WORLD OF MOLECULES

(1)

Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PÁZMÁNY PÉTER CATHOLIC UNIVERSITY

Consortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

PÁZMÁNY PÉTER CATHOLIC UNIVERSITY SEMMELWEIS

UNIVERSITY

(2)

WORLD OF MOLECULES

STATES OF MATTER

(Molekulák világa)

(Halmazállapotok)

KRISTÓF IVÁN

semmelweis-egyetem.hu

(3)

1. Hydrogen, 2. Oxygen, 3. Carbon, 4. Nitrogen, 5. Sulphur, 6. Sodium, 7. Silicon, 8. Boron, 9. ...

World of Molecules: States of matter

Previously – Case studies

(4)

http://commons.wikimedia.org/wiki/File:Elemental_abundances.svg

Previously - Abundance of chemical elements in the crust of the Earth

(5)

Previously - Carbon cycle

(6)

Previously - Nitrogen cycle

http://commons.wikimedia.org/wiki/File:Nitrogen_Cycle.svg

(7)

1. States of matter 2. Gas state

3. Gas laws

4. Liquid state

5. Properties of liquids, surface forces 6. Solid state

7. Crystal lattices 8. Plasma state

• gas: compressible fluid, with far away molecules

• liquid: mostly incompressible fluid, mobile structure

• solid: closely packed

molecules, immobile structures

• plasma: highly ionized gas state, usually at high

temperatues

• ...

States of matter

⎪ ⎭

⎪ ⎬

⎫

fluids

⎪ ⎭

⎪ ⎬

⎫

condensed matter

(11)

Gas state

(12)

Gas state

•

has no definite shape or volume

•

molecules have linear, rotational and vibrational motions

•

the kinetic energy of the molecules spreads over a wide range

•

no intermolecular structure observable, mostly randomness

•

diffusion

•

spreads the entire available volume

•

compressible

(13)

Kinetic gas theory

• the individual entities are molecules

• the distance between molecules is far greater than the size of molecules

• weak intermolecular forces

• linear, random motion in every direction

• collision between molecules and the wall are perfectly elastic

• conservation of momentum applies

• the speed of individual molecules are different, but their average is constant

constant

=

ΣW_kinetic _W_kinetic ₌ _constant ^W_kinetic ^∝ ^T

(14)

Maxwell-Boltzmann distribution of molecule speeds

http://it.wikipedia.org/wiki/File:Maxwell-Boltzmann_distribution_1.png

speed distribution of of 1 million gas

molecules

at -100, 20 and 600 degrees °C

(15)

Maxwell-Boltzmann distribution

• gives the number of molecules with certain speeds at constant temperatures

• increasing the temperature increases the possible states (i.e.

speeds) of individual molecules

• the randomness of the system increases with temperature

• Pressure

• can be explained by collision with the surrounding walls

• can be derived by statistical treatments

• connects the kinetic energy of molecules to the absolute temperature

Properties of gas state

T 2 k

mv 3 2 1

B 2 =

(16)

Ideal gases

• ideal

• size of molecules is negligible

• intermolecular forces are negligible

• Boyle’s law (1662)

• pV=constant at constant temperatures

• isotherms

• Charles’s law (1787)

• V ~ T at constant pressures:

• Gay-Lussac’s law (1802)

• p ~ T at constant volumes:

Gas laws

0

0 T

T V

V =

0 0

p T

p = T

(17)

combination of these laws

Law of combining volumes (1802, Gay-Lussac)

• The ratio between the volumes of the reactant gases and the products can be expressed in simple whole numbers.

(cf. stoichiometry)

• e.g. 1 liter H₂ + 1 liter Cl₂ = 2 liter HCl

Avogadro’s law (1811)

• the same volume of two gases contain the same number of molecules at constant p and T (elementary gases are diatomic)

Gas laws

0 0 0

p V pV

T = T

(18)

inverting Avogadro’s law

• the same amount of molecules has to occupy the same volume (at constant p, V and T)

• thus for ideal gases molar fraction equals volume fraction

• thus molar volume is the same

Ideal gas law

where p is pressure in Pa, V is volume in dm³, n is number of moles, R is the gas constant (8,314 J.mol^-1.K), T is the absolute temperature in K.

Gas laws

% %

v n

v = n

) 273 (

41 ,

22 dm³ at T K

V_m = =

nRT

pV =

(19)

Gas laws for mixtures

partial pressure : p

_i

• the pressure of the i-th component if that would occupy the whole volume

Dalton’s law (1801)

• the pressure of the gas mixture is the sum of the partial pressures

• can be derived from the ideal gas law: ⁱ ⁱ

p = p

∑

=

i i i

i i i i

i i i

pV nRT

pV n RT p n

x p x p

p n

p V n RT

=

= ⎫⎪⎬ = ⇒ = ⋅

= ⎪⎭

∑

(20)

Amagat’s law (1880) – law of partial volumes

• partial volume: V_i

• the volume of the gas mixture is the sum of the partial volumes

Raoult’s law (1882)

• liquid-gas equilibrium of two or more components

• assuming ideal gas and ideal solution

• vapor pressure: is the pressure of a gas in equilibrium with its liquid state. (p⁰)

i i

V V x

V V

= ⋅

=

∑

(21)

Raoult’s law (1882)

• the vapor pressure of a

liquid mixture is dependent on its composition (x_i) and vapor pressure (p_i⁰) of each chemical components.

0

p 1

0

p 2

p

1

p

2

1 2

1 0 x

x

=

1 2

0 1 x

x

=

0 0

1 2 1 1 2 2

p = p + p = p x⋅ + p x⋅

more volatile component: the one with the higher vapor pressure

(here: material 2)

i i

i p x

p = ⁰ ⋅

(22)

Real gases

• discrepancy compared to ideal gases: regions

where decreasing

Temperature results in an increase in pressure

• Van der Waals approximation

• molecules have volume

• cohesive intermolecular forces exist

Real gas laws

(23)

• Van der Waals gas law for real gases

• where

• a: represents the attractive force between molecules

• b: represents the volume of 1 mole of molecules excluded from the molar volume, V_m

• usually a and b are empirical constants, but can be derived from the critical point data of the material

Real gas laws

( )

2

-

p n a V n b n R T V

⎛ + ⋅ ⎞ ⋅ ⋅ =

⎜ ⎟

⎝ ⎠

c c

p b RT

p T a R

8 64 ,

27 ² ² =

= ^is_is^the_the^critical_critical^temperatu_pressure ^re

c c

p T

(24)

Liquid state

http://en.wikipedia.org/wiki/File:Water_drop_001.jpg

(25)

• has no definite shape

• has a definite volume

• molecules have vibrational and some rotational motions

• globally random structure

• locally ordered due to intermolecular forces (e.g. Hydrogen bonds

• mostly incompressible

• has attractive, cohesive forces

• surface tension: γ

• minimization of liquid surface

Liquid state

(26)

Liquid state

high pressure difference in liquids

• due to incompressibility and the liquids own weight

• in gravitational field:

• where h is the distance from surface, and ρ is density

Effect of intermolecular/cohesive forces

• surface tension

• mixing properties

• wetting, capillary effects

g h

p = ⋅ ρ ⋅

(27)

• the amount of attractive

interactions are maximum in the bulk of a liquid

• the internal pressure forces the liquid to contract the surface to a minimum surface tension: amount of

work required to create new area on the surface of a

liquid (J/m²=N/m)

Surface tension

(28)

Some surface tension values

• diethyl ether (20°C) 17.0 mN/m

• ethanol (20°C) 22.25 mN/m

• water (25°C) 71.97 mN/m

• mercury (15 °C) 487 mN/m

• Which of them is easier to jump into?

Surface tension

http://en.wikipedia.org/wiki/File:Povr%C5%A1inska_napetost_milnica.jpg

example of liquid surface minimization

(29)

• interactions between the molecules of the liquid and the surrounding materials, especially at a triple contact point (where gas, liquid and solid phases are present of different materials)

Young’s relation

with the surface tensions of the respective interfaces

Wetting

partial dewetting Θ > 90º

partial wetting or spreading Θ < 90º

θ γ

γ

_SG

−

_LS

=

_LG

⋅ cos

(30)

Wetting - different wetting scenarios

http://en.wikipedia.org/wiki/File:Water_droplet_in_oil_on_glass_surface.JPG | http://en.wikipedia.org/wiki/File:Water_droplet_in_oil_on_brass_surface.JPG | http://commons.wikimedia.org/wiki/File:Wetting.svg

(31)

Wetting - different wetting scenarios

http://en.wikipedia.org/wiki/File:Exploring_new_continents_1200728.JPG | http://commons.wikimedia.org/wiki/File:Water_drop_on_a_leaf.jpg

(32)

Capillary effects

http://en.wikipedia.org/wiki/File:Capillarity.svg

• adhesive/repulsive force

between liquid and solid at the triple contact point

• equilibrium between the adhesive force and

gravitational pull

where h is the height of the liquid in the capillary, r is the capillary radius

2 cos

h gr

γ θ

ρ

= ⋅

(33)

Capillary effects

thin layer chromatography capillary flow experiment

(34)

Solid state

http://en.wikipedia.org/wiki/File:Different_minerals.jpg

(35)

• has a definite shape

• has a definite volume

• molecules have only vibrational motion

• globally ordered structure

• in case of crystalline structures

• locally ordered structures – solids where no global order can be observed

• e.g. amorphous materials (glass, resins)

• incompressible

Solid state

(36)

crystalline structure

• orderly repeating pattern with fixed spatial positions

• only vibration of atoms is possible

• the optical properties and band structure of a crystal depend on the lattice structure

• the lattice structure can be classified according to the Bravais lattices (1850)

• grouping of crystal structures according to the axial system used to describe them

• 7 lattice systems can be subdivided to 14 lattices

Solid state

(37)

Bravais lattice system – in 2 dimensions

(38)

http://en.wikipedia.org/wiki/Crystal_structure

Lattice systems

• triclinic

• monoclinic

• orthorhombic

• tetragonal

• rhombohedral

• hexagonal

• cubic

• Lattice centerings:

• primitive,

• body-centered,

• single or multi face-centered,

(39)

• all of the naturally

occuring crystals can be classified into one of

these lattice systems

• the most common

lattices (c.f. red circles)

• hexagonal (e.g. graphite)

• bcc (metals)

• fcc (NaCl salt crystals)

(40)

Bravais lattice system

http://zh.wikipedia.org/zh/File:Sphalerite-unit-cell-3D-balls.png

crystal structure of

Sphalerite: (Zn,Fe)S

• face-centered cubic crystal

• note that this crystal structure classification is based on spatial

positions of atoms, not

their respective bond

order or structure

(41)

Crystal lattice structure of the elements

(42)

Plasma state

http://commons.wikimedia.org/wiki/File:Plasma_1090051.JPG

(43)

• first described in 1879, in a Crookes tube

• high energy state

• gas-like state, with ionized atoms or molecules

• also free electrons

• overall charge is roughly zero

• conducts electricity

• responds to electromagnetic fields (magnetizable)

• electrostatic interactions dominate in the interactions of the gas state

• collective behavior of charged particles, since they are affected by each other’s generated electromagnetic field

Plasma state

(44)

Occurence

• Universe

• almost everywhere, neutron stars, interstellar medium

• Nature

• lightning, ionosphere, Aurora Borealis (Northern lights)

• Artificial

• plasmaTV, fluorescent tube, semiconductor etchant, arc welding

Classification by electron density and temperature

Plasma state

(45)

Plasma state – ranges of plasma

(46)

Plasma state – Northern lights, natural phenomenon

http://it.wikipedia.org/wiki/File:Polarlicht_2.jpg

(47)

Phase diagram

Phase diagram of most compounds

• dashed line depicts the

behavior of incompressible liquids (e.g. water)

• Data for water

• Triple point

• pressure: 0.6117 kPa

• temperature: 273.16 K

• Critical point

• pressure: 22.064 kPa

• temperature: 647 K

(48)

Phase transitions

http://en.wikipedia.org/wiki/File:Phase_change_-_en.svg

(49)

Phase transitions

The phase of matter can change due to a change in

temperature or pressure (follow on the phase diagram) possible phase transitions

• solid → melting → liquid → boiling/evaporation → gas (vapor)

• solid → sublimation → gas

• gas → condensation → liquid → freezing → solid

• gas → deposition → solid

• gas → ionization → plasma

• plasma → recombination/deionization → gas

(50)

WORLD OF MOLECULES

WORLD OF MOLECULES

1. Hydrogen, 2. Oxygen, 3. Carbon, 4. Nitrogen, 5. Sulphur, 6. Sodium, 7. Silicon, 8. Boron, 9. ...

Previously – Case studies

1. States of matter 2. Gas state

3. Gas laws

4. Liquid state

5. Properties of liquids, surface forces 6. Solid state

7. Crystal lattices 8. Plasma state

Table of Contents

• gas: compressible fluid, with far away molecules

• liquid: mostly incompressible fluid, mobile structure

• solid: closely packed

molecules, immobile structures

• plasma: highly ionized gas state, usually at high

temperatues

• ...

⎪ ⎭

⎪ ⎬

⎫

⎪ ⎭

⎪ ⎬

⎫

has no definite shape or volume

molecules have linear, rotational and vibrational motions

the kinetic energy of the molecules spreads over a wide range

no intermolecular structure observable, mostly randomness

diffusion

spreads the entire available volume

compressible

Maxwell-Boltzmann distribution

• Pressure

Ideal gases

combination of these laws

Law of combining volumes (1802, Gay-Lussac)

Avogadro’s law (1811)

nRT

pV =

partial pressure : p

Dalton’s law (1801)

∑

∑

∑

Amagat’s law (1880) – law of partial volumes

Raoult’s law (1882)

∑

Raoult’s law (1882)

0

p 1

0

p 2

p

p

1 0 x

x

=

=

0 1 x

x

=

=

Real gases

• Van der Waals approximation

• Van der Waals gas law for real gases

• where

• usually a and b are empirical constants, but can be derived from the critical point data of the material

( )

-

p n a V n b n R T V

⎛ + ⋅ ⎞ ⋅ ⋅ =

⎜ ⎟

⎝ ⎠

high pressure difference in liquids

• due to incompressibility and the liquids own weight

• in gravitational field:

Effect of intermolecular/cohesive forces

• surface tension

• mixing properties

• wetting, capillary effects

g h