Gases: Properties and Gases: Properties and BehaviourBehaviour

Gas LawsGas LawsPartial PressuresPartial PressuresKinetic Theory and Ideal GasesKinetic Theory and Ideal GasesReal GasesReal GasesDiffusion and EffusionDiffusion and Effusion

Features of gasesFeatures of gases

Gases are always miscibleGases are always miscible Gases are compressibleGases are compressible Gases exert pressureGases exert pressure Gases are mostly nothing: less than 0.1 % of the Gases are mostly nothing: less than 0.1 % of the

volume is occupied by molecules (contrast 70 % volume is occupied by molecules (contrast 70 % for solids and liquids)for solids and liquids) The ideal gas law assumes molecules occupy The ideal gas law assumes molecules occupy

zero percentzero percent

Molecular interactionsMolecular interactions

The strength of the The strength of the interactions between interactions between molecules determines molecules determines the statethe state Strong attractions make Strong attractions make

for high melting point for high melting point ionic solidsionic solids

Weaker interactions Weaker interactions between molecules between molecules occur in liquidsoccur in liquids

Molecular interactions in gases are Molecular interactions in gases are negligiblenegligible

Gases are mostly empty space: Gases are mostly empty space: molecules occupy <0.1 % molecules occupy <0.1 % volumevolume

1,000 times less dense than 1,000 times less dense than solids and liquidssolids and liquids

Emptiness allows complete Emptiness allows complete mixingmixing

The Ideal gasThe Ideal gas

The ideal gas is defined as followsThe ideal gas is defined as follows Interactions between molecules are nonexistentInteractions between molecules are nonexistent Volume occupied by molecules is zeroVolume occupied by molecules is zero

CollisionsCollisions

There are two types of There are two types of collisioncollision Between the Between the

molecules and the molecules and the containercontainer

Between moleculesBetween molecules In the ideal gas these In the ideal gas these

collisions are perfectly collisions are perfectly elastic (no energy loss)elastic (no energy loss)

Collisions between billiard balls mirrors the collisions between the molecules of an ideal gas

Origins of pressureOrigins of pressure

Pressure is force per unit area F/APressure is force per unit area F/A Force is mass x acceleration F = maForce is mass x acceleration F = ma Molecules colliding with the walls of the container Molecules colliding with the walls of the container

exchange momentumexchange momentum

Origins of pressureOrigins of pressure

Pressure if force per unit area F/APressure if force per unit area F/A Force is mass x acceleration F = maForce is mass x acceleration F = ma Molecules colliding with the walls of the container Molecules colliding with the walls of the container

exchange momentumexchange momentum

Units of pressureUnits of pressure

The S.I. unit of pressure is the pascal (Pa)The S.I. unit of pressure is the pascal (Pa) 1 Pa = 1 N/m1 Pa = 1 N/m22, where N is the S.I. unit of force, where N is the S.I. unit of force

1 N = 1 kgm/s1 N = 1 kgm/s22

The weight of the air exerts pressure – The weight of the air exerts pressure – atmospheric pressureatmospheric pressure

This pressure is about 100,000 PaThis pressure is about 100,000 Pa

Older is betterOlder is better

101 kPa is an inconvenient way of measuring 101 kPa is an inconvenient way of measuring pressurepressure

Traditional units are still used in preference to the Traditional units are still used in preference to the SI systemSI system

Atmospheres, cm (or mm) of Hg and torr are the Atmospheres, cm (or mm) of Hg and torr are the most commonmost common

How do I measure the atmosphere? How do I measure the atmosphere? Let me count the waysLet me count the ways

1 atmosphere =1 atmosphere = 760 mm Hg = 76 cm Hg760 mm Hg = 76 cm Hg

14.7 psi14.7 psi

760 torr760 torr

1.01 bar1.01 bar

29.9 in Hg29.9 in Hg

Standard temperature and pressure Standard temperature and pressure (STP)(STP)

Standard conditions allow direct comparison of Standard conditions allow direct comparison of properties of different substancesproperties of different substances Standard temperature is 273 K (0Standard temperature is 273 K (0ºC)ºC) Standard pressure is 760 mm HgStandard pressure is 760 mm Hg

At STP, 1 mole of any ideal gas occupies 22.414 LAt STP, 1 mole of any ideal gas occupies 22.414 L

The barometer of pressureThe barometer of pressure

The weight of the air supports an equal weight of The weight of the air supports an equal weight of mercury (or other liquid)mercury (or other liquid)

Mercury being dense, the column is only 76 cm Mercury being dense, the column is only 76 cm compared to the height of the atmospherecompared to the height of the atmosphere

76 cm (760 mm) Hg = 1 atm76 cm (760 mm) Hg = 1 atm

Manometers measure pressure in a Manometers measure pressure in a containercontainer

(a) If the pressure inside the bulb is less than (a) If the pressure inside the bulb is less than atmospheric, the atmosphere pushes down more.atmospheric, the atmosphere pushes down more.

(b) If the pressure inside the bulb is above (b) If the pressure inside the bulb is above atmospheric, the column is pushed towards the atmospheric, the column is pushed towards the open end.open end.

Measuring pressure with a rulerMeasuring pressure with a ruler

The pressure in the container is given by The pressure in the container is given by atmospheric pressure plus (minus) the difference atmospheric pressure plus (minus) the difference in levels for pressures greater (lower) than in levels for pressures greater (lower) than atmosphericatmospheric

Gas LawsGas Laws

Physical properties of gases were among the first Physical properties of gases were among the first experiments performed in the “modern” scientific era, experiments performed in the “modern” scientific era, beginning in the 17th centurybeginning in the 17th century

All gases exhibit similar physical properties even if their All gases exhibit similar physical properties even if their chemical properties differ widelychemical properties differ widely

Properties can be summarized in a few simple lawsProperties can be summarized in a few simple laws Variables are pressure, volume, temperature and quantity. Variables are pressure, volume, temperature and quantity.

Keep one (or two) constant and vary the othersKeep one (or two) constant and vary the others

The four variablesThe four variables

Pressure (P)Pressure (P) Volume (V)Volume (V) Temperature (T in Kelvin)Temperature (T in Kelvin) Number of molecules (n in moles)Number of molecules (n in moles)

Variables and constantsVariables and constants

In the elementary gas laws two of the four In the elementary gas laws two of the four variables are kept constantvariables are kept constant

Each law describes how one variable reacts to Each law describes how one variable reacts to changes in another variablechanges in another variable

All the simple laws can be integrated into one All the simple laws can be integrated into one combined gas lawcombined gas law

The first experimental gas The first experimental gas lawlaw

Pressure increases, volume Pressure increases, volume decreases (T, n constant)decreases (T, n constant)

Boyle’s lawBoyle’s law

1PV

Mathematical formMathematical form

The volume of a fixed amount of an ideal gas The volume of a fixed amount of an ideal gas varies inversely with pressure at constant varies inversely with pressure at constant temperaturetemperature

PV = constantPV = constant P P αα 1/V 1/V

Charles’ LawCharles’ Law

Pressure and amount constantPressure and amount constant As temperature increases, the volume increasesAs temperature increases, the volume increases

Mathematical formMathematical form

The volume of a fixed amount of an ideal gas varies The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressuredirectly with absolute temperature at constant pressure

V V αα T T V/T = constantV/T = constant

NOTE: Temperature must be in Kelvin (ºC + 273)NOTE: Temperature must be in Kelvin (ºC + 273) At absolute zero there is no motion and the residual At absolute zero there is no motion and the residual

volume is that of the atoms – which is assumed to be zerovolume is that of the atoms – which is assumed to be zero

Avogadro’s LawAvogadro’s Law

Pressure and temperature constantPressure and temperature constant Increase the amount, the volume increasesIncrease the amount, the volume increases Summary of gas lawsSummary of gas laws

Mathematical formMathematical form

The volume of a fixed amount of an ideal gas varies The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressuredirectly with absolute temperature at constant pressure

V V αα T T V/T = constantV/T = constant NOTE: Temperature must be in Kelvin (ºC + 273)NOTE: Temperature must be in Kelvin (ºC + 273) At absolute zero there is no motion and the residual At absolute zero there is no motion and the residual

volume is that of the atoms – which is assumed to be zerovolume is that of the atoms – which is assumed to be zero

Mathematical formMathematical form

The volume of an ideal gas varies directly with its molar The volume of an ideal gas varies directly with its molar amount at constant T and Pamount at constant T and P

V V αα n n V/n = constantV/n = constant The same volume of any gas contains the same number of The same volume of any gas contains the same number of

moles at constant T,Pmoles at constant T,P The standard molar volume at 273 K and 1 atm is 22.414 LThe standard molar volume at 273 K and 1 atm is 22.414 L

Comparison with realityComparison with reality

The standard molar volume of 22.41 L can be compared with The standard molar volume of 22.41 L can be compared with the experimental values of common real gasesthe experimental values of common real gases

Agreement shows that these ideal gas laws can be widely Agreement shows that these ideal gas laws can be widely applied for real gasesapplied for real gases

Putting them together: the ideal gas Putting them together: the ideal gas lawlaw

PP11VV11/T/T11 = P = P22VV22/T/T22

PV = nRTPV = nRT R is the gas constant = 0.0821 L-atm/mol-KR is the gas constant = 0.0821 L-atm/mol-K

Note the units of R. This constant also appears in Note the units of R. This constant also appears in thermodynamic calculations, but with different units and thermodynamic calculations, but with different units and numerical value (8.315 k/K-mol). Use the one numerical value (8.315 k/K-mol). Use the one appropriate to the calculationappropriate to the calculation

Units of pressure – atmUnits of pressure – atm Units of temperature – KUnits of temperature – K Units of volume – LUnits of volume – L

Standard temperature and pressure: T = 0 ºC and P = 1 Standard temperature and pressure: T = 0 ºC and P = 1 atmatm

The combined gas lawThe combined gas law

Allows us to calculate change in one variable for Allows us to calculate change in one variable for changes in the three other variableschanges in the three other variables

PVk

nT Combined

Gas Law

AvogadroAmonton

CharlesBoyle

ApplicationsApplications

A system under an initial set of conditions A system under an initial set of conditions represented by a changes to a new set of represented by a changes to a new set of conditions bconditions b

If we know three of the conditions, the fourth can If we know three of the conditions, the fourth can be obtainedbe obtained

a a b b

a a b b

PV PV

n T n T

The “simple” laws are derived from The “simple” laws are derived from the combined lawthe combined law

For any change of conditions where a variable For any change of conditions where a variable does not change its value, a = bdoes not change its value, a = b

Example: if T and n are unchanged, Example: if T and n are unchanged,

Boyle’s law is regenerated: Boyle’s law is regenerated:

a a b b

a a a a

PV PV

n T n T

PV k

Getting some exerciseGetting some exercise

An exercise ball is at a pressure of 1000 mm Hg An exercise ball is at a pressure of 1000 mm Hg and has a volume of 60 Land has a volume of 60 L

When sat on, the volume is only 40 L. What is the When sat on, the volume is only 40 L. What is the new pressure?new pressure?

Check: P increases as V decreasesCheck: P increases as V decreases

a a b bPV PV(1000 )(60 )

150040

b ba

a

PV mmHg LP mmHg

V L

Stoichiometry and gas reactionsStoichiometry and gas reactions

Solids: mass and molar massSolids: mass and molar mass Solutions: volume and molaritySolutions: volume and molarity Gases: volume and ideal gas lawGases: volume and ideal gas law

Calculate volume of gas produced (product) or Calculate volume of gas produced (product) or consumed (reactant) in a reaction at given consumed (reactant) in a reaction at given conditions of P and Tconditions of P and T

Also can calculate molar mass or density of a Also can calculate molar mass or density of a gas using ideal gas lawgas using ideal gas law

Mixtures of gases: partial pressuresMixtures of gases: partial pressures

Dalton’s law states that, in a mixture of gases, each Dalton’s law states that, in a mixture of gases, each gas behaves independently of the others and exerts gas behaves independently of the others and exerts the same pressure that it would by itselfthe same pressure that it would by itself

The total pressure exerted is the sum of the individual The total pressure exerted is the sum of the individual (partial) pressures of the components of the mixture(partial) pressures of the components of the mixture

P = PP = P11 + P + P22 + P + P33 +… +…

Mole fractionMole fraction

The pressure exerted by component i =The pressure exerted by component i = PPii = n = nii(RT/V)(RT/V)

Where ni is the number of moles of iWhere ni is the number of moles of i The total pressure is then:The total pressure is then: PP(total)(total) = (n = (n11 + n + n22 + n + n33 + …)RT/V + …)RT/V

The mole fraction is the ratio of the moles of The mole fraction is the ratio of the moles of component I to the total number of moles ntotalcomponent I to the total number of moles ntotal

total

iii n

n

nnn

nX

...321

Mole fraction and the ideal gas lawMole fraction and the ideal gas law

But n = PV/RTBut n = PV/RT

total

ii n

nX

total

i

total

i

i P

P

RTV

P

RTV

PX

Mole fractions and partial pressuresMole fractions and partial pressures

The partial pressure exerted by any gas is equal to the The partial pressure exerted by any gas is equal to the mole fraction x the total pressuremole fraction x the total pressure

What is the partial pressure of each component if the total What is the partial pressure of each component if the total pressure is 600 mm Hg?pressure is 600 mm Hg?

totalii PXP

Visual summary of the gas lawsVisual summary of the gas laws