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THREE STATES OF THREE STATES OF MATTERMATTER

THREE STATES OF THREE STATES OF MATTERMATTER

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Property of Gases

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General Properties General Properties of Gasesof Gases

• There is a lot of “There is a lot of “freefree” ” space in a gas.space in a gas.

• Gases can be Gases can be expandedexpanded infinitely. infinitely.

• Gases fill containers Gases fill containers uniformlyuniformly and and completelycompletely..

• Gases Gases diffusediffuse and and mixmix rapidly.rapidly.

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Compressibility• Gases are easily compressed because of

the space between the particles.

• 10 times the

space between

particles to the

diameter of the

particle.

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Factors that Effect Factors that Effect Gas PressureGas Pressure

• Amount of Gas

• Volume

• Temperature

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Amount of Gas• Adding gas increases the number of

particles in a given container.

increases the number of collisions

increases the pressure in the container

Think of a dinner with the family compared to a frat party away at college.

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Volume• Pressure increases as size decreases.

The opposite is also true.

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Temperature• Increase temperature increases pressure.

this temperature increase increases the kinetic energy of the particles in the gas faster moving particles hit the walls

of the container withmore energy

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Properties of Properties of GasesGases

Gas properties can be modeled Gas properties can be modeled using math. Model depends on—using math. Model depends on—

• V = V = volumevolume of the gas (L) of the gas (L)• T = T = temperaturetemperature (K) (K)• n = n = amountamount (moles) (moles)• P = P = pressurepressure

(atmospheres) (atmospheres)

• Ideal Gas Law PV=n(RT)Ideal Gas Law PV=n(RT)

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PressurePressurePressure of air is Pressure of air is

measured with a measured with a BAROMETERBAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)

Hg rises in tube until force of Hg rises in tube until force of Hg (down) balances the Hg (down) balances the force of atmosphere force of atmosphere (pushing up). (Just like a (pushing up). (Just like a straw in a soft drink)straw in a soft drink)

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PressurePressureColumn height measures Column height measures

Pressure of atmospherePressure of atmosphere• 1 standard 1 standard atmosphereatmosphere

(atm) *(atm) *

= 760 = 760 mmmm Hg (or torr) * Hg (or torr) *

= 29.92 = 29.92 inchesinches Hg * Hg *

= 14.7 pounds/in= 14.7 pounds/in2 2 ((psipsi))

= 101.3 = 101.3 kPakPa (SI unit is (SI unit is PASCAL) *PASCAL) *

= about 34 feet of water!= about 34 feet of water!

* * MemorizeMemorize thesethese!!

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Pressure Conversions

A. What is 475 mm Hg expressed in atm?

B. The pressure of a tire is measured as 29.4 psi.

What is this pressure in mm Hg?

= 1.52 x 103 mm Hg

= 0.625 atm475 mm Hg x

29.4 psi x

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Pressure Conversions

A. What is 2 atm expressed in torr?

B. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa?

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The Gas Laws• Boyle’s Law

• Charles’ Law

• Gay-Lussac’s Law

• The Combined Gas Law

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And now, we pause for this commercial message from

STPOK, so it’s really not THIS kind

of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 deg C (273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

STP allows us to compare amounts of

gases between different pressures and temperatures

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Boyle’s LawBoyle’s LawP P αα 1/V 1/VThis means This means PressurePressure

and and VolumeVolume are are INVERSELYINVERSELY PROPORTIONAL. If PROPORTIONAL. If molesmoles and and temperaturetemperature are are constant (do not constant (do not change). For change). For example, P goes up example, P goes up as V goes down.as V goes down.

PP11VV11 = P = P22 V V22

Robert Boyle Robert Boyle (1627-1691). (1627-1691). Son of Earl ofSon of Earl of Cork, Ireland.Cork, Ireland.

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Boyle’s Law and Boyle’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

Boyle’s Law and Boyle’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

P proportional to 1/VP proportional to 1/V

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Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s LawA bicycle pump is a A bicycle pump is a

good example of good example of Boyle’sBoyle’s law. law.

As the As the volumevolume of the of the air trapped in the air trapped in the pump is pump is reducedreduced, , its pressure goes its pressure goes up, and air is up, and air is forced into the tire.forced into the tire.

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Charles’s LawCharles’s LawIf If nn and and PP are are

constant, constant, then V then V αα T T

VV and and TT are directly are directly proportional.proportional.

VV11 V V22

==

TT11 T T22

• If one If one temperaturetemperature

goes up, the goes up, the volumevolume goes up!goes up!

Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

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Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

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Gay-Lussac’s LawGay-Lussac’s LawIf If nn and and VV are are

constant, constant, then P then P αα T T

PP and and TT are directly are directly proportional.proportional.

PP11 P P22

==

TT11 T T22

• If one If one temperaturetemperature

goes up, the goes up, the pressurepressure goes up! goes up!

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

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Gas Pressure, Gas Pressure, Temperature, and Kinetic Temperature, and Kinetic

Molecular TheoryMolecular Theory

Gas Pressure, Gas Pressure, Temperature, and Kinetic Temperature, and Kinetic

Molecular TheoryMolecular Theory

P proportional to TP proportional to T

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Combined Gas Law• The good news is that you don’t

have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

P1 V1 P2 V2

= T1 T2

No, it’s not related to R2D2

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Learning Check A gas has a volume of 675 mL at 35°C and

0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?

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One More Practice Problem

A balloon has a volume of 785,000 L on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

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Avogadro’s Avogadro’s HypothesisHypothesisEqual volumes of gases at the same T Equal volumes of gases at the same T

and P have the same number of and P have the same number of molecules.molecules.

V = n (RT/P) = knV = n (RT/P) = kn

V and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

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Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular

TheoryTheory

Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular

TheoryTheory

P proportional to nP proportional to n

The gases in this The gases in this experiment are all experiment are all measured at the measured at the same T and V.same T and V.

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IDEAL GAS LAWIDEAL GAS LAW

Brings together gas Brings together gas properties.properties.

Can be derived from Can be derived from experiment and theory.experiment and theory.

BE SURE YOU KNOW BE SURE YOU KNOW THIS EQUATION!THIS EQUATION!

P V = n R TP V = n R T

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Using PV = nRTUsing PV = nRTP = PressureP = Pressure

V = VolumeV = Volume

T = TemperatureT = Temperature

N = number of molesN = number of moles

R is a constant, called the R is a constant, called the Ideal Gas ConstantIdeal Gas Constant

Instead of learning a different value for R for all the Instead of learning a different value for R for all the possible unit combinations, we can just possible unit combinations, we can just memorizememorize oneone value and value and convert the units to match R.convert the units to match R.

R = 0.0821R = 0.0821

L • atm

Mol • K

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Using PV = nRTUsing PV = nRTHow much NHow much N22 is required to fill a small room is required to fill a small room

with a volume of 960 cubic feet (27,000 L) to with a volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 745 mm Hg at 25 ooC?C?

SolutionSolution

1. Get all data into proper units1. Get all data into proper units

V = 27,000 LV = 27,000 L

T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K

P = 745 mm Hg (1 atm/760 mm Hg) P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm = 0.98 atm

And we always know R, 0.0821 L atm / mol KAnd we always know R, 0.0821 L atm / mol K

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Using PV = nRTUsing PV = nRTHow much NHow much N22 is req’d to fill a small room with a is req’d to fill a small room with a

volume of 960 cubic feet (27,000 L) to P = volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 745 mm Hg at 25 ooC?C?

SolutionSolution

2. Now plug in those values and 2. Now plug in those values and solve for the unknown.solve for the unknown.

PV = PV = nnRTRTn = (0.98 atm)(2.7 x 104 L)

(0.0821 L• atm/K • mol)(298 K)n =

(0.98 atm)(2.7 x 104 L)

(0.0821 L• atm/K • mol)(298 K)

n = 1.1 x 10n = 1.1 x 1033 mol (or about 30 kg of gas) mol (or about 30 kg of gas)

RT RTRT RT

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Learning Check

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mm Hg) in the tank in the dentist office?

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Learning Check

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

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Deviations from Deviations from Ideal Gas LawIdeal Gas Law

• Real molecules have volume.

The ideal gas consumes the entire amount of available volume. It does not account for the volume of the molecules themselves.

• There are intermolecular forces.

An ideal gas assumes there are no attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.– Otherwise a gas could not

condense to become a liquid.

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Gases in the AirThe % of gases in air Partial pressure (STP)

78.08% N2 593.4 mm Hg

20.95% O2 159.2 mm Hg

0.94% Ar 7.1 mm Hg

0.03% CO2 0.2 mm Hg

PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2

Total Pressure 760 mm Hg

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Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...

Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum ofDalton’s Law: total P is sum of PARTIALPARTIAL pressures.pressures.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

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Dalton’s Dalton’s LawLaw

John DaltonJohn Dalton1766-18441766-1844

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Health NoteWhen a scuba diver is several hundred feet under water, the high pressures cause N2 from the

tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form bubbles in

the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2 in scuba tanks used for

deep descents.

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Collecting a gas “over water”

• Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

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Table of Vapor Pressures for Water

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Solve This!

A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the gas?

768 torr – 17.5 torr = 750.5 torr

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GAS DENSITYGAS DENSITYGAS DENSITYGAS DENSITY

HighHigh densitydensity

Low Low densitydensity

22.4 L of ANY gas AT STP = 1 mole

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Gases and Gases and StoichiometryStoichiometry

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a in a flask with a

volume of 2.50 L. What is the volume of Ovolume of 2.50 L. What is the volume of O22 at at

STP?STP?

Bombardier beetle Bombardier beetle uses decomposition uses decomposition of hydrogen peroxide of hydrogen peroxide to defend itself.to defend itself.

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Gases and Gases and StoichiometryStoichiometry

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a volume in a flask with a volume

of 2.50 L. What is the volume of Oof 2.50 L. What is the volume of O22 at STP? at STP?

SolutionSolution1.1 g1.1 g HH22OO22 1 mol H 1 mol H22OO22 1 mol O 1 mol O22 22.4 L 22.4 L

OO22

34 g H34 g H22OO22 2 mol H 2 mol H22OO22 1 mol O 1 mol O22 = 0.36 L O2 at STP

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Gas Stoichiometry: Practice!

A. What is the volume at STP of 4.00 g of CH4?

B. How many grams of He are present in 8.0 L

of gas at STP?

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What if it’s NOT at STP?

• 1. Do the problem like it was at STP. (V1)

• 2. Convert from STP (V1, P1, T1) to the stated conditions (P2, T2)

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Try this one!How many L of O2 are needed to react 28.0 g NH3 at 24°C and 0.950 atm?

4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g)

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GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

• diffusiondiffusion is the is the gradual mixing of gradual mixing of molecules of different molecules of different gases.gases.

• effusioneffusion is the is the movement of movement of molecules through a molecules through a small hole into an small hole into an empty container.empty container.

HONORS HONORS onlyonly

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GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Graham’s law governs Graham’s law governs effusion and diffusion effusion and diffusion of gas molecules.of gas molecules.

Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of BRate for BRate for AHONORS HONORS

onlyonly

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GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Molecules effuse thru holes in a Molecules effuse thru holes in a rubber balloon, for example, at a rubber balloon, for example, at a rate (= moles/time) that israte (= moles/time) that is

• proportional to Tproportional to T

• inversely proportional to M.inversely proportional to M.

Therefore, He effuses more rapidly Therefore, He effuses more rapidly than Othan O22 at same T. at same T.

HeHe

HONORS HONORS onlyonly

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Gas DiffusionGas Diffusionrelation of mass to rate of relation of mass to rate of

diffusiondiffusion

Gas DiffusionGas Diffusionrelation of mass to rate of relation of mass to rate of

diffusiondiffusion• HCl and NH3 diffuse

from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

HONORS HONORS onlyonly