties of liquids

u  1)definite volume

u  2)fluidity (fluid-a substance that can flow and therefore conform to the shape of the container)

u  3)relatively high density- units g/cm3 or g/mL

u  4)relative incompressibility (noncompressibility) under a high pressure there is little change in volume; at 1000 atm, volume decreases by about 4%

u  5)dissolving ability- when one substance is added to another so that after mixing only one physical state is observed

u  6)ability to diffuse- only liquid will diffuse through another liquid in which it can be dissolved

u  7)surface tension- a force that tends to pull adjacent parts of a liquid's surface together, thus making the surface less penetrable by solid bodies.  surface tension is the result of attractive forces between particles                   ex. capillary action, meniscus forces

u   )Tendency to evaporate and boil

u   -vaporization: the process by which a liquid or solid changes to a gas

u   -evaporation: the process by which particles escape from the surface of a non-boiling liquid and enter the gaseous state

u   -boiling: the change of a liquid to bubbles of vapor that appear throughout the liquid when the equilibrium vapor pressure of the liquid equals the atmospheric pressure

u   -boiling point: the temperature at which a liquid boils at a certain pressure

u    

u   9)Tendency to solidify

u   -freezing: the physical change of a liquid to a solid

u   -equilibrium: a dynamic condition in which two opposing physical or chemical changes occur at equal rates in the same closed system

u          closed system- sample of matter being studied

u          phase- any part of a system that has uniform properties

u          condensation- the process by which a gas changes to a liquid

u          concentration- the number of particles per unit volume

u dynamic equilibrium

u evaporation=liquid + heat energy à vapor

u condensation=vaporàliquid+heat energy

u Henri Louis Le Chatelier(1850-1936) French chemist

u -Le Chatelier’s principle: if any of the factors determining an equilibrium are changed, the system will adjust itself in a way that tends to minimize the change and bring it back to equilibrium

u    Phase diagram- a graph of temperature versus pressure that indicates the conditions under which gaseous, liquids, and solid phase of a particular substance exist

u     

u    A. Triple point-indicates the temperature and pressure conditions at which the solid, liquid, and vapor of the substance can coexist at equilibrium              0.0060 atm and 0.01 °C

u    B. Normal freezing point 0°C at 1atm

u    C. Critical point

u    -Critical temperature Tc- the temperature above which the substance cannot exist in the liquid state.   374.1 °C

u    -Critical pressure Pc- the lowest pressure required for the substance to exist as a liquid at the critical temperature.  218.3 atm

u    D. Normal boiling point 100°C at 1atm

Gases

u  

u The Kinetic Theory description of a gas

u 1.    Matter is composed of very tiny particles

u 2.    The particles of matter are in continual motion

u 3.     The total kinetic energy of colliding particles remains constant

u   Properties of gases

u   1.    Expansion- a gas does not have a definite shape or volume.  It will fill or take on the shape of the container

u   2.    Pressure- force per unit area- the pressure of a gas is produced by the impact of the gas molecules on the wall of the container

u   3.    Low Density – Gases have low density and is usually measured in g/L. The density of a gas is about 1/1000 of the density of the same substance in the liquid or solid phase.

u   4.    Diffusion- mixability- two of more different gases will mix completely and uniformly when placed in the contact with each other.

u  Ideal gases vs. Real gases

u  Ideal gas- a gas which follows all of the assumptions of the kinetic theory at any temperature or pressure (there is no such gas.

u  Real Gas- under moderate conditions of temperature and pressure it behaves as an ideal gas, but if the temperature is very low or the pressure very high they deviate from ideal gas predictions

u Standard temperature and pressure- STP

u Standard temperature- ST= 0oC and 273 K

u Standard pressure- SP= 760 mm of Hg

u This is the pressure exerted by a column of mercury exactly 760mm high.

Avagadro’s Hypothesis

u Equal volumes of gas at the same temperature and pressure have equal numbers of molecules.

u That means ...

Avagadro’s Hypothesis

u Has the same number of particles as ..

Avagadro’s Hypothesis

u Has the same number of particles as ..

This is where we get the fact that
 22.4 L =1 mole

u Only at STP

•    0ºC

•    1 atm

u This way we compare  gases at the same temperature and pressure.

Think of it it terms of pressure.

u The same pressure at the same temperature should require that there be the same number of particles.

u The smaller particles must have a greater average speed to have the same kinetic energy.

Liquids

u Particles are in motion.

u Attractive forces between molecules keep them close together.

u These are called intermolecular forces.

•    Inter = between

•    Molecular = molecules

Breaking intermolecular forces.

u Vaporization - the change from a liquid to a gas below its boiling point.

u Evaporation - vaporization of an uncontained liquid ( no lid on the bottle ).

Evaporation

u Molecules at the surface break away and become gas.

u Only those with enough                     KE escape

u Evaporation is a cooling                 process.

u It requires heat.

u Endothermic.

Condensation

/Change from gas to liquid

/Achieves a dynamic equilibrium with vaporization in a closed system.

/What is a closed system?

/A closed system means                                          matter can’t go in or out.                                 (put a cork in it)

/What the heck is a                                                 “dynamic equilibrium?”

Dynamic equilibrium

/When first sealed the molecules gradually escape the surface of the liquid

Dynamic equilibrium

/When first sealed the molecules gradually escape the surface of the liquid

/As the molecules build up             above the liquid          some    condense back to a                 liquid.

Dynamic equilibrium

/As time goes by the rate of vaporization remains constant

/ but the rate of condensation increases because there                             are more molecules to                   condense.

/Equilibrium is reached                               when

Dynamic equilibrium

Rate of Vaporization =                                                 Rate of Condensation

/Molecules are constantly changing phase “Dynamic”

/The total amount of liquid and vapor remains constant “Equilibrium”

Vaporization

n   Vaporization is an endothermic process - it requires heat.

n   Energy is required to overcome intermolecular forces

n   Responsible for cool earth.

n   Why we sweat. (Never let them see you.)

u At higher temperature more molecules have enough energy

u Higher vapor pressure.

Boiling

u A liquid boils when the vapor pressure = the external pressure

u Normal Boiling point is the temperature a substance boils at 1 atm pressure.

u The temperature of a liquid can never rise above it’s boiling point

Changing the Boiling Point

u Lower the pressure (going up into the mountains).

u Lower external pressure requires lower vapor pressure.

u Lower vapor pressure means lower boiling point.

u Food cooks slower.

Changing the Boiling Point

u Raise the external pressure (Use a pressure cooker)

u Raises the vapor pressure needed.

u Raises the boiling point.

u Food cooks faster.

Solids

u Intermolecular forces are strong

u Can only vibrate and revolve in place.

u Particles are locked in place - don’t flow.

u Melting point is the temperature where a solid turns into a liquid.

u The melting point is the same as the freezing point.

u When heated the particles vibrate more rapidly ontil they shake themselves free of each other.

u Ionic solids have strong intermolecular forces so a high mp.

u Molecular solids have weak intermolecular forces so a low mp.

Crystals

u A regular repeating three dimensional arrangement of atoms in a solid.

u Most solids are crystals.

u Amorphous solids lack an orderly internal structure.

u Think of them as super cooled liquids.

Cubic

Body-Centered Cubic

Face-Centered Cubic

Phase Changes

Energy and Phase Change

u Heat of vaporization energy required to change one gram of a substance from liquid to gas.

u Heat of condensation energy released when one gram of a substance changes from gas to liquid.

u For water 540 cal/g

Energy and Phase Change

u Heat of fusion energy required to change one gram of a substance from solid to liquid.

u Heat of solidification energy released when one gram of a substance changes from liquid to solid.

u For water 80 cal/g

Calcualting Energy

u Three equations

u Heat = specific heat x mass x DT

u Heat = heat of fusion x mass

u Heat = heat of vaporization x mass

Numbers to Know

u For ice S.H. = 0.50 cal/g°C

u For water S.H = 1 cal/g°C

u For steam S.H. = 0.50 cal/g°C

u Heat of vaporization= 540

u Heat of fusion = 80 cal/g

How to do it

u The total heat = the sum of all the heats you have to use

u Go in order

Examples

u How much heat does it take to heat 12 g of ice at -6°C to 25°C water?

u How much heat does it take to heat 35 g of ice at 0 °C to steam at 150 °C?

The Gas Laws

u Describe HOW gases behave.

u Can be predicted by the theory.

u Amount of change can be calculated with mathematical equations.

The effect of adding gas.

u When we blow up a balloon we are adding gas molecules.

u Doubling the the number of gas particles doubles the pressure

 (of the same volume at the same temperature).

Pressure and the number of molecules are directly related

u More molecules means more collisions

u Fewer molecules means fewer collisions.

u Gases naturally move from areas of high pressure to low pressure  because there is empty space to move in.

u If you double the number of molecules

u If you double the number of molecules

u You double the pressure.

u As you remove molecules from a container

u As you remove molecules from a container the pressure decreases

u As you remove molecules from a container the pressure decreases

u Until the pressure inside equals th pressure outside

u Molecules naturally move from high to low pressure

Changing the size of the container

u In a smaller container molecules  have less room to move

u Hit the sides of the container more often

u As volume decreases pressure increases.

u As the pressure on a gas increases

u As the pressure on a gas increases  the volume decreases

u Pressure and volume are inversely related

Temperature

u Raising the temperature of a gas increases the pressure if the volume is held constant.

u The molecules hit the walls harder.

u The only way to increase the temperature at constant pressure is to increase the volume.

u If you start with 1 liter of gas at 1 atm pressure and 300 K

u and heat it to 600 K one of 2 things happens

u Either the volume will increase to 2 liters at 1 atm

•Or the pressure will increase to 2 atm.

•Or someplace in between

Ideal Gases

u In this chapter we are going to assume the gases behave ideally

u Does not really exist but makes the math easier and is a close approximation.

u Particles have no volume

u No attractive forces

Ideal Gases

u There are no gases for which this is true.

u Real gases behave this way at high temperature and low pressure.

Daltons’ Law of Partial Pressures

u The total pressure inside a container is equal to the partial pressure due to each gas.

u The partial pressure is the contribution by that gas.

u P_Total = P₁ + P₂ + P₃

u For example

u We can find out the pressure in the fourth container

u By adding up the pressure in the first 3

Examples

u What is the total pressure in a balloon filled with  air if the pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is 620 mm Hg?

u In a second balloon the total pressure is 1.3 atm. What is the pressure of oxygen if the pressure of nitrogen is 720 mm Hg?

Boyle’s Law

u At a constant temperature pressure and volume are inversely related

u As one goes up the other goes down

u P x V = K                 (K is some constant)

_u    Easier to use   P₁ x V₁=P₂ x V₂

Examples

u A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is change to 1.5 atm what is the new volume?

u A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to  volume to 43 L?

Charles’ Law

u The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant.

u V = K x T     (K is some constant)

u V/T= K

_u    V₁/T₁= V₂/T₂

Examples

u What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure.

u What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC?

Gay Lussac’s Law

u The temperature and the pressure of a gas are directly realted at constant volume.

u P = K x T     (K is some constant)

u P/T= K

_u    P₁/T₁= P₂/T₂

Examples

u What is the pressure inside a 0.250 L can of  deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC?

u At what temperature will the can above have a presure of 2.2 atm?

Putting the pieces together

u The Combined Gas Law Deals with the situation where only the number of molecules stays constant.

_u    (P₁ x V₁)/T₁= (P₂ x V₂)/T₂

u Lets us figure out one thing when two of the others change.

Examples

u A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to  17 atm. What is the new volume?

u If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?

u The combined gas law contains all the other gas laws!

u If the temperature remains constant.

u The combined gas law contains all the other gas laws!

u If the pressure remains constant.

The Fourth Part

u Avagadro’s Hypothesis

u V is proportional to number of molecules at constant T and P.

u V is proportional to moles.

u V =  K n    ( n is the number of moles.

u Gets put into the combined gas Law

The Ideal Gas Law

u P x V = n x R x T

u Pressure  times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin.

u This time R does not depend on anything, it is really constant

u R = 0.0821 (L atm)/(mol K)

The Ideal Gas Law

u R = 62.4 (L mm Hg)/(K mol)

u We now have a new way to count moles. By measuring T, P, and V. We aren’t restricted to STP.

u n = PV/RT

Examples

u How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg?

u What is the pressure exerted by 1.8 g of H₂ gas exert in a 4.3 L balloon at 27ºC?

Density

u The Molar mass of a gas can be determined by the density of the gas.

u D=      mass    = m                                          Volume      V

u Molar mass = mass =     m                                                 Moles       n    

u n =    PV                                                                                  RT

u Molar Mass =      m                                                                                        (PV/RT)

u Molar mass =  m RT                                                                                V   P

u Molar mass =    DRT                                                                                         P    

At STP

u At STP determining the amount of gas required or produced is easy.

u 22.4 L = 1 mole

u For example                                                           How many liters of  O₂ at STP are       required to produce 20.3 g of H₂O?

Not At STP

u Chemical reactions happen in MOLES.

u If you know how much gas - change it to moles

u Use the Ideal Gas Law        n = PV/RT

u If you want to find how much gas -  use moles to figure out volume   V = nRT/P

Example #1

u HCl(g) can be formed by the following reaction

u 2NaCl(aq) + H₂SO₄ (aq)                                                                    2HCl(g) + Na₂SO4(aq)

u What mass of NaCl is needed to produce 340 mL of  HCl at 151 atm at 20ºC?

Example #2

u 2NaCl(aq) + H₂SO₄ (aq)                                                                     2HCl(g) + Na₂SO4(aq)

u What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react?

Ideal Gases don’t exist

u Molecules do take up space

u There are attractive forces

u otherwise there would be no liquids

Real Gases behave like Ideal Gases

u When the molecules are far apart

u The molecules do not take up as big a percentage of the space

u We can ignore their volume.

u This is at low pressure

Real Gases behave like Ideal gases when

u When molecules are moving fast.

u Collisions are harder and faster.

u Molecules are not next to each other very long

u Attractive forces can’t play a role.

Diffusion

u Effusion Gas escaping through a tiny hole in hole in a container.

u Depends on the speed of the molecule

Graham’s Law

u The rate of effusion and diffusion is inversely proportional to the square root molar mass of the molecules.

^u    Kinetic energy = 1/2 mv²

u m is the mass v is the velocity

Graham’s Law

u bigger molecules move slower at the same temp. (by Square root)

u  Bigger molecules effuse and diffuse slower

u Helium effuses and diffuses faster than air -escapes from balloon.

Gas Law equations

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