Chapter 2Chapter 2

GasesGases

12.1 Characteristics of Gases12.1 Characteristics of Gases Properties of Gases

because gas particles are far apart,

gases are fluids (they can flow)gases have low densitygases are highly compressiblegases completely fill a container

Properties of Gasesbecause gas particles are far apart,

gases are fluids (they can flow)gases have low densitygases are highly compressiblegases completely fill a container

12.1 Characteristics of Gases12.1 Characteristics of Gases Gas Pressure

Rene Descarte (1596-1650): rejected idea of void or vacuum

Pierre Gassendi (1592-1655): revived atomism; promoted idea of atoms moving in a void

Evangelista Torricelli (1608-1647): built a mercury barometer in 1643; created a vacuum

Gas PressureRene Descarte (1596-1650): rejected idea of void or vacuum

Pierre Gassendi (1592-1655): revived atomism; promoted idea of atoms moving in a void

Evangelista Torricelli (1608-1647): built a mercury barometer in 1643; created a vacuum

Mercury BarometerMercury Barometer

12.1 Characteristics of Gases12.1 Characteristics of Gases Gas Pressure

Blaise Pascal (1623-1662): tested atmospheric pressure at prompting of Descarte; found that pressure drops with altitude; believed in the vacuum

Gas PressureBlaise Pascal (1623-1662): tested atmospheric pressure at prompting of Descarte; found that pressure drops with altitude; believed in the vacuum

12.1 Characteristics of Gases12.1 Characteristics of Gases Gas Pressure

pressure is force divided by areaforce: Newton (1 kgm/s2 = 1 N)area: meter squared (m2)pressure: Pascal (1 Pa = 1 N/1 m2)

for comparisons, standard temperature and pressure (STP): 0C and 1 atm

Gas Pressurepressure is force divided by area

force: Newton (1 kgm/s2 = 1 N)area: meter squared (m2)pressure: Pascal (1 Pa = 1 N/1 m2)

for comparisons, standard temperature and pressure (STP): 0C and 1 atm

Pressure UnitsPressure Units

12.1 Characteristics of Gases12.1 Characteristics of Gases Kinetic-Molecular Theory

gas particles are in constant, rapid, random motion

particles far apart relative to size

pressure due to collisions of particles with the walls of their container

Kinetic-Molecular Theorygas particles are in constant, rapid, random motion

particles far apart relative to size

pressure due to collisions of particles with the walls of their container

12.1 Characteristics of Gases12.1 Characteristics of Gases Kinetic-Molecular Theory

gas temperature is proportional to average kinetic energygas molecules have a range of speeds

increasing temperature shifts the distribution

Kinetic-Molecular Theorygas temperature is proportional to average kinetic energygas molecules have a range of speeds

increasing temperature shifts the distribution

Gas Molecules Energy DistributionGas Molecules Energy Distribution

12.2 The Gas Laws12.2 The Gas Laws Measurable Properties of Gases

P = pressure exerted by gasV = total volume occupied by gas

T = temperature in kelvins of gas

n = number of moles of gas

Measurable Properties of GasesP = pressure exerted by gasV = total volume occupied by gas

T = temperature in kelvins of gas

n = number of moles of gas

12.2 The Gas Laws12.2 The Gas Laws Robert Boyle (1627-1691):

published The Spring of Air in 1660, which explained his most famous experimentBoyle put mercury in a j-tube (manometer), and saw that when he doubled the pressure, the volume of air in short end halved

Robert Boyle (1627-1691): published The Spring of Air in 1660, which explained his most famous experimentBoyle put mercury in a j-tube (manometer), and saw that when he doubled the pressure, the volume of air in short end halved

Boyle’s ExperimentBoyle’s Experiment

Boyle’s LawBoyle’s Law

12.2 The Gas Laws12.2 The Gas Laws Robert Boyle

Boyle’s law: PV = kP1V1 = P2V2

Robert BoyleBoyle’s law:

PV = kP1V1 = P2V2

Boyle’s LawBoyle’s Law

12.2 The Gas Laws12.2 The Gas Laws Jacques Charles: discovered that

a gas’s volume is proportional to temperature at constant pressure in 1787Charles’s law:

V/T = kV1/T1 = V2/T2

Jacques Charles: discovered that a gas’s volume is proportional to temperature at constant pressure in 1787Charles’s law:

V/T = kV1/T1 = V2/T2

Charles’s LawCharles’s Law

12.2 The Gas Laws12.2 The Gas Laws Joseph Gay-Lussac (1778-1850):

discovered in 1802 that increasing temperature at constant volume resulted in a proportional increase in pressureGay-Lussac’s law:

P = kTP/T = kP1/T1 = P2/T2

Joseph Gay-Lussac (1778-1850): discovered in 1802 that increasing temperature at constant volume resulted in a proportional increase in pressureGay-Lussac’s law:

P = kTP/T = kP1/T1 = P2/T2

Gay-Lussac’s LawGay-Lussac’s Law

12.2 The Gas Laws12.2 The Gas LawsGay-Lussac’s law of combining volumes (1809): gases combine in simple proportions by volume, and volume of products is related to volume of reactantsexample 1: 2 volumes of H2 react with 1 volume of O2 to make 2 volumes of water

allowed Avogadro to deduce diatomic molecules (and more)

Gay-Lussac’s law of combining volumes (1809): gases combine in simple proportions by volume, and volume of products is related to volume of reactantsexample 1: 2 volumes of H2 react with 1 volume of O2 to make 2 volumes of water

allowed Avogadro to deduce diatomic molecules (and more)

Combining VolumesCombining Volumes

12.2 The Gas Laws12.2 The Gas Laws Amadeo Avogadro (1776-1856):

proposed in 1811 that equal volumes of all gases contain equal numbers of particlesAvogadro’s law:

V = kn1 mol of any gas at 0C and 1 atm occupies 22.41 L

Amadeo Avogadro (1776-1856): proposed in 1811 that equal volumes of all gases contain equal numbers of particlesAvogadro’s law:

V = kn1 mol of any gas at 0C and 1 atm occupies 22.41 L

Avogadro’s LawAvogadro’s Law

12.2 The Gas Laws12.2 The Gas Laws Stanislao Cannizzaro (1826-

1910): ~1858, deduced that Gay-Lussac’s law of combining volumes and Avogadro’s law could be used to calculate atomic and molecular weights relative to hydrogen; drew distinction between atoms and molecules; made a table of atomic weights

Stanislao Cannizzaro (1826-1910): ~1858, deduced that Gay-Lussac’s law of combining volumes and Avogadro’s law could be used to calculate atomic and molecular weights relative to hydrogen; drew distinction between atoms and molecules; made a table of atomic weights

Gas Laws SummaryGas Laws Summary

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Ideal Gas Law

no gas perfectly obeys Boyle’s law, Charles’s law, Gay-Lussac’s law, or Avogadro’s law

although not perfect, these laws work well for most gases and most conditions

ideal gas: model gas that perfectly obeys gas laws

Ideal Gas Lawno gas perfectly obeys Boyle’s law, Charles’s law, Gay-Lussac’s law, or Avogadro’s law

although not perfect, these laws work well for most gases and most conditions

ideal gas: model gas that perfectly obeys gas laws

Ideal Gases vs. Real GasesIdeal Gases vs. Real Gases

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Ideal Gas Law

ideal gasesdo not condense to liquids at low temperatures

do not have particles attracted to or repulsed by each other

have particles of no volumedo not exist

Ideal Gas Lawideal gases

do not condense to liquids at low temperatures

do not have particles attracted to or repulsed by each other

have particles of no volumedo not exist

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Ideal Gas Law: combines four

variables, P, V, T, and n, into one equationPV = nRTR is a proportionality constantR = 8.314 LkPa

molK

Ideal Gas Law: combines four variables, P, V, T, and n, into one equationPV = nRTR is a proportionality constantR = 8.314 LkPa

molK

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Gas Behavior and Chemical

FormulasDiffusion: movement of particles from high concentration to low concentrationparticles of lower mass diffuse more quickly than particles of higher mass

diffusion increases entropy

Gas Behavior and Chemical FormulasDiffusion: movement of particles from high concentration to low concentrationparticles of lower mass diffuse more quickly than particles of higher mass

diffusion increases entropy

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Gas Behavior and Chemical

FormulasEffusion: passage of gas particles through a small openingGraham’s law: rate of diffusion and effusion of a gas are inversely proportional to the square root of the gas’s density

Gas Behavior and Chemical FormulasEffusion: passage of gas particles through a small openingGraham’s law: rate of diffusion and effusion of a gas are inversely proportional to the square root of the gas’s density

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Gas Behavior and Chemical

FormulasGraham’s law, cont.

where vA and vB are molecular speeds of gases A and B and

MA and MB are the molar masses of gases A and B

Gas Behavior and Chemical Formulas

Graham’s law, cont.

where vA and vB are molecular speeds of gases A and B and

MA and MB are the molar masses of gases A and B

A A

B B

v M

v M

12.3 Molecular Comp. of Gases12.3 Molecular Comp. of Gases Gas Behavior and Chemical

FormulasGraham’s law, cont.

Graham’s law is easy to derive: solve the equation for the ratio of speeds between vA and vB

Gas Behavior and Chemical Formulas

Graham’s law, cont.Graham’s law is easy to derive: solve the equation for the ratio of speeds between vA and vB 2 21 1

2 2A A B BM M

12.3 The Gas Laws12.3 The Gas Laws John Dalton (1766-1844):

discovered that each gas in a mixture produces its own pressure as if it was aloneDalton’s law of partial pressure: total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gasesPtotal = PA + PB + PC

John Dalton (1766-1844): discovered that each gas in a mixture produces its own pressure as if it was aloneDalton’s law of partial pressure: total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gasesPtotal = PA + PB + PC