Ch. 13.1 The Nature of Ch. 13.1 The Nature of Gases Gases The Kinetic Molecular Theory The Kinetic Molecular Theory based on the idea that particles are based on the idea that particles are constantly moving constantly moving (Kinetic comes from (Kinetic comes from the Greek word the Greek word kinetos kinetos which means which means “to to move move”) can be applied to solid, liquid, or gas can be applied to solid, liquid, or gas We will look as it applies to gases We will look as it applies to gases The particles in a gas are The particles in a gas are considered to be small, hard considered to be small, hard spheres with an insignificant spheres with an insignificant volume. volume. Particles are relatively far apart Particles are relatively far apart No attractive or repulsive forces exist between No attractive or repulsive forces exist between the particles the particles Particles are in continuous, Particles are in continuous, rapid, random motion rapid, random motion Fill the container they are in Fill the container they are in Particles collide with each other and Particles collide with each other and container walls container walls All collisions between particles All collisions between particles and container walls are and container walls are perfectly elastic perfectly elastic there is no net loss of energy when there is no net loss of energy when particles collide particles collide Total kinetic energy (KE) remains the Total kinetic energy (KE) remains the same same Pressure Pressure P : force per unit area on a surface P : force per unit area on a surface Newton Newton – SI unit for force SI unit for force (1 kg*m/s (1 kg*m/s 2 ) As surface area decreases, pressure increases As surface area decreases, pressure increases Pressure exerted by a gas depends on Pressure exerted by a gas depends on volume volume temperature temperature number of molecules number of molecules A F = = Area Force Pressure Measuring Pressure Measuring Pressure barometer barometer instrument used to measure instrument used to measure atmospheric pressure atmospheric pressure first one created by Torricelli first one created by Torricelli in early 1600s in early 1600s glass tube filled with mercury glass tube filled with mercury is inverted in a dish is inverted in a dish mercury flows out of the tube mercury flows out of the tube until pressure of the Hg inside until pressure of the Hg inside the tube is equal to the the tube is equal to the atmospheric pressure on the atmospheric pressure on the Hg in the dish Hg in the dish Measuring Pressure Measuring Pressure manometer: manometer: measures pressure of gas in a container measures pressure of gas in a container gas has less pressure than atmosphere if gas has less pressure than atmosphere if the Hg is closer to chamber the Hg is closer to chamber gas has more pressure than atmosphere if gas has more pressure than atmosphere if the Hg is further from chamber the Hg is further from chamber Units of Pressure Units of Pressure millimeters of mercury (mmHg) millimeters of mercury (mmHg) from mercury barometer from mercury barometer torr torr ( torr torr) from from Toricelli Toricelli inventing barometer inventing barometer atmosphere of pressure ( atmosphere of pressure (atm atm) Pascal (Pa) = 1N/m Pascal (Pa) = 1N/m 2 (SI unit) (SI unit) named after French scientist named after French scientist PSI PSI – pounds per square inch pounds per square inch 1 1 atm atm = 760 mmHg = 14.7 = 760 mmHg = 14.7 psi= psi= 101.325 101.325 kPa kPa
Transcript
Ch. 13.1 The Nature ofCh. 13.1 The Nature ofGasesGases
The Kinetic Molecular TheoryThe Kinetic Molecular Theory
based on the idea that particles arebased on the idea that particles areconstantly moving constantly moving (Kinetic comes from(Kinetic comes fromthe Greek word the Greek word kinetos kinetos which means which means ““totomovemove””))
can be applied to solid, liquid, or gascan be applied to solid, liquid, or gas We will look as it applies to gasesWe will look as it applies to gases
The particles in a gas areThe particles in a gas areconsidered to be small, hardconsidered to be small, hardspheres with an insignificantspheres with an insignificant
volume.volume.
Particles are relatively far apartParticles are relatively far apart No attractive or repulsive forces exist betweenNo attractive or repulsive forces exist between
the particlesthe particles
Particles are in continuous,Particles are in continuous,rapid, random motionrapid, random motion
Fill the container they are inFill the container they are in Particles collide with each other andParticles collide with each other and
container wallscontainer walls
All collisions between particlesAll collisions between particlesand container walls areand container walls are
perfectly elasticperfectly elastic
there is no net loss of energy whenthere is no net loss of energy whenparticles collideparticles collide
Total kinetic energy (KE) remains theTotal kinetic energy (KE) remains thesamesame
PressurePressure P : force per unit area on a surfaceP : force per unit area on a surface
Newton Newton –– SI unit for force SI unit for force (1 kg*m/s(1 kg*m/s22)) As surface area decreases, pressure increasesAs surface area decreases, pressure increases
Pressure exerted by a gas depends onPressure exerted by a gas depends on volumevolume temperaturetemperature number of moleculesnumber of molecules
instrument used to measureinstrument used to measureatmospheric pressureatmospheric pressure
first one created by Torricellifirst one created by Torricelliin early 1600sin early 1600s
glass tube filled with mercuryglass tube filled with mercuryis inverted in a dishis inverted in a dish
mercury flows out of the tubemercury flows out of the tubeuntil pressure of the Hg insideuntil pressure of the Hg insidethe tube is equal to thethe tube is equal to theatmospheric pressure on theatmospheric pressure on theHg in the dishHg in the dish
If V is decreased and the # ofIf V is decreased and the # ofmolecules stays constant, there will bemolecules stays constant, there will bemore molecules hitting the walls permore molecules hitting the walls perunit areaunit area
BoyleBoyle’’s Law: P and Vs Law: P and V BoyleBoyle’’s Law:s Law: the V of fixed mass the V of fixed mass
of gas varies inversely with P at aof gas varies inversely with P at aconstant T.constant T.
PV = k (k is a constant)PV = k (k is a constant)
What kind of graph is V What kind of graph is V vsvs. P?. P?
If we have a set of newIf we have a set of newconditions for the same sampleconditions for the same sampleof gas, they will have same k so:of gas, they will have same k so:
2211VPVP =
BoyleBoyle’’s Laws Law BoyleBoyle’’s Law: P and Vs Law: P and V Discovered by IrishDiscovered by Irish
chemist, Robertchemist, RobertBoyleBoyle
Used a J-shapedUsed a J-shapedtube to experimenttube to experimentwith varyingwith varyingpressures inpressures inmultistory homemultistory homeand effects onand effects onvolume of enclosedvolume of enclosedgasgas
Example: BoyleExample: Boyle’’s Laws Law
Consider a 1.53-L sample of gaseous SOConsider a 1.53-L sample of gaseous SO22 at ata pressure of 5.6 atm. If the pressure isa pressure of 5.6 atm. If the pressure ischanged to 1.5 atm at constantchanged to 1.5 atm at constanttemperature, what will be the new volumetemperature, what will be the new volumeof the gas?of the gas?
L 5.7tm 1.5
L) (1.53 tm) (5.6V2 =
!=
a
a
2
11
22211
P
VPV so VPVP ==
CharlesCharles’’ Law: V and T Law: V and T if P is constant, gases expand when heatedif P is constant, gases expand when heated
when T increases, gas molecules movewhen T increases, gas molecules movefaster and collide with the walls more oftenfaster and collide with the walls more oftenand with greater forceand with greater force
to keep the P constant, the V must increaseto keep the P constant, the V must increase
CharlesCharles’’ Law: V and T Law: V and T Problem: if we use Celsius,Problem: if we use Celsius,
we could end up withwe could end up withnegative values fromnegative values fromcalculations in gas laws forcalculations in gas laws forvolumesvolumes
we need a T system with nowe need a T system with nonegative values: negative values: KelvinKelvinTemperature ScaleTemperature Scale starts at -273.15 ° C =starts at -273.15 ° C =
absolute zeroabsolute zero = 0 K = 0 K lowest possible temperaturelowest possible temperature
15.273+= CKo
balloon going intoliquid nitrogen
CharlesCharles’’ Law: V and T Law: V and T CharlesCharles’’ Law: Law: the V of fixed mass of gas at the V of fixed mass of gas at
constant P varies directly with Kelvin T.constant P varies directly with Kelvin T.
V = kTV = kT
k is a constant for a certain sample of gask is a constant for a certain sample of gasthat depends on the mass of gas and Pthat depends on the mass of gas and P
What kind of graph is V vs. T?What kind of graph is V vs. T?
If we have a set of new conditions for theIf we have a set of new conditions for thesame sample of gas, they will have same ksame sample of gas, they will have same kso:so:
2
2
1
1
T
V
T
V=
CharlesCharles’’ Law Law
discovered by French physicist, Jacquesdiscovered by French physicist, JacquesCharles in 1787Charles in 1787
first person to fill balloon with hydrogenfirst person to fill balloon with hydrogengas and make solo balloon flightgas and make solo balloon flight
Bad Idea?Bad Idea?
Example: CharlesExample: Charles’’ Law & Temp. Law & Temp.
A sample of gas at 15°C and 1 A sample of gas at 15°C and 1 atm atm has ahas avolume of 2.58 L. What volume will this gasvolume of 2.58 L. What volume will this gasoccupy at 38°C and 1 occupy at 38°C and 1 atmatm??
1
21
2
2
2
1
1
T
TVV so
T
V
T
V==
L 2.79K 288
L) (2.58K) (311V2 =
!=
Gay-LussacGay-Lussac’’ssLaw: P and TLaw: P and T Remember:Remember:
P is the result of collisions of moleculesP is the result of collisions of moleculeswith container wallswith container walls
Force and frequency of collisions dependsForce and frequency of collisions dependson average KEon average KE
KE depends on TKE depends on T
If the T increases, collisions occurIf the T increases, collisions occurmore often and with higher force somore often and with higher force sothe P must increasethe P must increase
Gay-LussacGay-Lussac’’s Law: P and Ts Law: P and T Gay-LussacGay-Lussac’’s Law:s Law: the P of fixed mass of gas the P of fixed mass of gas
at constant V varies directly with Kelvin T.at constant V varies directly with Kelvin T.
P = kTP = kT
What kind of graph is P vs. T?What kind of graph is P vs. T?
If we have a set of new conditions for theIf we have a set of new conditions for thesame sample of gas, they will have same ksame sample of gas, they will have same kso:so:
2
2
1
1
T
P
T
P=
Gay-LussacGay-Lussac’’s Laws Law
discovered in 1802discovered in 1802by Joseph Gay-by Joseph Gay-LussacLussac
Example: Gay-LussacExample: Gay-Lussac’’s Laws Law
The gas in an aerosol can is at a pressure ofThe gas in an aerosol can is at a pressure of3.00 3.00 atm atm at 25°C. Directions on the canat 25°C. Directions on the canwarn the user not to keep the can in a placewarn the user not to keep the can in a placewhere temperature exceeds 52°C. Whatwhere temperature exceeds 52°C. Whatwould the gas pressure be in the can atwould the gas pressure be in the can at52°C?52°C?
1
21
2
2
2
1
1
T
TPP so ==
T
P
T
P
atm 3.27K 298
K) (325atm) (3.00P2 =
!=
How to Remember which lawHow to Remember which lawgoes with each pair of variables:goes with each pair of variables:
P V
T
Boyle’s
Charles’Gay-Lussac’s
Combined Gas LawCombined Gas Law
a gas often changes in T, P, and V alla gas often changes in T, P, and V allat onceat once
the other gas laws can be combinedthe other gas laws can be combinedinto one lawinto one law
Combined Gas Law-Combined Gas Law- relationship relationshipbetween P, V, and T of a fixed amountbetween P, V, and T of a fixed amountof gasof gas
2
22
1
11
T
VP
T
VP= 122211 TVPTVP =OR
Example: Combined Gas LawExample: Combined Gas Law
A Helium-filled balloon has volume ofA Helium-filled balloon has volume of50.0 L at 25°C and 1.08 50.0 L at 25°C and 1.08 atmatm. What. Whatvolume will it have at 0.855 volume will it have at 0.855 atm atm andand10.0°C?10.0°C?
21
211
2
2
22
1
11
PT
TPVV so
T
PV
T
PV==
L 0.06(0.855atm)K) (298
L) (50.0(1.08atm)(283K)V2 =
!
!!=
ExampleExample A balloon containing 5.5 L of air at 25CA balloon containing 5.5 L of air at 25C
and 755 and 755 torr torr is put at the bottom of theis put at the bottom of theocean. The new temperature is 4 C and theocean. The new temperature is 4 C and thenew volume is 2300 new volume is 2300 mLmL. What is the new. What is the newpressure?pressure?
21
211
2
2
22
1
11
VT
TPVP so
T
PV
T
PV==
torr19403L)(277K)(0.2
)torr)(298K(5.5L)(755P2 ==
AvagadroAvagadro’’s s Hypothesis Hypothesis (10.2)(10.2)
Equal volumes of gases at the sameEqual volumes of gases at the sametemperature and pressure containtemperature and pressure containequal number of particles (molecules,equal number of particles (molecules,atoms,atoms, etc)etc)
1 mole of a gas at STP occupies 1 mole of a gas at STP occupies 22.4 L22.4 L
Ideal Gas LawIdeal Gas Law PV = PV = nRTnRT
P = pressureP = pressure V = volumeV = volume n = number of molesn = number of moles R = ideal gas constantR = ideal gas constant T = temperatureT = temperature
Ideal Gas LawIdeal Gas Law Where did R come from?Where did R come from? If you have 1 mole of gas at STPIf you have 1 mole of gas at STP
PV = PV = nRT nRT R = R = PV/nTPV/nT R =R = (1 (1 atm atm * 22.4 L) / (1 mol * 273K)* 22.4 L) / (1 mol * 273K) R = 0.0821 LR = 0.0821 L••atm atm / mol / mol ••KK
Ideal Gas LawIdeal Gas Law Where did R come from?Where did R come from? If you have 1 mole of gas at STPIf you have 1 mole of gas at STP
PV = PV = nRT nRT R = R = PV/nTPV/nT R =R = (1 (1 atm atm * 22.4 L) / (1 mol * 273K)* 22.4 L) / (1 mol * 273K) R = 0.0821 LR = 0.0821 L••atm atm / mol / mol ••KK
Ideal Gas LawIdeal Gas Law WhatWhat is the volume occupied by 1.24 molis the volume occupied by 1.24 mol
of a gas at 35.0ºC if the pressure is 0.949of a gas at 35.0ºC if the pressure is 0.949atmatm??
A helium-filled weather balloon has aA helium-filled weather balloon has avolume of 240 L at 99kPa andvolume of 240 L at 99kPa and 0.00°C. How0.00°C. Howmany moles of helium are in the balloon?many moles of helium are in the balloon?How many grams of He?How many grams of He?
Real Real vsvs. Ideal Gases. Ideal Gases
ideal gas is defined by the KMTideal gas is defined by the KMT most gases behave close to the idealmost gases behave close to the ideal
whenwhen high temperature high temperature –– so they have enough so they have enough
KE to overcome attractive forcesKE to overcome attractive forces low pressure low pressure –– so they are very spread so they are very spread
outout
Gases with little attraction are moreGases with little attraction are moreideal (monatomic gases)ideal (monatomic gases)
Gas Gas Stoichiometry Stoichiometry (12.2)(12.2)
Stoich Stoich is back!is back!
Remember: 1 mol of a gas at STPRemember: 1 mol of a gas at STPoccupies 22.4Loccupies 22.4L
If theIf the reaction is at STP we can easilyreaction is at STP we can easilydo mol to volume conversionsdo mol to volume conversions(replacing a mol to mass conversion)(replacing a mol to mass conversion)
How many liters of NO2 can beHow many liters of NO2 can beproduced from 34L of Oproduced from 34L of O22 at STP? at STP?
!
34L O2"1molO
2
22.4LO2
"2molNO
2
1molO2
"22.4L NO
2
1molNO2
= 68LNO2
Notice the 22.4L cancel in the equation.Notice the 22.4L cancel in the equation.Remember Remember AvagadroAvagadro’’s s Hypothesis?Hypothesis?
DaltonDalton’’s Laws Law
The contribution each gas in a mixture makes toThe contribution each gas in a mixture makes tothe total vapor pressure is called partial pressure.the total vapor pressure is called partial pressure.
In a mixture of gases, the total pressure is theIn a mixture of gases, the total pressure is thesum of the partial pressures of the gases.sum of the partial pressures of the gases.
PPtotaltotal = P= P11 + P + P22 + P + P33 + + ……
As measured by percentage, the partial pressure ofAs measured by percentage, the partial pressure ofa gas will not change even if you change totala gas will not change even if you change totalpressure, temperature or volume. (The partialpressure, temperature or volume. (The partialpressure of oxygen in the atmosphere is alwayspressure of oxygen in the atmosphere is always21%)21%)
DaltonDalton’’s Laws Law
PPtotaltotal = P= P11 + P + P22 + P + P33 + + ……
A gas mixture containing oxygen,A gas mixture containing oxygen,nitrogen, and carbon dioxide hasnitrogen, and carbon dioxide hasa total pressure of 32.9 a total pressure of 32.9 kPakPa..
The spontaneous mixing of the particles of twoThe spontaneous mixing of the particles of twosubstances caused by their random motionsubstances caused by their random motion
EffusionEffusion The process by which gas particles passThe process by which gas particles pass
through a tiny openingthrough a tiny opening
Molecules of low molar mass effuse andMolecules of low molar mass effuse anddiffuse faster than molecules of high massdiffuse faster than molecules of high mass
