11

CHAPTER 5

STATES OF

MATTER

3 HOURS5.1 GAS

5.2 LIQUID

5.3 SOLID

5.4 PHASE DIAGRAM

22

LECTURE 1

GASLearning Outcomes:(a) Explain qualitatively the basic assumptions of the kinetic

molecular theory of gases for an ideal gas.

(b) Define gas laws:

i.Boyle’s law

ii.Charles’s law

iii.Avogadro’s law

(c) Sketch and interpret the graphs of Boyle’s and Charles’s Laws.

33

In principle, the 3 states of matter are

interconvertible

44

● There are four parameters describing the

gaseous state:

Parameter Unit (SI)

● Quantity, n moles

● Volume, V litres

● Temperature, T kelvin

● Pressure, P pascal/ Nm-2

55

1 atm = 101325 Pa

= 101.325 kPa

= 101325 Nm-2

= 760 mmHg

= 760 torr

1 Pa = 1 Nm-2

1 mmHg = 1 torr

0°C = 273.15 K

Relationship between units:

Example:

Convert 749 mmHg to atm

Solution:

1 atm = 760 mmHg

0.986 atm = 749 mmHg

66

Kinetic Molecular Theory of Gases

4 basic assumption (postulate) :

1. The gas consists of tiny particles of negligible volume.

2. Intermolecular forces attraction do not existbetween gas particles.

3. The molecules of a gas are in continuous random motion. The gaseous particles are perfectly elastic.

4. The average kinetic energy of the gas molecules is directly proportional to the absolute temperature.

77

Ideal gas behaviour

1. The gas consists of tiny particles of negligible volume.

1. Intermolecular forces attraction do not exist between gas particles.

8KMP/ChemUnit/SK017-09/10 8

GAS

LAW

AVOGADRO’S

LAW

CHARLES’S

LAW

BOYLE’S LAW

99

BOYLE’S LAW

( The pressure –volume relationship)

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

● As the pressure (P) increases, the volume (V) decreases.

● V= 1/P at constant T and n

● P1V1 = k1 (a constant)

P1V1 = P2V2

1010

1111

Graph A : Pressure against Volume

Illustrate that : pressure is inversely proportional to

volume

12KMP/ChemUnit/SK017-09/10 12

Graph B : Pressure against 1/Volume

Illustrate that : P is directly proportional to 1/ V

13KMP/ChemUnit/SK017-09/10 13

Graph C: PV against Pressure, P

Illustrate that: PV = constant

1414

CHARLES’S LAW

( The Temperature – Volume relationship)

● The volume of a fixed amount of gas at constant pressure is

directly proportional to the absolute temperature

V ∝ T at constant P and n

V = constant

T

T in Kelvin (K) !!!

T(K) = T°C + 273.15

V1 = V2

T1 T2

1515

Variation of gas volume with temperature at constant temperature

T

P

1

P

2

1616

AVOGADRO’S LAW

( The Volume-amount relationship)

At constant pressure and temperature, the volume of a gas is

directly proportional to number of moles of the gas present.

V ∝ n ( P and T remain constant )

…………….. 4

1717

Avogadro’s “equal volumes-equal numbers” hypothesis can be stated in either of two ways:

1. At the same temperature and pressure, equal volume of different gases contain the same number of molecules (or atoms if the gas is monatomic).

1. Equal numbers of molecules of different gases compared at the same temperature and pressure occupy equal volumes.

At constant P and T, if VCO2 = VN2 = VAr ⇒ nCO2 = nN2 = nAr

At STP: T = 273.15K (0°C), P = 1.0 atm;

1 mol of gas = (6.023x1023 particles) = 22.4 dm3.

The volume of 22.4 dm3 gases at STP is called molar volume of a gas at STP

1818

IDEAL GAS

» V ∝ n.T

P

» V = R. n.T

P

Where R = gas constant

19KMP/ChemUnit/SK017-09/10 19

The Ideal EquationPV = nRT ……………...............

(6)

P = cRT

R= gas constant

= 0.08206 L atm K-1 mol-1

= 8.314 N m K-1 mol -1

2020

Gas constant

* SI unit

L mmHg mol -1 K-1

2121

Dalton’s Law states that the total

pressure of a mixture of gases is

the sum of the partial pressures

of all the components in the

mixture

Definition:

2222

Partial pressures is the pressures of individual gas components in the mixture.

Partial pressure of gas A in the mixture is given as:

PA = XA . Ptotal

XA = mole fraction of gas A in the mixture= nA/ntotal

The total mole fraction of all gasses in the mixture is equal to 1

XA + XB + XC = 1

2323

In a mixture of gases A, B and C, the total pressure PT is the result of collisions of 3 types of molecules, A, B and C, with the wall of container. Thus, according to the Dalton’s law,

PTotal = PA + PB + PC

= nART + nBRT + nCRTV V V

= RT ( nA + nB + nC )

V

= nTotalRT

V

A B C

Combining

the gases

PT = PA + PB + PC

nTotal = nA + nB + nC

Volume and temperature are constant

2424

The ratio number of moles of gas A to the total number of moles,

XA = nA = PA ( because PA = nART/V)

ntotal Ptotal PT nTRT/V

Mole fraction of gas A PA = XA PT

Where :

XA + XB + XC + ….. = 1

2525

Learning Outcomes:

(f) Explain the ideal and non-ideal behaviors of gases

in terms of intermolecular forces and molecular

volume.

(g) Explain the conditions at which real gases approach

the ideal behavior.

2626

Real Gases- Deviation From Ideality

● Boyle’s Law and Charles Law have led to the derivation of an ideal gas equation, PV=nRT.

● Ideal gas obey the equation and fits the assumption of the Kinetic Molecular Theory.

● However, real gases showed deviation from ideal behavior.

● There are two main reason:● Volume of molecules

● Intermolecular forces

27KMP/ChemUnit/SK017-09/10 27

Volume of molecules

•Ideal gas assume that gases consist of tiny molecules that does not occupy any space.

•However, for a real gas, the molecules have a certain volume.

•When a gas is compressed, the volume of the gas is decreased.

•Thus, the volume of molecules begins to occupy a sizable portion of the container.

28KMP/ChemUnit/SK017-09/10 28

Intermolecular forces

•Ideal gas assume that, there are no attractive force or repulsive force between gaseous particles.

•However,•When the volume of a container becomes smaller (by increasing the pressure)

•The distance between molecules decrease•The force of attraction between the molecules increase.

•These caused the behavior of real gases to deviate from ideal behavior.

29

PV

RT

1.0

Figure A (at constant temperature)

3030

● For 1 mole of ideal gas, the value of PV/RT is equal to 1.

● The lines plotted display the deviation of real gases from the ideal behavior.

● However, all the lines converge to 1.0 when P is near zero.

● Thus, real gas behave ideally at very low pressure.

31

● When gases are compressed, the molecules are closed enough to experience the attractive force among them.(curve below 1.0, PV<RT)

● NH3 (polar molecule) shows the largest deviation because it has strongest attractive force.

● At higher pressure, the molecules are pushed too close to each other that cause the repulsive forces among them.

● This repulsion makes them less compressible, hence the line above 1.0, PV>RT.

31

32Figure B ( at different temperatures)

3333

● Figure B shows the real gases display deviation from ideal behavior.

● However, when the temperatures increases, the line PV/RT against P for N2 approaches the dotted line for ideal gas.

● Thus, real gases behave almost ideally at high temperature.

3434

VAN DER WAALS’ EQUATION

3535

● The ideal gas law equation, PV=nRT shows the variables of gas (P, V and T) in a single equation.

● But, it does work in a real gases, especially at high temperature and low pressure.

● In a real gas:● The molecules have a finite volume.

● The molecules experience intermolecular forces

● It fails to obey the ideal gas equation and gas laws, but obeys Van der Waals equation better.

● So that, for the real gases the equation needs to be adjusted.

● The 2 parameters that need to be adjusted are P and V

3636

PRESSURE

● Attractive forces that act between molecules have an effect on the speed of the moving molecules.

● The molecules that experience this attractive will move slower.

● As a result they will give less impact to the wall of the container when collided.

● The pressure exerted by the real gases therefore is less compared to the ideal gas.

3737

● Since Preal < Pideal, the term P need to be

corrected by adding a coefficient,

to fit the ideal gas situation.

● ☞ Pideal = P real + n2a

V2

Where:

● n = number of moles

● a = positive constant

(intermolecular forces)

Depends on the strength of the attractive forces

acting between molecules.

The higher the value of a, the stronger forces among the molecules.

n2a

V2

3838

VOLUME

● Volume within which the molecules cannot move because of their own finite volume (the volume of the gas molecules).

● Therefore the effective volume available is not V (volume of a container) but a new value, V-the excluded volume.

V = Vcontainer – nb

Where,

n= moles of molecules

b= a constant representing the volume occupied by a molecule

3939

● Combining both factors, we get:

40

Difference between Ideal Gas Equation

and non-Ideal/Real Gas Equation

Ideal Gas Non-Ideal/Real Gas

PV = nRT (P + an2) ( V – nb) = nRT

V2

Volume of gas molecules is

negligible.

Volume of gas molecules is

significant. Gas volume for

real gas is corrected using

nb to take into account

volume of gas molecules.

Attractive forces between

gas molecules is negligible.

Attractive forces between

gas molecules is significant.

The n2a/V2 term is used to

correct real gas pressure to

include attractive forces. 40

4141

✰ Real gases tend to behave ideally at:

✰ low pressures

✰ high temperatures

At low pressure.

● The molecules in a gas are far apart

● the attractive forces are negligible

● the volume of the molecules is almost zero compared

to the average intermolecular distance (the gas will

behave ideally ).

At higher temperature

● The kinetic energy of the molecules is high.

● therefore, the intermolecular forces between them

can be ignored.

4242

Learning Outcomes:

(a) Explain the properties of liquid : shape, volume,

surface tension , viscosity, compressibility and

diffusion.

LECTURE 2

LIQUID

4343

PROPERTIES OF LIQUID

● SHAPE AND VOLUME

• A liquid has a definite/fixed volume but not a definite/fixed shape.

• The particles are arranged closely but not rigidly.

• held together by a strong intermolecular forces but not

strong enough to hold the particles firmly in place

• ∴ particles able to move freely

Thus, a liquid flows to fit the shape of its container and is

confined to a certain volume.

4444

The properties of Liquids

gas liquid

4545

COMPRESSIBILITY

● In liquid, the particles are so closed with one

another.

● Thus, there is very little empty space.

● Therefore, liquid are much more difficult to

compress than gases (nearly incompressible) and

also much denser under normal condition.

4646

● Diffusion

● Diffusion rate of a liquid is much slower than gas

but faster than solids.

● Due to :

● molecules are closely packed compared to gases

● lower kinetic energy than gases

● stronger intermolecular attractive forces between the

molecules compared to gases

47KMP/ChemUnit/SK017-09/10 47

● SURFACE TENSION, γ

● The surface tension is the amount of energy required to stretch or increase the surface of a liquid by a unit area.

● Molecules within a liquid are pulled in all directions by intermolecular forces.

● However, molecules at the surface are pulled downward and sideways by neighbouring molecules, but not upward away from the surface.

4848

• These intermolecular attractions thus tend to pull the

molecules into the liquid

• Caused the surface to stretch and tighten.

• The surface tension decreases with increased

temperature.

• The intensity of molecular motions increase,

• The intermolecular forces become less

effective.

4949

VISCOSITY

● Viscosity is the internal resistance of liquid to flow.

● It opposite with fluidity which is the ability of the liquid to flow

● It will reduce the flow of liquid.

● Increases with strength of intermolecular forces but decreases with temperature.

5050

The factors affecting the viscosity are:

● The size of the molecules

➢Molar mass (Mr) increase, resistance increase, more

viscous the liquid.

● The intermolecular forces acting between molecules.

➢The stronger the attractive forces, the viscosity

increase.

● The temperature of the liquid.

➢Viscosity decreases with increased temperature.

5151

Learning Outcomes:

(b) Explain vaporisation and condensation

processes based on kinetic molecular theory and

intermolecular forces.

(c) Define vapour pressure and boiling point.

(d) Explain boiling process.

5252

Vaporisation

● The process of changing the state from liquid to vapour.

● Molecules in liquid moves quite freely.

● Some molecules have higher kinetic energy (move faster) than some other molecules (move slower).

● Molecules at the surface that posses enough kinetic energy to overcome the attractive intermolecular forces can escape as vapour in the gas phase.

5353

● The rate of vaporisation increases with:

● A rise in temperature.

● An increase in the surface area of the liquid.

● A decrease in the intermolecular forces of

attraction in the liquid.

● A decrease in external pressure.

5454

Condensation

● The process of changing from vapour to liquid.

● Occurs when the vapour molecules are cooled ( lose kinetic energy) or when pressure is exerted ( molecules are closer together).

● If a gas is cooled, ➢ The molecules are moving slowly and closer together.

➢ They were able to attract each other and with molecules in the liquid state. (form back into liquid)

5555

Molecules

having high

kinetic energy

can overcome the

attractive forces

and vaporisation

A vapour

pressure

exerted by

molecules on

the surface of

the liquid

A molecule may lose

its energy during

collision and get

trapped among the

liquid molecules

leading to

condensation

Vaporisation and condensation

process

5656

VAPOUR PRESSURE

● Vapour pressure is the pressure exerted by vapour molecules while in the state of dynamic equilibrium with its liquid.

● Dynamic equilibrium: rate of forward reaction is exactly equal to the rate of the reverse reaction ( rate of vaporisation and condensation are equal)

5757

Vapour Pressure

The vapour

pressure is

constant.

Known as the

equilibrium

vapour

pressure

Dynamic Equilibrium

The rate of

vaporisation and the

rate of condensation

are equal

Number of molecules

leaving the liquid

surface is the same as

the number the of

vapour molecules

entering the liquid

state

5858

BOILING POINT

● Boiling point of a liquid is defined as the temperature

at which it’s vapour pressure equals the external

pressure.

● The normal boiling point is the temperature at which

the vapour pressure of the liquid is equal to 1 atm.

5959

SOLIDLearning outcomes:(a) Explain the fixed-shape of a solid.

(b) Apply the kinetic concepts to explain the process of :

● Freezing (solidification)

● Melting (fusion)

● Sublimation

● Deposition

(c) Differentiate between amorphous and crystalline solids.

(d) State the following types of crystalline solids with appropriate

examples:

● Metallic

● Ionic

● Molecular covalent

● Giant covalent

6060

Properties of Solid

● Particles are arranged closely together;

● Only vibrate and rotate in fixed position.

● Rigid arrangement.

● Cannot move freely.

● Has definite shape and volume.

● Has strong forces between the particles.

● Has high densities.

● Non-compressibility.

● Extremely slow diffusion.

● Less energy compared to liquids and gasses.

6161

gas liquid

solid

6262

In principle, solid, liquid and gas states are

interconvertible

solid gas

liquid

sublimation

deposition

63KMP/ChemUnit/SK017-09/10 63

Melting process

● The melting point is the temperature at which a solid

changes into a liquid.

X(s) X(l)

● When heated:

● The kinetic energy of particles increases.

● The extent/limit of rotation and vibration increases.

● A point is reached when the kinetic energy is high enough

to overcome the intermolecular forces between them.

64KMP/ChemUnit/SK017-09/10 64

Freezing (solidification) process

● A liquid is changing into a solid

X(l) X(s)

● When the temperature is lowered, the kinetic energy of a liquid particles decreases.

● The vibration decreases (kinetic energy decrease).

● A point is reached when the intermolecular forces are strong enough to hold the particles together in a fixed and orderly arrangement.

● The liquid freezes.

● The freezing point of a liquid is constant, and the value is the same as the melting point of its solid.

6565

Sublimation Process

● The process by which a substances goes directly from

solid to the gaseous state without passing through the

liquid state.

X(s) X(g)

● Examples: iodine and naphthalene

6666

Deposition

● The process where the particles in gas phase are

transformed into solid phase directly during a cooling

process.

X(g) X(s)

6767

2 types of solid

Crystalline solid☺In crystalline solid the particles (atoms, molecules or ions)

are arranged in an orderly manner.

☺It is formed when a saturated liquid is cooled slowly.

☺Its atoms, molecules or ions occupy specific position

☺Eg : salt, sugar, pyrites

Crystalline

Armophous

6868

☺Amorphous solid

☺They are called amorphous which means without

shape or form

☺Non-crystalline solid

☺Particles are randomly arranged and have no ordered

structure.

☺It is formed when a saturated liquid is cooled rapidly.

☺Eg: glass, plastics, gels

69

Differences between amorphous

and crystalline solids

Amorphous Crystalline

Non crystalline solid Crystalline solid

Random structure Ordered structure

Formed when cooled rapidly Formed when cooled slowly

No definite melting point Well defined melting point

Shatter irregularly Shatter to crystalline shaped

pieces69

7070

TYPES OF

CRYSTALLINESOLID

IONIC

MOLECULAR COVALENT

METALLIC

GIANT COVALENT

7171

Ionic Crystals

● The particles are made up of cations and anions

respectively.

● There are electrostatic forces of attraction between

cations and anions.

● Example: ionic crystal of NaCl:

7272

Metallic Crystal

● The particles in metallic crystals are metal atoms of the same metal. Examples, sodium, magnesium and aluminium.

● They are bound together by metallic bond,

● (recall* metallic bond= the electrostatic attraction between the lattice of positive ions and this sort of ‘sea’ of electrons).

7373

Molecular Covalent Crystals

● The particles consists of simple molecules which are held together by weak van der Waals forces.

● Generally, this type of solid has very low boiling and melting point.

● Examples: iodine, I2, phosphorus,P4 and sulphur,S8

7474

Giant Covalent Crystals● Very large molecules.

● Consists of strong covalent bonds binding its particles.

● The covalent bond gives gigantic structure

● The particles are non-metal.

● Examples: diamond, graphite and fullerene.

● Generally, the giant crystal structure are hard and have high melting and boiling points.

7575

Diamond

Carbon atom

Covalent bond

7676

Graphite

Van der

Waals

forces

Carbon atom

Covalent bond

7777

Fullerene

78

LECTURE 3:

PHASE DIAGRAMLearning Outcomes:

(a) Define phase, triple point and critical point

(b) Identify triple and critical point on the phase diagram

(c) Sketch the phase diagram of H2O and CO2

(d) Compare the phase diagram of H2O with CO2 and

explain the anomalous behavior of H2O

79

Phase, Triple point and Critical point

Phase

The phases of a system are parts of it which are separated by

a distinct boundary, such as solid, liquid and gas.

Triple point

The point at which the three lines representing the

solid/liquid, liquid/vapour and solid/vapour equilibriums

meet.

Critical point

The point above which it is not possible to liquefy as gas,

however great the pressure

80

Example

The number of phases in a system is denoted P.

● A gas or gaseous mixture, is a single phase (P = 1 )

● A crystal is a single phase ( P = 1 ).

● Two totally miscible liquids form a single phase

(P = 1)

● An alloy of two metals is a two-phase system ( P = 2 ) if the metals are immiscible, but

a single-phase system ( P = 1 ) if they are miscible.

81

A phase diagram

Showing the relationship between the different

phases of a given substance under varying

conditions of temperature & pressure

Phase Diagram

82

Phase diagram of water

B

C

A

Solid

Liquid

Vapour

1

Critical

Point

Boiling

PointT

Triple Point

273.16 373.15 374

Temperature / K

218

6.0 x 10-3

Pressure/atm

ATB :Solid phaseBTC : Liquid phaseATC :Vapour phase

83

Phase Diagram for Water

B

C

A

SolidLiquid

Vapour

1

Critical

Point

Boiling

PointT

Triple Point

273.16 373.15 374Temperature / K

218

6.0 x 10-3

T-C : Represents the variation of boiling temp. with pressureT-B : Represents the variation of melting temp. with pressureT-A : Represents the variation of sublimation temp. with

pressure

84

B

C

A

SolidLiquid

Vapour

1

Critical

Point

Boiling

PointT

Triple Point

273.15 373.15 374Temperature / K

218

6.0 x 10-3

At temperatures between 273.15 K and 373.15 K under atmospheric pressure, the stable phase is liquid water

Phase Diagram for Water

85

T is an unique point at which the three lines representing the solid/liquid, liquid/vapour and solid/vapour equilibriums meet is called the triple point

The triple point for water is 273.16 K and 6.0 x 10-3 atm

At the other extreme of the liquid/vapour line is the critical point, above which it is not possible to liquefy as gas, however great the pressure

Phase Diagram for Water

86

Phase Diagram for Carbon Dioxide

B

C

A

72.9

Solid Liquid

Vapour

5.2

1

Critical

Point

T

Triple

Point

195 216.4 304 Temperature / K

T-C : Represents the variation of boiling temp. with pressureT-B : Represents the variation of melting temp. with pressureT-A : Represents the variation of sublimation temp. with pressure

ATB : Solid phase

BTC : Liquid phase

ATC : Vapour phase

87

Phase Diagram for Carbon Dioxide

-The phase diagram of carbon dioxide is more typical,

showing a rightward sloping melting temperature line

-Solid carbon dioxide is denser than liquid carbon dioxide

Triple point for carbon dioxide is 216.4 K and 5.2 atm

The triple point is above atmospheric pressure, so that at

atmospheric pressure carbon dioxide sublimes, so ‘dry ice’,

which is solid carbon dioxide, changes directly from solid

to gas