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Kinetic Theory of Gases

1. Gases are composed of molecules whose size is negligible compared to the

average distance between them.

2. Molecules move randomly in straight lines in all directions and at various speed.

They collide each other and with the wall of the container ( pressure).

3. The forces of attraction or repulsion between two molecules in a gas are very

weak or negligible.

4. When molecules collide with one another, the collisions are elastic, the total

kinetic energy remains constant.

5. The average molar kinetic energy of the particles of a gas is proportional to the

absolute temperature, T (R = 8.314 J/molK - universal gas constant):

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Molecular Speed in Gases

Maxwell-Boltzmann distribution for molecular speed, in gases:

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https://www.youtube.com/watch?v=yOgCIv9XgG4

Pressure of a Gas

The particles of a gas are in constant motion and they collide with the wall of

the container, consequently they exert force on any surface. E. Torricelli (1608 -

1647) measured the ambient pressure first:

SI unit of pressure: pascal = newton/m2 = joule/m3

Pa = N/m2 = J/m3 (energy-density)

Non-SI unit: Hgmm = torr = 0.1333 kPa

Atmospheric pressure at sea level: 760 Hgmm = 101.325 kPa

Standard pressure in chemistry: 100 kPa = bar

Imperial unit: psi = pound/inch2 = 6.895 kPa. 4

The manometer measures pressure difference, P = gh

Pressure of a Gas

Barometer formula:

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h

A gas (and other phases) can be characterized by

volume (V), pressure (P),

temperature (T), amount (n)

thermodynamic state variables that can be

represented on phase diagrams

Gas Laws

The Pressure - Volume Relationship: Boyle’s Law

At constant temperature, and – amount they are inversely proportional: PV = const.

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The Temperature – Volume/Pressure Relationship

At constant pressure the volume of any fixed amount of a gas varies directly

with absolute temperature: V/T = const. Charles’Law

at constant volume: P/T = const. Gay-Lussac’s Law

t = (T 273.15) oC – the Celsius scale:

at constant pressure: Vt = V0(1 + t/273.15)

at constant volume: Pt = P0(1 + t/273.15)

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The Volume - Amount Relationship: Avogadro’s Law

Molar gas volume, Vm at 0.1 MPa and

at 0 oC: 22.41 dm3/mol

at 25 oC: 24.50 dm3/mol

(standard temperature and pressure, STP).

At fixed temperature and - pressure:

V/n = Vm = const.

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The Ideal Gas Law

R = 8.314 J/mol.K - universal gas constant

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The van der Waals Equation

a, b - constants are charactesistic for the given gas and they are determined experimentally.

For one mol of any ideal gas the PV/RT = 1 mol:

Substantial alterations, particularly at high

pressures.

The PV = nRT is valid for any gas if P 0.

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Liquefaction of Gases

occurs under conditions that permit the intermolecular attractive forces to bind the gas

molecules together in the liquid form.

Critical temperature is the temperature above which it is impossible to liquefy the gas,

no matter how high the applied pressure is. Phase boundary disappears at critical point.

Critical pressure is the minimum pressure needed to liquefy a gas at its critical

temperature. When most compressed gases are allowed to expand to a lower pressure,

they cool. Joule - Thomson effect

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Liquids

- retain their volumes but not their shape

- assume the shapes of their container

- a change in pressure has almost no effect on the volume

- the diffusion of liquids is much slower than the diffusion of gases

Surface tension: a molecule at the surface experiences a net force toward the

interior of the liquid. It is the energy required to create a unit surface (N/m = J/m2).

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Evaporation

The kinetic energies of the molecules of a liquid follow a Maxwell-Boltzmann

distribution. The molecules with kinetic energy high enough can escape from

the liquid, and enter the gas phase. The energy required to vaporize one mole of

liquid at a given temperature is called the molar enthalpy of vaporization, Hvap.

It decreases with temperature and goes to zero at critical temperature.

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Vapour Pressure

- Evaporation: the change of a liquid to the gaseous state

- Condensation: the change of a gas to the liquid state

- State of equilibrium: the rate of evaporation equals the rate of condensation.

At equilibrium (C) the concentration of the molecules in the vapour state is constant.

The pressure of vapour in equilibrium with a liquid at a given temperature is called the

equilibrium vapour pressure.

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Vapour Pressure Curves

As the temperature increases the kinetic energy of molecular motion becomes greater

and the vapour pressure exponentially increases. Vapour pressure gives an indication of

the strength of the intermolecular forces (e.g. H-bonding).15

Boiling point is the temperature at which the vapour pressure of a liquid equals the external

pressure (C). Therefore the boiling point depends on the external pressure. The temperature

of a boiling liquid remains constant until all the liquid has been vaporized. The higher the rate

at which heat is added to a boiling liquid, the faster the liquid boils.

Freezing-, or melting point of a liquid (B) is the temperature at which solid and liquid

are in equilibrium. All three phases at equilibrium at the single triple point (A).

Boiling-, and Melting Point

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Solutions

A solution is a homogenous mixture of two or more substances:

solute(s) + solvent = liquid solution.

Concentration of a solution: quantity (mole number, mass, volume) of the solute in a unit

quantity (volume, mass, mole number) of solution (or solvent).

See in detail in Chemistry Laboratory Manual 2019, pp. 16 – 17.

Solubility: the maximum amount of solute that will dissolve in a definite quantity of solvent

at a given temperature, resulting a saturated solution. The supersaturated solution is a

metastable state of the system.

Solute Solvent

Liquid

Gas

Liquid

Solid

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The attraction of ions or molecules for water molecules called hydration, and for

molecules of any other solvent is called solvation.

The Dissolution Process

Rule of thumb: polar materials dissolve in polar solvents, and nonpolar substances

are soluble in nonpolar solvents:

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Oil is not soluble in water Ionic salt (NaCl) is soluble in water

Enthalpy of Solution for Ionic Compounds

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HSoln = HL + Hhyd(cation) + Hhyd(anion)

here it is endothermic with + 4 kJ/mol

is the sum of negative lattice-, and hydration (for the cation and anion) energies:

Henry’s law: the solubility of a gas is

directly proportional to the partial

pressure of the gas above the solution:

c = concentration of dissolved gas

P = pressure of the gas

kH = constant (absorption coefficient)

Solubility of Gases in Liquids

Decompression sickness in joints(e.g. the bends for scuba divers) 20

Vapour Pressure of Solutions

Solution is prepared from two volatile components A and B.

Raoult’s law for an ideal solution states that its

vapor pressure is the sum of the partial pressures:

P = PA + PB

PA = xA PAo PB = xB PB

o

where P A, Bo is the vapour pressure of pure A or B.

P = xA PAo + xB PB

o

xA and xB are the mole fractions of A and B:

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Deviations from Raoult’s Law: Azeotropes

Positive deviation with maximumof vapour pressure. The vapour pressure is higher than either of the pure component. The liquid boils at lower temperature than either of the two components minimum boiling azeotrope.

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Negative deviation with minimumof vapour pressure. The vapour pressure is lower than either of the pure component. The liquid boils at higher temperature than either of the two components maximum boiling azeotrope.

ethanol/water: 96 % b.p. 78.2 oC

HCl/water: 20.2 % b.p. 108.6 oC

The vapour in equilibrium with a boiling azeotropehas the same concentration for the components as the liquid.

Distillation

- simple distillation

- fractional distillation

- vacuum distillation

rotary vacuum distillation

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The vapour pressure of pure, volatile solvent A, PAo is lowered by xBPA

o.

and xA = 1 xB

Solution of a Non-volatile Compound

Raoult’s law:

P = xA PAo + xB PB

o

as PBo = 0

P = xA PAo

P = (1 – xB) PAo

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Boiling-, and Freezing Point of Solutions

The lowering of vapour pressure in solutions results in boiling point elevation (tb)

and freezing point depression (tf). Vapour pressure curves of a pure solvent and a

solution of a non-volatile compound at molal concentration of 1 mol/kg:

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Molecular Mass Determination

The actual tb and tf are proportional to the molal concentration (cm):

tb = Tbcm and tf = Tf cm

solvent boiling point Tb freezing point Tf

acetic acid 118.1 +3.07 16.6 -3.90

benzene 80.1 +2.53 5.5 -5.12

camphor - - 179 39.7

carbon tetrachloride 76.8 +5.02 -22.8 -29.8

water 100.0 +0.512 0.0 -1.86

In Rast method the camphor is used as a solvent.

ms - mass of the solute (g)M - molecular mass (g/mol)msolvent - mass of the solvent (kg)

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Osmosis

In osmosis the solvent flows through

the membrane to equalize the

solute concentration on both

sides of the membrane.

Osmotic pressure, equals to the pressure that when applied to the solution

just stops osmosis. From the ideal gas law:

= cRT c = n/V - concentration in mol/m3 = mmol/dm3

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Osmosis and Cell

Hypertonic solution:a solution having a greater effective concentration than the cell fluid

Hypotonic solution:a solution having a lower effective concentration than the cell fluid

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Colligative Properties

The properties of solutions that depend principally upon the concentration

of dissolved particles, rather than upon the nature of these particles, are called

colligative properties:

- lowering of vapour pressure

- freezing point depression

- boiling point elevation

- osmotic pressure

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Solids

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Crystal Structure

A crystal structure is a symmetrical array of atoms, ions or molecules arranged in a

repeating, three dimensional pattern.

Crystal lattice: 3-D symmetrical pattern of points that defines a crystal.

Unit cell: smallest unit of a crystal lattice from which we can imagine creating a crystal by

repeating it in three dimensions.

Lattice points are centers of cations, anions, molecules, etc.

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Seven different types of unit cells characterized by edge lengths

a, b, c and angles , , :

In network crystals atoms are joined by a network of covalent bonds.

Ag, Cu, Na, Fe

fairly high m.p., hard or soft,

malleable, ductile, good electrical

conductor

metallic bondspositive ions and mobile electrons

metallic

H2, Cl2, CH4

low m.p., soft, nonconductor

dispersion and dipole-dipole

forcesmoleculesmolecular

diamond, SiC, SiO2

very high m.p., very hard, nonconductor

covalent bondsatomsnetwork

NaCl, KNO3

high m.p., hard, brittle, good

electrical conductor in molten state

electrostatic attractions

positive and negative ions

ionic

ExamplePropertiesAttractive

forcesParticlesLattice

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