Gases

Edward Wen, PhD

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Properties of Gases

• expand to completely fill their container• take the shape of their container• low density

much less than solid or liquid state• compressible when pressure is changed.• mixtures of gases are always homogeneous

(common air)• fluid

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Properties of Gas: Indefinite Shape & Volume

Gas molecules: have enough kinetic energy

and little attractionskeep moving around and

spreading out fill the container of whatever

shape

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Comparison: Gas, Liquid, SolidState Shape Volume Compress Flow Solid Fixed Fixed No No

Liquid Indef. Fixed No Yes Gas Indef. Indef. Yes Yes

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Kinetic Molecular Theory

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Pressure: Gases PushingWhat are Gas molecules doing?• constantly in motion• as they move and strike a surface,

they push on that surfacepush = force

• Pressure of gas: total amount of force exerted by gas molecules hitting the entire surface at any one instant

pressure = force per unit area

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Measuring Air Pressure• use a barometer:

column of mercury supported by air pressure

• Force of the air on the surface of the mercury

Gravity on the column of mercury

gravity

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Common Units of PressureUnit Average Air Pressure at

Sea Levelpascal (Pa) 101,325

kilopascal (kPa) 101.325

atmosphere (atm) 1 (exactly)

millimeters of mercury (mmHg) 760 (exactly)

torr (torr) 760 (exactly)

pounds per square inch (psi, lbs./in2) 14.7

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Practice: Convert Pressure between units

• 735.0 mmHg = ? atm

• 35. psi = ? torr

Ans: 0.9671 atm

Ans: 1.8 × 103 torr

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Pressure of a Gas, P• Cause: constant movement of the

gas molecules and their collisions with the surfaces around them

• Pressure depends on:number of gas particles in a given volumevolume of the containeraverage speed of the gas particles

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The Effect of Gas Pressure• whenever there is a Pressure

difference, a gas will flow from area of High pressure area of Low pressure

the bigger the difference in pressure, the stronger the flow of the gas

• if there is something in the gas’ path, the gas will try to push it along as the gas flows

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Gas Pressure in Soda StrawsStraw at idle:Pressure of theair inside the straw = Pressureof the air outsidethe straw liquid levels isthe same on bothsides

Suction of the straw:Pressure of the

air inside the straw is< Pressure

of the air outsidethe straw

liquid is pushedup the straw bythe outside air

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Atmospheric Pressure & Altitude

• Altitude↑ Atmospheric pressure↓• At the surface, P = 14.7 psi, • At 10,000 ft altitude, P = 10.0 psi• Rapid changes in atmospheric pressure may

cause your ears to “pop” an imbalance in pressure on either side of your ear drum (driving or flying)

Demo: Can you make a piece of paper uphold a bottle of water?

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Boyle’s LawFor the gas contained• Pressure of a gas is inversely

proportional to its volume: P 1/V

constant T and amount of gas

• P x V = constant• P1 x V1 = P2 x V2Q: How does the size of an air

bubble change along the way it rises from the deep water to the surface?

∝

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Soda bottle Submarine

Pressure surge when bottle being squeezedVolume of the air inside the dropper decreasesWater filling up the dropperIncreased density of dropper (Massdropper/Volume↑)Dropper sinking!

Pinside

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Boyle’s Experiment• added Hg to a J-

tube with air trapped inside

• Plotting Volume of air vs. Air pressure

Inverse Volume vs Pressure of Air, Boyle's Expt.

0

20

40

60

80

100

120

140

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Inv. Volume, in-3

Pres

sure

, inH

g

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When you double the pressure on a gas,the volume reduces to one half, (as long as the temperature and amount of gas do not change)

Example:Boyle’s Law

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Example:• A cylinder equipped with a

moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume if the applied pressure is decreased to 1.0 atm?

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InformationGiven: P1 = 4.0 atm V1 = 6.0 L

P2 = 1.0 atmFind: V2 = ? L

Example:A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume if the applied pressure is decreased to 1.0 atm?

Answer: 24 L

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We’re losing altitude.Quick Professor, give yourlecture on Charles’ Law!

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Charles’ LawFor the gas contained and at constant

Pressure:• Volume is directly proportional to

temperature V Tconstant P and amount of gasgraph of V vs T is straight line

• as T increases, V also increases• Kelvin K = °C + 273• V = constant x T

if T measured in Kelvin

2

2

1

1TV

TV

=∝

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Charles’ Law in ActionThe density of common air depends on the

temperature. Higher T, lower Density

• Why the air vents for the air conditioning system are located at the ceiling?

• When measuring the weight of an object, why the high temperature of the object can affect the measurement?

Example:Charles’ Law

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Example:• A sample of gas has a

volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at 0°C, its volume decreases to 2.57 L. What was the initial temperature in kelvin and in celsius? (assume constant pressure)

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InformationGiven: V1 = 2.80 L

V2 = 2.57 L T2 = 0°CFind: temp1 in K and °C

Example:A gas has a volume of 2.80 L at an unknown temperature. When the sample is at 0°C, its volume decreases to 2.57 L. What was the initial temperature in kelvin and in celsius?

T1 = 297 K = 24 °C

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Gay-Lussac’s LawFor the gas contained at constant

Volume:• Pressure is directly proportional to

temperature P Tconstant V and amount of gasgraph of P vs T is straight line

• as T increases, P also increases• Kelvin K = °C + 273• P = constant x T

if T measured in Kelvin

1 2

1 2

P PT T

=∝

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Gay-Lussac’s Law in Action

The pressure of gas in a sealed container depends on the temperature. Higher T, higher Pressure

• Keep the propane container in a cool place, avoid from direct sunlight.

Example:Gay-Lussac’s Law

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Example:• The tire on a bicycle stored in a cool garage at 18°C

had a pressure of 30. psi. What is the pressure inside the tire after riding the bike at 35°C? Assume the volume of the tire remains constant.

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InformationGiven: T1 = 18°C, P1 = 30. psi

T2 = 35°CFind: P2 in psi.

The tire on a bicycle stored in a cool garage at 18°C had a pressure of 30. psi. What is the pressure inside the tire after riding the bike at 35°C? Assume the volume of the tire remains constant.

T1 = 291 K, T2 = 308 K, P2 = 32 psi

P, V, T

Keep P

P

Keep V

PT V TPV

Keep T

V T

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Avogadro’s Law

• Volume directly proportional to the number of gas molecules

V = constant x nconstant P and Tmore gas molecules = larger volume

• count number of gas molecules by moles

• Equal Volumes of gases contain Equal numbers of molecules

the gas doesn’t matter

2

2

1

1

nV

nV

=

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Avogadro’s Law

Example:Avogadro’s Law

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Example:• A 4.8 L sample of helium gas contains 0.22 mol helium.

How many additional moles of helium must be added to obtain a volume of 6.4 L? (assume constant pressure and temperature)

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InformationGiven: V1 = 4.8 L, n1 =0.22 mol

V2 = 6.4 LFind: n2, mol and added mol

Example:A 4.8 L sample of helium gas contains 0.22 mol helium. How many additional moles of helium must be added to obtain a volume of 6.4 L?

0.07 mole

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Combined Gas Law• Boyle’s Law : Pressure and

Volumeat constant temperature

• Charles’ Law : Volume and absolute Temperature

at constant pressure

Volume of a sample of gas when both the Pressure and Temperature change

( ) ( )( )

( ) ( )( )2

22

1

11T

VPT

VP •=

•

2

2

1

1TV

TV

=

2211 VPVP •=•

Example:The Combined Gas Law

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InformationGiven: V1 = 158 mL, P1 = 755 mmHg,

t1 = 34°CV2 = 108 mL, t2 = 85°C

Find: P2, mmHg

Example:A sample of gas has a volume of 158 mL at a pressure of 755 mmHg and a temperature of 34°C. The gas is compressed to a volume of 108 mL and heated to 85°C, what is the final pressure in mmHg?

P2 = 31.25 10 mmHg×

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Ideal Gas Law• Combined Gas Law + Avgadro’s Law

Ideal Gas Law

• R is called the Gas Constant• the value of R depends on the units of P and V

R = 0.0821 atm/K · mol convert P to atm and V to L

• Application of Ideal Gas law: when T, P, V of a gas all changes

( ) ( )( ) ( ) nRTPVor R

TnVP

==••

Example:

The Ideal Gas LawRequiring Unit Conversion

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Example:• Calculate the number of moles of gas in a basketball

inflated to a total pressure of 24.2 psi with a volume of 3.2 L at 25°C

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InformationGiven: V = 3.2 L, P = 24.2 psi,

t = 25°CFind: n, mol

Example:Calculate the number of moles of gas in a basketball inflated to a total pressure of 24.2 psi with a volume of 3.2 L at 25°C

n 0.22 mol=

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Air: Mixtures of Gases• Air is a mixture (N2 , O2)• Each gas in the mixture behaves independently

of the other gasesthough all gases in the mixture have the same volume and temperature

all gases completely occupy the container, so all gases in the mixture have the volume of the container

Gas % in Air, by volume Gas % in Air,

by volumenitrogen, N2 78 argon, Ar 0.9oxygen, O2 21 carbon dioxide, CO2 0.03

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Dalton’s Law: Partial Pressure

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Zn metal reactswith HCl(aq) toproduce H2(g).

Because waterevaporates, somewater vapor getsmixed in withthe H2.

The gas flowsthrough the tubeand bubbles intothe jar, where itdisplaces the water in the jar.

Collecting gas over water

Pgas = PH2O + PH2

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Standard Conditions (STP)

• Common reference points for comparing

Standard Temperature & Pressure• Standard Pressure = 1.00 atm• Standard Temperature = 0°C = 273 K

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Molar Volume of a Gas at STPDefinition: The volume of 1 (exact) mole gas at STP • Use the Ideal Gas Law: PV = nRT

L4.22atm1.00

273K Kmole

atmL 0.0821 mole 1

PT R n V =

ו

•×

=××

=

• 1 mole of any gas at STP will occupy 22.4 L==> Molar volume• can be used as a conversion factor

as long as you work at STP1 mol ≡ 22.4 L

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Molar VolumeSo muchempty spacebetween moleculesin the gas state,

the volume of thegas is not effectedby the size of themolecules, (underideal conditions).

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Density of Gas at STP

• Since every exactly one mole of any gas has a volume of 22.4 L, whereas the mass of such gas would be as the molar mass in grams

• Density of Gas = Molar mass / Molar Volume

Example: • Density of Oxygen gas at STP

= 32.00 g/mol / 22.4 L/mol = 1.43 g/L

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Density of Common Gases

At STP, the density of common gases (in g/L) as:

• H2 0.0900 • He 0.179• CH4 0.716• N2 1.25 • Air 1.29• O2 1.43• CO2 1.96• Cl2 3.17

• Which one, hydrogen gas or helium gas, is better in blimps in providing lift?

• Why carbon dioxide is used in putting out fire? What if its density is less than the air?

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Real Gases• Ideal gas laws assume

1) No Attractions between gas molecules2) No Volume: gas molecules do not take up

spacebased on the Kinetic-Molecular Theory

• Real gases: often do not behave like Ideal gases at High pressure (“Squeezed”) or Low temperature (“Frozen”)

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Ideal vs. Real