BEHAVIOR OF GASESBEHAVIOR OF GASES

Unit 8Unit 8

ChemistryChemistry

LangleyLangley

**Corresponds to Chapter 14 in the Prentice Hall Chemistry Book

PROPERTIES OF GASESPROPERTIES OF GASES

No definite shape/volumeNo definite shape/volume Expands to fill its containerExpands to fill its container

Easily compressed (squeezed into a Easily compressed (squeezed into a smaller container)smaller container) Compressibility is a measure of how much Compressibility is a measure of how much

the volume of matter decreases under the volume of matter decreases under pressurepressure

Gases are easily compressed because of Gases are easily compressed because of the space between the particles in a gasthe space between the particles in a gas

PROPERTIES OF A GASPROPERTIES OF A GAS

Factors Affecting Gas PressureFactors Affecting Gas Pressure Amount of GasAmount of Gas

Increase amount, increase pressureIncrease amount, increase pressure VolumeVolume

Reduce volume, increase pressureReduce volume, increase pressure TemperatureTemperature

Increase temperature, increase pressureIncrease temperature, increase pressure

Relationship between pressure, Relationship between pressure, temperature, and volume is explained temperature, and volume is explained through the Gas Lawsthrough the Gas Laws

GAS LAWSGAS LAWS

Boyle’s LawBoyle’s Law Charles’ LawCharles’ Law Gay-Lussac’s LawGay-Lussac’s Law Combined Gas LawCombined Gas Law Ideal Gas LawIdeal Gas Law Dalton’s Law of Partial PressureDalton’s Law of Partial Pressure Graham’s LawGraham’s Law

BOYLE’S LAWBOYLE’S LAW

If the temperature is constant, as the If the temperature is constant, as the pressure of a gas increases, the volume pressure of a gas increases, the volume decreasesdecreases

For a given mass of gas at constant For a given mass of gas at constant temperature, the volume of a gas varies temperature, the volume of a gas varies inversely with pressureinversely with pressure As volume goes up, pressure goes downAs volume goes up, pressure goes down As volume goes down, pressure goes upAs volume goes down, pressure goes up

PP11VV11 = P = P22VV22

BOYLE’S LAWBOYLE’S LAW

Real Life ExampleReal Life Example As you push on the end of a syringe, the As you push on the end of a syringe, the

volume inside the syringe decreases as the volume inside the syringe decreases as the pressure on the syringe increasespressure on the syringe increases

Mathematical Example 1:Mathematical Example 1: PP11 = 758 torr = 758 torr VV11 = 5.0L = 5.0L P P22

= ?= ? VV22 = 3.5L = 3.5L

BOYLE’S LAWBOYLE’S LAW

Mathematical Example 2Mathematical Example 2 If 4.41 dmIf 4.41 dm33 of nitrogen gas are collected at a of nitrogen gas are collected at a

pressure of 94.2 kPa, what will the volume pressure of 94.2 kPa, what will the volume be for this gas at standard pressure if the be for this gas at standard pressure if the temperature does not change?temperature does not change?

CHARLES’ LAWCHARLES’ LAW

As the temperature of an enclosed gas As the temperature of an enclosed gas increases, the volume increases, if the increases, the volume increases, if the pressure is constantpressure is constant

The volume of a fixed mass of gas is directly The volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the proportional to its Kelvin temperature if the pressure is kept constantpressure is kept constant As volume goes up/down, temperature goes As volume goes up/down, temperature goes

up/downup/down VV11 = V = V22

Temperature must be in Temperature must be in Kelvin! TKelvin! T11 T T22

CHARLES’ LAWCHARLES’ LAW

Real Life ExampleReal Life Example Balloon Lab-As the temperature of the water Balloon Lab-As the temperature of the water

is increased, the volume of the balloon is is increased, the volume of the balloon is increased.increased.

Coke Can-Fill a coke can with a small Coke Can-Fill a coke can with a small amount of water, as you heat the water amount of water, as you heat the water inside to near boiling, immediately invert the inside to near boiling, immediately invert the coke can into ice-cold water so the coke can coke can into ice-cold water so the coke can is experiencing a dramatic drop in is experiencing a dramatic drop in temperature, volume of can will decrease temperature, volume of can will decrease (can will crush in on itself)(can will crush in on itself)

CHARLES’ LAWCHARLES’ LAW

Mathematical Example 1Mathematical Example 1 VV11 = 250mL T = 250mL T11 = 300K = 300K V V22

= 321mL T= 321mL T22 = ? = ?

Mathematical Example 2Mathematical Example 2 With a constant pressure, the volume of a With a constant pressure, the volume of a

gas is increased from 15.0L to 32.0L. If the gas is increased from 15.0L to 32.0L. If the new temperature is 20.0°C, what was the new temperature is 20.0°C, what was the original temperature?original temperature?

GAY-LUSSAC’S LAWGAY-LUSSAC’S LAW

As the temperature of an enclosed gas As the temperature of an enclosed gas increases, the pressure increases, if the increases, the pressure increases, if the volume is constantvolume is constant

The pressure of a gas is directly proportional to The pressure of a gas is directly proportional to the Kelvin temperature if the volume remains the Kelvin temperature if the volume remains constantconstant

PP11 = P = P22

Temperature must be in Temperature must be in Kelvin! TKelvin! T11 T T22

GAY-LUSSAC’S LAWGAY-LUSSAC’S LAW

Real Life ExampleReal Life Example TiresTires

The faster a car goes, the higher the temperature The faster a car goes, the higher the temperature of the tire gets and the higher the pressure inside of the tire gets and the higher the pressure inside the tiresthe tires

Mathematical Example 1Mathematical Example 1 PP11 = ? = ? TT11 = 456K = 456K

P P22 = 789mmHg = 789mmHg TT22 = 326K = 326K

GAY-LUSSAC’S LAWGAY-LUSSAC’S LAW

Mathematical Example 2Mathematical Example 2 The pressure in a tire is 1.8 atm at 20°C. The pressure in a tire is 1.8 atm at 20°C.

After a 200 mile trip, the pressure reading for After a 200 mile trip, the pressure reading for the tire is 1.9 atm. What is the temperature the tire is 1.9 atm. What is the temperature inside the tire at that new pressure?inside the tire at that new pressure?

COMBINED GAS LAWCOMBINED GAS LAW

Combines Boyle’s, Charles’, and Gay-Lussac’s Combines Boyle’s, Charles’, and Gay-Lussac’s lawslaws

Describes the relationship among temperature, Describes the relationship among temperature, pressure, and volume of an enclosed gaspressure, and volume of an enclosed gas

Allows you to perform calculation for situations Allows you to perform calculation for situations IF and ONLY IF the amount of gas is constantIF and ONLY IF the amount of gas is constant

PP11VV11 = P = P22VV22 Temperature must be in Temperature must be in

Kelvin! Kelvin!

TT11 T T22

IDEAL GAS LAWIDEAL GAS LAW

When you need to account for the number of When you need to account for the number of moles of gas in addition to pressure, moles of gas in addition to pressure, temperature, and volume, you will use the Ideal temperature, and volume, you will use the Ideal Gas EquationGas Equation

Modified version of the Combined Gas LawModified version of the Combined Gas Law PV = nRTPV = nRT

n = number of molesn = number of moles R = ideal gas constantR = ideal gas constant

0.08206 (L-atm/mol-K)0.08206 (L-atm/mol-K) 62.4 (L-mmHg/mol-K)62.4 (L-mmHg/mol-K) 8.314 (L-kPa/mol-K)8.314 (L-kPa/mol-K)

IDEAL GAS LAWIDEAL GAS LAW

Mathematical Example 1Mathematical Example 1 What is the pressure in atm exerted by 0.5 What is the pressure in atm exerted by 0.5

moles of Nmoles of N22 in a 10L container at 298 in a 10L container at 298

Kelvin?Kelvin?

Mathematical Example 2 Mathematical Example 2 What is the volume in liters of 0.250 moles What is the volume in liters of 0.250 moles

of Oof O22 at 20°C and 0.974 atm? at 20°C and 0.974 atm?

IDEAL GAS LAWIDEAL GAS LAW

Mathematical Example 3Mathematical Example 3 What is the temperature of 76 grams of ClWhat is the temperature of 76 grams of Cl22

in a 24L container at 890mmHg?in a 24L container at 890mmHg?

Mathematical Example 4Mathematical Example 4 A deep underground cavern contains A deep underground cavern contains

2.24x102.24x1066L of CHL of CH44 at a pressure of at a pressure of 1.50x101.50x1033kPa and a temperature of 315K. kPa and a temperature of 315K. How many kilograms of CHHow many kilograms of CH44 does the cavern does the cavern contain?contain?

IDEAL vs. REAL GASESIDEAL vs. REAL GASES

Ideal gases follow the gas laws at all Ideal gases follow the gas laws at all conditions of pressure and temperatureconditions of pressure and temperature Conforms exactly to the all the assumptions Conforms exactly to the all the assumptions

of the kinetic theory (no volume, no particle of the kinetic theory (no volume, no particle attraction)attraction)doesn’t existdoesn’t exist

Real gases differ mostly from an ideal Real gases differ mostly from an ideal gas at low temperature and high gas at low temperature and high pressurepressure Under other conditions, behave as an ideal Under other conditions, behave as an ideal

gas wouldgas would

DALTON’S LAWDALTON’S LAW

In a mixture of gases, the total pressure is the In a mixture of gases, the total pressure is the sum of the partial pressure of the gasessum of the partial pressure of the gases Partial pressure is the contribution each gas in a Partial pressure is the contribution each gas in a

mixture makes to the total pressuremixture makes to the total pressure

At constant volume and temperature, the total At constant volume and temperature, the total pressure exerted by a mixture of gases is pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the equal to the sum of the partial pressures of the component of gasescomponent of gases

PPtotaltotal = P = P11 + P + P22 + P + P33 + … + …

DALTON’S LAWDALTON’S LAW

Mathematical Example 1Mathematical Example 1 In a container there are 4 gases with the In a container there are 4 gases with the

following pressures: Gas 1-2.5 atm, Gas 2-following pressures: Gas 1-2.5 atm, Gas 2-1.9 atm, Gas 3-798 mmHg, Gas 4-2.1 atm; 1.9 atm, Gas 3-798 mmHg, Gas 4-2.1 atm; find the total pressure in the container.find the total pressure in the container.

DALTON’S LAWDALTON’S LAW

Mathematical Example 2Mathematical Example 2 In a sample of HCl gas, the pressure of the In a sample of HCl gas, the pressure of the

gas is found to be 0.87 atm. If hydrogen gas is found to be 0.87 atm. If hydrogen makes up 34% of the gas, what is the makes up 34% of the gas, what is the pressure of the hydrogen?pressure of the hydrogen?

GRAHAM’S LAWGRAHAM’S LAW

The ratio of the speeds of two gases at the The ratio of the speeds of two gases at the same temperature is equal to the square root same temperature is equal to the square root of the inverted molar massesof the inverted molar masses The relative rate of diffusionThe relative rate of diffusion Diffusion is the tendency of molecules to move Diffusion is the tendency of molecules to move

toward areas of lower concentration to areas of toward areas of lower concentration to areas of higher concentration until the concentration is higher concentration until the concentration is uniform throughoutuniform throughout

Gases of lower molar mass diffuse and effuse faster Gases of lower molar mass diffuse and effuse faster than gases of higher molar massthan gases of higher molar mass Effusion is when gas particles escape through tiny holes in Effusion is when gas particles escape through tiny holes in

a containera container

GRAHAM’S LAWGRAHAM’S LAW

√√(Molar Mass(Molar MassBB/Molar Mass/Molar MassAA))

The rates of effusion of two gases are The rates of effusion of two gases are inversely proportional to the square roots inversely proportional to the square roots of their molar masses of their molar masses Use periodic table to get molar massesUse periodic table to get molar masses

GRAHAM’S LAWGRAHAM’S LAW

Mathematical Example 1Mathematical Example 1 What is the ratio of the speeds of Helium What is the ratio of the speeds of Helium

compared to Oxygen?compared to Oxygen?

Mathematical Example 2Mathematical Example 2 If CoIf Co22 has a speed of 22 m/s at 20°C, what is has a speed of 22 m/s at 20°C, what is

the speed of HCl at the same temperature?the speed of HCl at the same temperature?