GasesGasesChapter 24 Chapter 24

p 371 – 393p 371 – 393

Need calculatorsNeed calculators

PropertiesProperties• Low density• Fill containers• Pressure in all directions• Diffuse quickly• Compressible

Kinetic TheoryKinetic Theory

Image from Casiday and FreyDepartment of Chemistry, Washington University

Kinetic TheoryKinetic Theory1. Constant random motion2. Higher temp → faster motion

(Higher Ek)3. Minimal forces between particles4. Size of particles negligible cf

distance between them5. Particles collide with each other &

with walls with perfectly elastic collisions

QuestionsQuestions• Why does a hot air balloon float in

the air?• Activity 23.1 p 372

Gas PressureGas Pressure• Caused by constant collisions• Force per unit area, P = F/a • Units

– SI: Pascal (1 newton per m2) – very small value! – Chemists prefer kPa.– Meteorologists prefer hpa (=millibar)

Gas PressureGas Pressure• More units

– PSI (pounds force per sq inch) USA– mmHg (mm of mercury in a barometer)– Atmosphere (atm)– 1 atm = 101.3 kPa = 760 mm Hg

Mercury BarometerMercury Barometer

Mercury barometer for Mercury barometer for measuring pressure in measuring pressure in

a vessela vessel

Units of TemperatureUnits of Temperature• SI – degrees Celsius

– Based on 0ºC = freezing pt of water– 100ºC = boiling temp of water at sea

level– Celsius sometimes called centigrade

• USA – degrees Fahrenheit– Water freezes at 32ºF and boils at 212ºF– Complex origins!

Units of VolumeUnits of Volume• SI – cubic metre (very big)• Chemists prefer L and mL• 1 m3 = 1000 L • 1 cm3 = 1 mL• 1 L = 1000 cm3

Behaviour of Behaviour of GasesGases

RelationshipsRelationships

Pressure and VolumePressure and Volume

• Experiment results p 375

Image from Wikipedia

Boyle’s LawBoyle’s Law• Boyle – first to publish a formula –

1662• Fixed mass of gas (sealed)• Fixed temperature• Pressure x volume is constant• PV = k• P1V1 = P2V2 = P3V3 etc• Qs p 376

Temperature and volumeTemperature and volume

Animation from Wikipedia

Charles’ LawCharles’ Law• Discovered around 1787• Volume increases with temperature

BUT …

Charles’ LawCharles’ Law

0 Temp ºC100 200

1

2

Volume (L)

273 Temp K373 4730

-273

Charles’ LawCharles’ Law• Fixed mass of gas (sealed)• Fixed pressure• Volume ÷ temperature is constant• NB: Must use temperature in Kelvin• V/ T = k• V1= V2

T1 T2

• Qs p 380

QuestionQuestion• PV = k

V/ T = kDoes that mean PV = V/ T?

• NO!• k means a constant for that

experiment but depends on the mass you choose etc.

Gay-Lussac’ LawGay-Lussac’ Law• Discovered around 1809• Pressure increases with temperature

BUT …• Same issue as Charles’ law

Gau-Lussac’s LawGau-Lussac’s Law

0 Temp ºC100 200

100

200

Pressure

273 Temp K373 4730

-273

Gay-Lussac’ LawGay-Lussac’ Law• Fixed mass of gas (sealed)• Fixed volume• Pressure ÷ temperature is constant• NB: Must use temperature in Kelvin

• P/ T = k

• P1= P2

T1 T2

Combined Gas LawCombined Gas Law• Previous laws - mass and one other

measure fixed• Fixed mass of gas (sealed)• Combine

• P1 V1 = P2 V2

T1 T2

• Qs p 381

STPSTP• Standard temperature and pressure• 0ºC which is 273 K)• 1 atm which is

– 101.3 kPa or – 760 mm Hg

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

• Mixture of non-reacting gases• Constant T & V• Pressure exerted by each gas:

“partial pressure”

• PT = P1 + P2 + P3 etc

• Gases act independently

Collecting GasCollecting Gas

• Convenient to collect over water

• Calculate volume of the gas & Volume of water vapour

• Use Dalton’s law• Qs p 382 & 384

Avagadro’s HypothesisAvagadro’s Hypothesis• Equal volumes of gases

(at same T & P) …• Same number of particles

(molecules)• 1 mole of gas at STP - 22.4L• n = V/22.4 (at STP, vol in L)• Avagadro’s number?

6 x 1023

SLCSLC• Standard laboratory conditions• 25ºC ie 298 K• 1 atm ie 101.3 kPa• Calculate molar volume at SLC

(to check answer see bottom of p 385)

• Sample questions + Q 9 & 10 p 385

VariablesVariables• Combined gas law

– Fixed amount of gas– Other 3 variables P, V & T can vary

• What about a variable amount of gas?

• Remember Avagadro’s hypothesisNever mind what kind of gas …

Combined Gas LawCombined Gas Law• P1 V1 = P2 V2

T1 T2

• PV = k (constant)

T

• Consider 1 mole of gas at STP

• 101.3 x 22.4 = k (constant)

273

• What is the constant?

General Gas EquationGeneral Gas Equation• For one mole of gas

• PV = 8.31

T

• For 2 moles of gas or more?

• PV = 8.31 x 2

T

• PV = 8.31 x n

T

General Gas EquationGeneral Gas Equation• PV = n x 8.31

T• Call 8.31 R – universal gas constant• Only if we use Kelvin, litres & kPa or

Kelvin, m3 and Pa• Can use other units but need different R • Rearrange:

PV= nRT• What is temperature changes?• What if pressure changes?

Use?Use?• PV= nRT• Any pure sample of gas

– known P, V & T – we can calculate n

• Any sample of gas collected over water– known P, V & T + pp of H2O

Use Dalton’s law of partial pressure)– we can calculate n

QuestionsQuestions• Examine sample problem p 386/7• Do Q 11 p 387• Review questions: do even numbers

from 2 to 32.

Stoichiometry & GasesStoichiometry & Gases• Last year:equation such as

• H2 + ½ O2 → H2Ocalculate mole ratio

• Used for mass & concentration to calculate n

• Now use PV = nRT to calculate n• Still use mass ratio as before

QuestionsQuestions• Sample problems p 387 & 388.• Q 12 p 388• Sample problems p 389 & 390

Real GasesReal Gases

• Consider sample of O2

• Cool it more, and more, and more …• What happens at particle level?

Charles’ LawCharles’ Law

1

2

Volume (L)

273 Temp K373 4730

Assumptions of Kinetic Assumptions of Kinetic TheoryTheory

1. Constant random motion2. Higher temp → faster motion

(Higher Ek)3. Minimal forces between particles4. Size of particles negligible cf

distance between them5. Particles collide with each other &

with walls with perfectly elastic collisions

Ideal and Real GasesIdeal and Real Gases• Real gases – laws work reasonably well for

limited range of conditions– Room temp and above– Low pressure (atm & less)

• Break down badly as we approach condensation conditions

• Ideal gas – one for which gas laws work for all conditions – no such gas.

• Ideal gas – often used for calculations

Review QuestionsReview Questions• All the rest!