starter describe the differences between various states of matter

Starter Starter

Describe the differences between Describe the differences between various states of mattervarious states of matter

Physical Characteristics Physical Characteristics of Gasesof Gases

Kinetic Molecular TheoryKinetic Molecular Theory

The Kinetic Molecular The Kinetic Molecular TheoryTheory

based on the idea that particles are based on the idea that particles are constantly movingconstantly moving

can be applied to solid, liquid, or can be applied to solid, liquid, or gasgas

provides a model of ideal gas provides a model of ideal gas behavior so only an approximationbehavior so only an approximation

Gases consist of tiny particles Gases consist of tiny particles that are very far apartthat are very far apart

most volume is empty space-low densitymost volume is empty space-low density allows gases to be easily compressedallows gases to be easily compressed

All collisions between particles All collisions between particles and container walls are elasticand container walls are elastic there is no net loss of energy when there is no net loss of energy when

particles collideparticles collide total kinetic energy stays constant total kinetic energy stays constant

even though it can be transferred even though it can be transferred between particlesbetween particles

Particles are in continuous, Particles are in continuous, rapid, random motionrapid, random motion

since they are moving, they have KEsince they are moving, they have KE KE overcomes their attractive forcesKE overcomes their attractive forces

No forces of attraction or No forces of attraction or repulsionrepulsion

like billiard ballslike billiard balls bounce apart immediatelybounce apart immediately

Average kinetic energy Average kinetic energy depends on temperaturedepends on temperature

KE increases as temperature increasesKE increases as temperature increases KE = ½mvKE = ½mv22

where m = mass of particlewhere m = mass of particle where v = velocity of particlewhere v = velocity of particle

so at the same T, lighter particles so at the same T, lighter particles have higher speeds than heavier oneshave higher speeds than heavier ones

velocity and temperature are directly velocity and temperature are directly proportional proportional

Real vs. Ideal GasesReal vs. Ideal Gases

ideal gas is defined by the KMTideal gas is defined by the KMT most gases behave close to the most gases behave close to the

ideal whenideal when high temperature – so they have high temperature – so they have

enough KE to overcome attractive enough KE to overcome attractive forcesforces

low pressure – so they are very spread low pressure – so they are very spread outout

Gases with little attraction are more Gases with little attraction are more ideal (monatomic gases)ideal (monatomic gases)


PressurePressure

PressurePressure P : force per unit area on a surfaceP : force per unit area on a surface

Newton – SI unit for force (1 kg*m/sNewton – SI unit for force (1 kg*m/s22)) why would shoes with smaller diameter heel why would shoes with smaller diameter heel

not be allowed on gym floor?not be allowed on gym floor? As surface area decreases, pressure As surface area decreases, pressure

increasesincreases Pressure exerted by a gas depends onPressure exerted by a gas depends on

volumevolume temperaturetemperature number of moleculesnumber of molecules

A

F

Area

ForcePressure

Measuring PressureMeasuring Pressure barometerbarometer

instrument used to measure instrument used to measure atmospheric pressureatmospheric pressure

first one created by Torricelli first one created by Torricelli in early 1600sin early 1600s

glass tube filled with mercury glass tube filled with mercury is inverted in a dishis 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 dishHg in the dish

Measuring PressureMeasuring Pressure manometer:manometer:

measures pressure of gas in a containermeasures pressure of gas in a container gas has less pressure than atmosphere gas has less pressure than atmosphere

if the Hg is closer to chamberif the Hg is closer to chamber gas has more pressure than atmosphere gas has more pressure than atmosphere

if the Hg is further from chamberif the Hg is further from chamber

Units of PressureUnits of Pressure

millimeters of mercury (mmHg)millimeters of mercury (mmHg) from mercury barometerfrom mercury barometer

torr (torr) torr (torr) from Toricelli inventing barometerfrom Toricelli inventing barometer

atmosphere of pressure (atm)atmosphere of pressure (atm) Pascal (Pa) = 1N/mPascal (Pa) = 1N/m22 (SI unit) (SI unit)

named after French scientistnamed after French scientist

1 atm = 760 mmHg = 760 torr = 101.325 kPa1 atm = 760 mmHg = 760 torr = 101.325 kPa

Practice ConversionsPractice Conversions

Convert 0.927 atm toConvert 0.927 atm to mmHg mmHg

torrtorr

kPakPa

mmHgatm

mmHgatm 70552.704

1

760927.0

kPakPaatm

kPaatm 9.93928.93

1

325.101927.0

torratm

torratm 70552.704

1

760927.0

Practice ConversionsPractice Conversions

Convert 148.6 kPa Convert 148.6 kPa toto atmatm

mmHgmmHg

torrtorr

atmatm

kPa 467.1466568.1325.101

16.148

mmHgkPa

mmHgkPa 111559.1114

325.101

7606.148

torrkPa

torrkPa 111559.1114

325.101

7606.148

Temperature ScalesTemperature Scales

Convert the following to K or Convert the following to K or 00CC

0 0 00CC 5 K5 K 20 20 00CC -50 -50 00CC 100 K100 K 100 100 00CC

StarterStarterThe pressure of a gas is measured as The pressure of a gas is measured as

49 torr. Convert this pressure to 49 torr. Convert this pressure to atmospheres, kiloPascals, and mmHg.atmospheres, kiloPascals, and mmHg.

Pull out your homework so I can check it. Pull out your homework so I can check it.

Starter: Pressure Starter: Pressure ConversionsConversions

The pressure of a gas is measured as 49 The pressure of a gas is measured as 49 torr. Represent this pressure in torr. Represent this pressure in atmospheres, Pascals, and mmHg.atmospheres, Pascals, and mmHg.

atm 0.064 torr760

1atm torr49

Pa 6500 torr760

Pa 101,325 torr49

mmHg 49 torr49

Physical Properties of Physical Properties of GasesGases

Gas Laws:Gas Laws:

Relationships between volume, temperature, Relationships between volume, temperature, pressure, and amount of gas.pressure, and amount of gas.

Boyle’s Law: P and Boyle’s Law: P and VV

as one as one increasesincreases, the , the

other other decreasesdecreases inversely proportionalinversely proportional pressure is caused by moving pressure is caused by moving

molecules hitting container wallsmolecules hitting container walls If V is decreased and the # of If V is decreased and the # of

molecules stays constant, there will molecules stays constant, there will be more molecules hitting the walls be more molecules hitting the walls per unitper unit

Boyle’s Law: P and VBoyle’s Law: P and V Boyle’s Law:Boyle’s Law: the V of fixed mass the V of fixed mass

of gas varies inversely with P at of gas varies inversely with P at a constant T.a constant T.

PV = kPV = k k is a constant for a certain k is a constant for a certain

sample of gas that depends on sample of gas that depends on the mass of gas and Tthe mass of gas and T

What kind of graph is V vs. P?What kind of graph is V vs. P? If we have a set of new If we have a set of new

conditions for the same sample conditions for the same sample of gas, they will have same k so:of gas, they will have same k so:

2211 VPVP

Boyle’s LawBoyle’s Law

Boyle’s Law: P and VBoyle’s Law: P and V Discovered by Irish Discovered by Irish

chemist, Robert chemist, Robert BoyleBoyle

Used a J-shaped Used a J-shaped tube to experiment tube to experiment with varying with varying pressures in pressures in multistory home multistory home and effects on and effects on volume of enclosed volume of enclosed gasgas

Example: Boyle’s LawExample: Boyle’s Law

Consider a 1.53-L sample of gaseous SOConsider a 1.53-L sample of gaseous SO22 at a pressure of 5.6 x 10at a pressure of 5.6 x 1033 Pa. If the Pa. If the pressure is changed to 1.5 x 10pressure is changed to 1.5 x 1044 Pa at Pa at constant temperature, what will be the constant temperature, what will be the new volume of the gas?new volume of the gas?

L 0.57Pa 101.5

L) (1.53 Pa) 10 (5.6V

4

3

2

2

1122211 P

VPV so VPVP

Charles’ Law: V and TCharles’ Law: V and T if P is constant, gases expand when if P is constant, gases expand when

heatedheated when T increases, gas molecules move when T increases, gas molecules move

faster and collide with the walls more faster and collide with the walls more often and with greater forceoften and with greater force

to keep the P constant, the V must to keep the P constant, the V must increase increase

Charles’ Law: V and TCharles’ Law: V and T Problem: if we use Celsius, Problem: if we use Celsius,

we could end up with we could end up with negative values from negative values from calculations in gas laws for calculations in gas laws for volumesvolumes

we need a T system with we need a T system with no negative values: no negative values: Kelvin Kelvin Temperature ScaleTemperature Scale starts at -273.15 ° C = starts at -273.15 ° C =

absolute zeroabsolute zero = 0 K = 0 K lowest possible temperaturelowest possible temperature

15.273CK balloon going into liquid nitrogen

Charles’ Law: V and TCharles’ Law: V and T Charles’ Law:Charles’ Law: the V of fixed mass of gas the V of fixed mass of gas

at constant P varies directly with Kelvin at constant P varies directly with Kelvin T.T.

V = kTV = kT k is a constant for a certain sample of gas k is a constant for a certain sample of gas

that 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 the If we have a set of new conditions for the

same sample of gas, they will have same same sample of gas, they will have same k so:k so:

2

2

1

1

T

V

T

V

Charles’ LawCharles’ Law

discovered by French physicist, Jacques discovered by French physicist, Jacques Charles in 1787Charles in 1787

first person to fill balloon with hydrogen first person to fill balloon with hydrogen gas and make solo balloon flightgas and make solo balloon flight

Example: Charles’ Law & Example: Charles’ Law & Temp.Temp.

A sample of gas at 15°C and 1 atm has a A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What volume will this volume of 2.58 L. What volume will this gas occupy at 38°C and 1 atm?gas occupy at 38°C and 1 atm?

1

212

2

2

1

1

T

TVV so

T

V

T

V

L 2.79K 288

L) (2.58K) (311V2

Pressure vs Volume vs Pressure vs Volume vs TempTemp

P

V

V

T

T

P

P/V = k

T/V = k

P/T = k


Dalton’s Law of Partial Dalton’s Law of Partial PressurePressure


John DaltonJohn Dalton responsible for atomic theoryresponsible for atomic theory also studied gas mixturesalso studied gas mixtures

the P of gas mixture is the sum of the the P of gas mixture is the sum of the individual pressures of each gas aloneindividual pressures of each gas alone

the P that each gas exerts in the the P that each gas exerts in the mixture is independent of the P that mixture is independent of the P that are exerted by other gasesare exerted by other gases


the total P of a mixture of gases is the total P of a mixture of gases is equal to the sum of partial P of equal to the sum of partial P of component gases, no matter how component gases, no matter how many different gasesmany different gases

PPTT = P = P11 + P + P22 + P + P33 + … + …

Partial Pressure-Partial Pressure- P of each gas in P of each gas in mixturemixture

Why?Why?

the particles of each gas in a the particles of each gas in a mixture have an equal chance mixture have an equal chance to hit the wallsto hit the walls

so each gas exerts P so each gas exerts P independent of that exerted independent of that exerted by other gasesby other gases

total P is result of the total # total P is result of the total # of collisions per unit of wall of collisions per unit of wall areaarea

Water DisplacementWater Displacement gas produced is less dense than water gas produced is less dense than water

so it replaces the water in the bottleso it replaces the water in the bottle gas collected is not pure because it gas collected is not pure because it

contains vapor from the watercontains vapor from the water

PPTT = P = Pgasgas + P + Pwaterwaterequal to atmospheric pressure

set for a certain T

ExampleExample Oxygen gas from decomposition of KClOOxygen gas from decomposition of KClO33 was was

collected by water displacement. The collected by water displacement. The barometric pressure and the temperature barometric pressure and the temperature during the experiment were 731.0 torr and during the experiment were 731.0 torr and 20.020.0°°C respectively. If the partial pressure of C respectively. If the partial pressure of water vapor is 17.5 torr at 20.0water vapor is 17.5 torr at 20.0°°C. What was C. What was the partial pressure of oxygen collected?the partial pressure of oxygen collected?

PPTT = P = PO2O2 + P + PH2OH2O

731.0 torr = P731.0 torr = PO2O2 + 17.5 + 17.5

PPO2O2 = 713.5 torr = 713.5 torr

ExampleExample

Find the partial pressure by 2 gases Find the partial pressure by 2 gases (A and B) mixed if the overall (A and B) mixed if the overall pressure is 790 mmHg. The percent pressure is 790 mmHg. The percent by volume is A: 20% and B: 80%.by volume is A: 20% and B: 80%.

PPTT = P = PAA + P + PB B = 790 mmHg= 790 mmHg A: 0.20 x 790 = 158 mmHgA: 0.20 x 790 = 158 mmHg B: 0.80 x 790 = 632 mmHgB: 0.80 x 790 = 632 mmHg

Starter Starter

How many grams of NO gas are in How many grams of NO gas are in 6200 mL of gas at STP?6200 mL of gas at STP?

Molecular Molecular Composition of GasesComposition of Gases

Ideal Gas LawIdeal Gas Law

Ideal Gas LawIdeal Gas Law relationship among P, V, T, and number of relationship among P, V, T, and number of

moles of gas (n)moles of gas (n) combination of all the laws we learnedcombination of all the laws we learned helps us approximate “real” gas behaviorhelps us approximate “real” gas behavior

where where R: ideal gas constantR: ideal gas constant 0.08206 L atm/mol K (use most often)0.08206 L atm/mol K (use most often) 8.314 J/mol K (only for when P is in Pascals)8.314 J/mol K (only for when P is in Pascals)

check units before using equationcheck units before using equation

nRTPV

ExampleExample

What is the P in atm exerted by a 0.500 What is the P in atm exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L mol sample of nitrogen gas in a 10.0 L container at 298 K?container at 298 K?

V

nRTPnRTPV

atmL

KKmol

atmLmol

P 22.10.10

)298)(08206.0)(500.0(

ExampleExample

What is the volume in liters of 0.250 What is the volume in liters of 0.250 mol of oxygen gas at 20.0°C and mol of oxygen gas at 20.0°C and 0.974 atm?0.974 atm?

P

nRTVnRTPV

Latm

KKmol

atmLmol

V 18.6974.0

)2.293)(08206.0)(250.0(

ExampleExample What mass of chlorine gas is in a What mass of chlorine gas is in a

10.0 L tank at 27°C and 3.50 atm?10.0 L tank at 27°C and 3.50 atm?

RT

PVnnRTPV

molK

KmolatmL

Latmn 42.1

).300(08206.0

)0.10)(50.3(

22 101685668.1001

)4527.35(242.1 gCl

mol

gmolCl

Finding Molar Mass Finding Molar Mass

mass of one mole of substancemass of one mole of substance units : g/molunits : g/mol represented by Mrepresented by M

n

m

moles

massMMolarMass

#

MolarMass

mass

M

mn

Finding Molar MassFinding Molar Mass At 28°C and 0.974 atm, 1.00 L of At 28°C and 0.974 atm, 1.00 L of

gas has a mass of 5.16g. What is the gas has a mass of 5.16g. What is the molar mass?molar mass?

RT

PVnnRTPV

molK

KmolatmL

Latmn 0394.0

)301)(08206.0(

)00.1)(974.0(

molgmol

gM /131

0394.0

16.5

Finding DensityFinding Density

nRTPV

mRTPMVRTM

mPV

V

mD

DRT

PM

V

m

P

DRTM

M

mn

Finding Molar MassFinding Molar Mass

The density of dry air at sea level (with The density of dry air at sea level (with pressure of exactly 1 atm) is 1.225 g/L at pressure of exactly 1 atm) is 1.225 g/L at 15°C. What is the molar mass of air?15°C. What is the molar mass of air?

P

DRTM

mol

g

atm

KKmol

atmLLg

M 8.281

)288)(08206.0)(22.1(

Finding DensityFinding Density

What is the density of carbon monoxide What is the density of carbon monoxide gas at STP? gas at STP?

RT

MPD

P

DRTM

L

g

KKmol

atmL

atmmolg

D 250.1)15.273)(08206.0(

)1)(0104.28(

Finding DensityFinding Density A sample of gas has a mass of 50.0 g and A sample of gas has a mass of 50.0 g and

volume of 26.0 L at 25C and 1.2 atm. volume of 26.0 L at 25C and 1.2 atm. What is the molar mass of the gas? What is the molar mass of the gas?

molgatm

KKmol

atmLLg

M /39)2.1(

)298)(08206.0)(92.1(

LgL

g

V

mD /92.1

0.26

0.50

P

DRTM

starter describe the differences between various states of matter

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