ElementsElements that exist as gases at that exist as gases at 252500C and 1 atmosphereC and 1 atmosphere

homonuclear homonuclear diatomic diatomic gasesgases

monatomic monatomic noble gasesnoble gases

Physical Characteristics of GasesPhysical Characteristics of Gases

Take on volume and shape of containerTake on volume and shape of container

Most compressible state of matterMost compressible state of matter

FlowFlow

Form homogeneous mixtures with other Form homogeneous mixtures with other gasesgases

ExampleExample: air: air

NN22, O, O22, Ar, CO, Ar, CO22, trace gases (includes H, trace gases (includes H22))

Lower densities Lower densities vs.vs. liquids and solids liquids and solids

Exert Exert pressurepressure

SI Unit of PressureSI Unit of Pressure: pascal : pascal (Pa)(Pa)

Conversion FactorsConversion Factors::

Pressure = Pressure = ForceForceAreaArea

((ForceForce = mass x acceleration) = mass x acceleration)

PressurePressure: force exerted by : force exerted by gas molecules striking a gas molecules striking a given areagiven area

1 Pa = 1 N/m1 Pa = 1 N/m22

1 atm 1 atm = = 760 mmHg 760 mmHg = = 760 torr760 torr = = 101,325 Pa 101,325 Pa = = 101.325 kPa101.325 kPa

Measuring Standard Atmospheric Measuring Standard Atmospheric PressurePressure

BarometerBarometer: used : used to measure to measure atmospheric atmospheric pressurepressure Hg will rise 760 Hg will rise 760

mm up the tube mm up the tube at standard at standard atmospheric atmospheric pressurepressure

Standard Standard Pressure:Pressure:

1 atm1 atm

760 mmHg760 mmHg

Atmospheric Pressure and AltitudeAtmospheric Pressure and Altitude

Sea Sea LevelLevel

1 1 atmatm

4 4 milesmiles

0.5 0.5 atmatm

10 10 milesmiles

0.2 0.2 atmatm

This bottle was This bottle was closed at closed at ~2,000 m ~2,000 m

altitude then altitude then brought back to brought back to sea level; it was sea level; it was crushed by air crushed by air

pressurepressure

ManometersManometers: used to measure gas : used to measure gas pressurepressure

As pressure (As pressure (hh) increases) increases – – volume volume decreasesdecreases

Boyle studied the relationship Boyle studied the relationship between pressure and volume of a between pressure and volume of a gasgas

Boyle’s Law: Pressure-Volume Boyle’s Law: Pressure-Volume RelationshipRelationship

For a fixed amount of gas at constant For a fixed amount of gas at constant temperature, the temperature, the volume of gas is inversely volume of gas is inversely proportional to the pressureproportional to the pressure

If pressure goes up, volume goes down and If pressure goes up, volume goes down and vice-versavice-versa

PP11 xx V V11 = P = P22 xx V V22

Sample ProblemSample Problem

A sample of chlorine gas A sample of chlorine gas occupies a volume of 946 mL occupies a volume of 946 mL at a pressure of 726 mmHg. at a pressure of 726 mmHg. What is the pressure of the What is the pressure of the gas if the volume is reduced gas if the volume is reduced at constant temperature to at constant temperature to 154 mL?154 mL?

Charles studied the relationship Charles studied the relationship between temperature and volume between temperature and volume of a gasof a gas

As temperature increasesAs temperature increases – – volume volume increasesincreases

Charles’ Law: Temperature-Charles’ Law: Temperature-Volume RelationshipVolume Relationship

For a fixed amount of gas at constant For a fixed amount of gas at constant pressure, the pressure, the volume of gas is directly volume of gas is directly proportional to the Kelvin temperatureproportional to the Kelvin temperature

If temperature goes up, volume goes up and If temperature goes up, volume goes up and vice-versavice-versa

VV11 V V22

TT1 1 T T22

==

V V αα T T

TT (K) = (K) = TT ( (00C) + 273.15C) + 273.15

Charles’ Charles’ LawLaw

Temperature Temperature mustmust be bein Kelvinin Kelvin

Variation of gas volume with Variation of gas volume with temperaturetemperatureat constant pressure:at constant pressure:

VV11 V V22

TT1 1 T T22

==

Sample ProblemSample Problem

A sample of carbon monoxide A sample of carbon monoxide gas occupies 3.20 L at 125 gas occupies 3.20 L at 125 00C. C. At what temperature will the At what temperature will the gas occupy a volume of 1.54 gas occupy a volume of 1.54 L if the pressure remains L if the pressure remains constant?constant?

Gay-Lussac’s Law: Temperature-Gay-Lussac’s Law: Temperature-Pressure RelationshipPressure Relationship

For a fixed amount of gas at constant volume, For a fixed amount of gas at constant volume, the the pressure of gas is directly proportional to pressure of gas is directly proportional to the Kelvin temperaturethe Kelvin temperature

If temperature goes up, pressure goes up and If temperature goes up, pressure goes up and vice-versavice-versa

PP11 P P22

TT1 1 T T22

==

The other laws can be obtained from this law by The other laws can be obtained from this law by holding one quantity (pressure, volume, or temp) holding one quantity (pressure, volume, or temp) constantconstant

It also enables you to do calculations for It also enables you to do calculations for situations in which situations in which nonenone of the variables are of the variables are constant!!constant!!

Combined Gas LawCombined Gas Law

Sample ProblemSample Problem

The volume of a gas-filled The volume of a gas-filled balloon is 30.0L at 40.0 balloon is 30.0L at 40.0 °°C C and 153 kPa. What volume and 153 kPa. What volume will the balloon have at will the balloon have at standard temperature and standard temperature and pressure?pressure?

Avogadro studied the relationship Avogadro studied the relationship between number of molecules and between number of molecules and volume of a gasvolume of a gas

Avogadro’s Law: Quantity-Volume Avogadro’s Law: Quantity-Volume RelationshipRelationship

At constant temperature and pressure, the At constant temperature and pressure, the number of moles of gas is directly proportional to number of moles of gas is directly proportional to its volumeits volume

If number of moles goes up, volume goes up and If number of moles goes up, volume goes up and vice-versavice-versa

VV11 V V22

nn1 1 n n22

==

The Ideal Gas LawThe Ideal Gas Law

Ideal Gas LawIdeal Gas Law: used to describe the : used to describe the behavior of an “ideal gas”behavior of an “ideal gas”

R: ideal gas constant with varying values R: ideal gas constant with varying values

(depending on required units)(depending on required units)

Advantage of ideal gas law over Advantage of ideal gas law over combined gas law is it permits you to combined gas law is it permits you to solve for the solve for the of a contained gasof a contained gas

Molar VolumeMolar Volume

Molar volume: volume occupied by 1 mol of a gas ( Molar volume: volume occupied by 1 mol of a gas ( ) )

SI units: SI units:

To solve for, rearrange ideal gas law:To solve for, rearrange ideal gas law:

PV = nRTPV = nRT

V/n = V/n =

QUESTION:QUESTION:

Find molar volume of a gas at STP (1 atm, and 273.15 K)Find molar volume of a gas at STP (1 atm, and 273.15 K)

ANSWER:ANSWER:

MolMolar volume of any gas at STP is !ar volume of any gas at STP is !

Gas Densities and Molar MassGas Densities and Molar Mass

Density = m/VDensity = m/V

Units: g/LUnits: g/L

Rearranging the ideal-gas equation with Rearranging the ideal-gas equation with MM as molar mass as molar mass (g/mol) we get:(g/mol) we get:

PVPV = = nRT nRT oror n/V n/V = =

Multiply both sides by Multiply both sides by MM

nnMM / /VV = =

nnMM / /VV = (mol)(g/mol) / (L) = g/L = (density!) = (mol)(g/mol) / (L) = g/L = (density!)

nnMM / /VV = =

relates density to the properties of gasesrelates density to the properties of gases

Sample ProblemSample Problem

A large natural gas storage A large natural gas storage tank is kept at 2.20 atm. On a tank is kept at 2.20 atm. On a cold day, when the cold day, when the temperature in -15temperature in -15°C, the °C, the volume of gas in the tank is volume of gas in the tank is 28,500 ft28,500 ft33. What is the . What is the volume of the same quantity volume of the same quantity of gas when the temperature of gas when the temperature is 31°C?is 31°C?

Sample ProblemsSample Problems

Cyclopropane is used as a general Cyclopropane is used as a general anesthetic. It has a molar mass of anesthetic. It has a molar mass of 42.0 g/mol. What is the density of 42.0 g/mol. What is the density of cyclopropane gas at 25cyclopropane gas at 25°C and 1.02 °C and 1.02 atm?atm?

Calculate the average molar mass Calculate the average molar mass of dry air if it has a density of 1.17 of dry air if it has a density of 1.17 g/L at 21°C and 740.0 torr.g/L at 21°C and 740.0 torr.

Sample ProblemSample Problem

A 5.00 L container is filled with nitrogen A 5.00 L container is filled with nitrogen gas to a pressure of 3.00 atm at 523 K. gas to a pressure of 3.00 atm at 523 K. What is the volume of a container that What is the volume of a container that is used to store the same gas at STP?is used to store the same gas at STP?

Tennis balls are filled with air of nitrogen Tennis balls are filled with air of nitrogen gas to a pressure above atmospheric gas to a pressure above atmospheric pressure to increase their bounce. If a pressure to increase their bounce. If a tennis ball has a volume of 144 cmtennis ball has a volume of 144 cm33 and and contains 0.33 g of nitrogen, what is the contains 0.33 g of nitrogen, what is the pressure inside the ball at 24pressure inside the ball at 24°C?°C?

Sample ProblemsSample Problems

What volume of nitrogen gas at 720 What volume of nitrogen gas at 720 torr and at 23torr and at 23°C is required to react °C is required to react with 7.35 L of hydrogen gas at the with 7.35 L of hydrogen gas at the same temperature and pressure to same temperature and pressure to yield ammonia gas?yield ammonia gas?

4NH4NH33(g)(g) + 5O + 5O22(g)(g) 4NO 4NO(g)(g) + 6H + 6H22OO(g)(g)

How many liters of NHHow many liters of NH33(g)(g) at 850°C and at 850°C and 5.00 atm are required to react with 5.00 atm are required to react with 1.00 mol of O1.00 mol of O22(g)(g) in this reaction? in this reaction?

Dalton’s Law of Partial PressureDalton’s Law of Partial Pressure

At constant volume and temperature, At constant volume and temperature, the the total pressure exerted by a total pressure exerted by a of the component of the component gasesgases

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

Sample ProblemSample Problem

What is the total pressure What is the total pressure exerted by a mixture of 2.00g exerted by a mixture of 2.00g of Hof H22 and 8.00 g of N and 8.00 g of N22 at 273 at 273 K in a 10.0 L vessel?K in a 10.0 L vessel?

Kinetic Molecular TheoryKinetic Molecular Theory

KMT gives us an understanding of gas KMT gives us an understanding of gas pressure at the molecular level:pressure at the molecular level:

Pressure results from the Pressure results from the on the walls of container on the walls of container

As temperature increases, average As temperature increases, average … …

……creating more chances for collisions with creating more chances for collisions with walls of container, sowalls of container, so

Assumptions of Kinetic Molecular Assumptions of Kinetic Molecular TheoryTheory

1.1. Gases consist of a large number of Gases consist of a large number of molecules in molecules in (n is high) (n is high)

2.2. Volume of individual molecules is Volume of individual molecules is compared to volume of compared to volume of (V is high) (V is high)

3.3. forces (forces forces (forces between gas molecules) are between gas molecules) are

4.4. Energy can be transferred between Energy can be transferred between molecules, but average KE is molecules, but average KE is ( (at constant temperatureat constant temperature))

5.5. Average KE of molecules is proportional to Average KE of molecules is proportional to

6.6. At any given temperature, the molecules of At any given temperature, the molecules of any gas have the any gas have the

Root-Mean-Squared SpeedRoot-Mean-Squared Speed

Root-mean-square speedRoot-mean-square speed (rms): the sq root (rms): the sq root of the avg of the squared speeds of gas of the avg of the squared speeds of gas molecules in a samplemolecules in a sample

Symbol: Symbol:

SI unit: SI unit:

The higher the temp, the The higher the temp, the

The lower the molar mass, The lower the molar mass, MM, the , the

The higher the temp, the higher The higher the temp, the higher the rms…the rms…

The lower the molar mass the The lower the molar mass the higher the rms…higher the rms…

Graham’s Law of EffusionGraham’s Law of Effusion

EffusionEffusion: the escape of a : the escape of a gas through gas through

A balloon will deflate over A balloon will deflate over time due to time due to

Graham’s Law of EffusionGraham’s Law of Effusion: : the rate of effusion of a the rate of effusion of a gas (gas (rr) is inversely ) is inversely proportional to the square proportional to the square root of the gas’s molar root of the gas’s molar massmass

Diffusion and Mean Free PathDiffusion and Mean Free Path

DiffusionDiffusion: is the: is the

Diffusion is faster for light gas molecules Diffusion is faster for light gas molecules becausebecause

Behavior of Real GasesBehavior of Real Gases

Real gases deviate from ideal gases!Real gases deviate from ideal gases!

Especially at:Especially at:

LowLow

HighHigh

Small containerSmall container

Because…Because…

Gas molecules have “real” volume and take up spaceGas molecules have “real” volume and take up space

Gas molecules interact with one anotherGas molecules interact with one another

We need to correct Ideal Gas Law for volume and We need to correct Ideal Gas Law for volume and intermolecular attractions…intermolecular attractions…

The van der Waals Equation for The van der Waals Equation for Real GasesReal Gases

aa and and bb are empirically-determined constants for each gas are empirically-determined constants for each gas

2

2

V

annbV

nRTP

nRTnbVV

anP

2

2

Corrects forCorrects forCorrects forCorrects for Corrects forCorrects forCorrects forCorrects for

Sample ProblemsSample Problems

What is the pressure exerted by one mole of What is the pressure exerted by one mole of argon at a volume of 2.00 L and at 300 K argon at a volume of 2.00 L and at 300 K when it acts as an ideal gas and as a non-when it acts as an ideal gas and as a non-ideal gas? ideal gas?

a a = 1.34 L= 1.34 L22-atm/mol-atm/mol22 bb = 0.0322 L/mol = 0.0322 L/mol

Consider a sample of 1.00 mole of COConsider a sample of 1.00 mole of CO22 confined to a volume of 3.00 L at 0.0 confined to a volume of 3.00 L at 0.0 °C. °C. Calculate the pressure of gas when it acts as Calculate the pressure of gas when it acts as an ideal gas and a non-ideal gas?an ideal gas and a non-ideal gas?

a a = 3.59 L= 3.59 L22-atm/mol-atm/mol22 bb = 0.0427 L/mol = 0.0427 L/mol