GASES

bullPressurebull Temperaturebullnumber of moleculesbullVolume

Parameters to describe gases

force = m x a = kg x ms2 = Newton area (N)Barometer ndash a device used to measure

atmospheric pressureEvangelista Torricelli (early 1600s) used mercury for the first type of barometer

PRESSURE

The SI unit for pressure is named after Blaise Pascal

A Pascal is defined as 1 Newtonacting on an area of one square meter 1 Nm2

Units of pressure760 mm Hg = 760 torr = 1 atmosphere (atm) =

1013 kPa (kilopascals) = 147 psi

Relationship between Pressure Force and AreaForce = mass x acceleration

(On Earth acceleration is a constant due to gravity)

Force =

500 N

Force =

500 N

Area of contact = 325 cm2

Pressure = force area

= 500 N = 15 Ncm2

325 cm2

Area of contact = 13 cm2

Pressure = force area

= 500 N = 385 Ncm2

13cm2

Area of contact = 65 cm2

Pressure = force area

= 500 N = 77 Ncm2

65 cm2

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

bullPressurebull Temperaturebullnumber of moleculesbullVolume

Parameters to describe gases

force = m x a = kg x ms2 = Newton area (N)Barometer ndash a device used to measure

atmospheric pressureEvangelista Torricelli (early 1600s) used mercury for the first type of barometer

PRESSURE

The SI unit for pressure is named after Blaise Pascal

A Pascal is defined as 1 Newtonacting on an area of one square meter 1 Nm2

Units of pressure760 mm Hg = 760 torr = 1 atmosphere (atm) =

1013 kPa (kilopascals) = 147 psi

Relationship between Pressure Force and AreaForce = mass x acceleration

(On Earth acceleration is a constant due to gravity)

Force =

500 N

Force =

500 N

Area of contact = 325 cm2

Pressure = force area

= 500 N = 15 Ncm2

325 cm2

Area of contact = 13 cm2

Pressure = force area

= 500 N = 385 Ncm2

13cm2

Area of contact = 65 cm2

Pressure = force area

= 500 N = 77 Ncm2

65 cm2

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

force = m x a = kg x ms2 = Newton area (N)Barometer ndash a device used to measure

atmospheric pressureEvangelista Torricelli (early 1600s) used mercury for the first type of barometer

PRESSURE

The SI unit for pressure is named after Blaise Pascal

A Pascal is defined as 1 Newtonacting on an area of one square meter 1 Nm2

Units of pressure760 mm Hg = 760 torr = 1 atmosphere (atm) =

1013 kPa (kilopascals) = 147 psi

Relationship between Pressure Force and AreaForce = mass x acceleration

(On Earth acceleration is a constant due to gravity)

Force =

500 N

Force =

500 N

Area of contact = 325 cm2

Pressure = force area

= 500 N = 15 Ncm2

325 cm2

Area of contact = 13 cm2

Pressure = force area

= 500 N = 385 Ncm2

13cm2

Area of contact = 65 cm2

Pressure = force area

= 500 N = 77 Ncm2

65 cm2

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

The SI unit for pressure is named after Blaise Pascal

A Pascal is defined as 1 Newtonacting on an area of one square meter 1 Nm2

Units of pressure760 mm Hg = 760 torr = 1 atmosphere (atm) =

1013 kPa (kilopascals) = 147 psi

Relationship between Pressure Force and AreaForce = mass x acceleration

(On Earth acceleration is a constant due to gravity)

Force =

500 N

Force =

500 N

Area of contact = 325 cm2

Pressure = force area

= 500 N = 15 Ncm2

325 cm2

Area of contact = 13 cm2

Pressure = force area

= 500 N = 385 Ncm2

13cm2

Area of contact = 65 cm2

Pressure = force area

= 500 N = 77 Ncm2

65 cm2

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Relationship between Pressure Force and AreaForce = mass x acceleration

(On Earth acceleration is a constant due to gravity)

Force =

500 N

Force =

500 N

Area of contact = 325 cm2

Pressure = force area

= 500 N = 15 Ncm2

325 cm2

Area of contact = 13 cm2

Pressure = force area

= 500 N = 385 Ncm2

13cm2

Area of contact = 65 cm2

Pressure = force area

= 500 N = 77 Ncm2

65 cm2

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Standard temperature and pressure are definedas 1 atm of pressure and 0C

When describing gases Kelvin temperature is typically used

Kelvin = degC + 273

STP

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Grahamrsquos Law

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

NH3 + HCl NH4Cl

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Grahamrsquos law of Effusion

The rates of effusion ofgases at the same T andP are inversely proportional to thesquare roots of their molar masses

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Derivation of Grahamrsquos LawComparing two gases ldquoArdquo and ldquoBrdquoAt the same T their KE is equal

KEA = KEB

frac12 MAvA2 = frac12 MBvB

2

Multiplying both sides by 2 and rearranging tocompare velocities gives

vA2 = MB

vB2 MA

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Now take the square root of both sides

=

This shows that =

This can also be used when dealing with densitiesof gases

= =

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

The total pressure of a mixture of gases isequal to the sum of the partial pressures ofthe component gases

PT = P1 + P2 + P3 +

Daltonrsquos Law of partial pressures

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

bull Many gases are collected over water thus according to Daltonrsquos law of partial pressures you must account for the vapor pressure of the water

Patm = Pgas + PH2O

A table of water vapor pressures will be provided for you

COLLECTING GASES OVER WATER

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Boylersquos Law - 1662pressure-volume relationship thevolume of a fixed mass of gas variesinversely with the pressure at constanttemperature

PV = kP1V1 = P2V2

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Boylersquos Law graph

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

volume-temperature relationship volume of a fixed massof gas at constant pressure varies directly with the Kelvintemperature) His experiments showed that all gases expand to thesame extent when heated through the same temperatureinterval Charles found that the volume changes by 1273of the original volume for each Celsius degree at constantpressure and an initial temperature of 0C

V = k V1 = V2

T T1 T2 (Kelvin temp)

Charlesrsquos Law - 1787

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Charlesrsquos Law graph

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

pressure-temperature relationship The pressure of a fixed mass of gas at constant volume variesdirectly with the Kelvin temperature For everyKelvin of temperature change the pressure of aconfined gas changes by 1273 of the pressure at0C

P = k P1 = P2 (Kelvin temp)

T T1 T2

Gay-Lussacrsquos Law - 1802

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Gay-Lussac graph

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Combined gas law

pressure volume and temperature relationship

PV = k P1V1 = P2V2

T T1 T2

(Kelvin temp)

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

at a constant T and P the volumes of gaseousreactants and products can be expressed asratios of small whole numbers

Gay-Lussacrsquos Law of Combining Volumes - 1808

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Avogadrorsquos Law

equal volumes of gases at the same T and Pcontain the same number of molecules The volume occupied by one mole of a gas atSTP is known as

standard molar volume of gas 224 liters

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

bull The Ideal Gas Law is the mathematical relationship among pressure volume temperature and the number of moles of a gas

bull Combining Boylersquos Law Charlesrsquos Law and Avogadrorsquos Law gives us V = nRT or more

P

commonly seen as PV = nRT

Ideal Gas Law

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

R = PV = (1 atm)(224 l) = 0082 latm nT (1 mol)(27315K) molK

Other values for R (depending on P units)624 ltorr (or mm Hg) 8314 l kPa mol K mol K

R ndash the ideal gas law constant

Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

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Variations on the ideal gas law can be used to findMolar mass or density (n [moles] = mM)

PV = mRT or M = mRT m= mass M PV M = molar mass

Density is mV so substituting that into the ideal gas equation gives us

M = mRT = DRT which then gives us D = MP PV P RT

Variations on the ideal gas law

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Deviations of real gases from ideal behavior

bull The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other Real molecules however do have finite volumes and they do attract one another

bull In 1873 Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

P = nRT - n2a V-nb V2

Correction for Correction for volume of molecules molecular attractions

The volume is decreased by the factor nb which accounts for thefinite volume occupied by gas molecules The pressure is decreased by the second term which accounts for the attractiveforces between gas molecules The magnitude of a reflects howstrongly the gas molecules attract each other The more polar the molecules of a gas are the more they will attract each other

At very high pressures and very low temperatures deviationsfrom ideal behavior may be considerable

Van der Waals equation

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

Good videos for Gases

bull Leidenfrost Effect of H2Ohttpwwwwimpcomwateruphill bull bull httpwwwyoutubecomwatchv=gojuu3AJajAbull ldquoboiling water at room temperaturerdquobull bull httpwwwyoutubecomwatchv=nmKIZtg9itAbull Balloons and marshmallowsbull bull Grahamrsquos Law

httpwwwyoutubecomwatchv=Ff1eL_8kQLAbull

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