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Third Year Chemistry

• 2nd semester: Physical (2007-2008)•May exams

• Physical: 4 lecturers 8 topics• Dónal Leech: one topic

•Thermodynamics•Mixtures and phase diagrams

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Phase Equilibria Phase transitions

Changes in phase without a change in chemical composition

Gibbs Energy is at the centre of the discussion of transitions Molar Gibbs energy

Gm = G/n

Depends on the phase of the substance

A substance has a spontaneous tendency to change into a phase with the lowest molar Gibbs

energy

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Variation of G with pressure We can derive (see

derivation 5.1 in textbook) that Gm = Vmp

Therefore Gm>0 when p>0

Can usually ignore pressure dependence of G for condensed states

Can derive that, for a gas:

Gm = RT ln(pf/pi)

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To be presented in Lecture

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Variation of G with temperature

Gm = -SmTCan help us to understand why transitions occur

The transition temperature is the temperature when the molar Gibbs energy of the two phases are equal.

The two phases are in EQUILIBIRIUM at this temperature

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Phase diagrams

Map showing conditions of T and p at which various phases are thermodynamically stable

At any point on the phase boundaries, the phases are in dynamic equilibrium

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Location of phase boundaries Clapeyron equation (see derivation 5.4)

Clausius-Clapeyron equation (derivation 5.5)

TVT

Hp

trs

trs

constant11

lnln

ln

1212

2

TTR

Hpp

TRT

Hp

vap

vap

Constant is

vapS/R

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Derivations

dGm = Vmdp – SmdTdGm(1) = dGm(2)

Vm(1)dp – Sm(1)dT = Vm(2)dp – Sm(2)dT

{Vm(2) – Vm(1)}dp = {Sm(2) – Sm(1)}dT

trsV dp = trsS dT

T trsV dp = trsH dT

dp/dT = trsH/(T trsV)

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Derivations: liquid-vapour transitions

To be presented in lecture

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Characteristic points When vapour pressure is equal to external pressure

bubbles form: boiling pointNormal bp: 1 atm, Standard bp: 1 bar When a liquid is heated in a closed vessel the liquid

density eventually becomes equal to the vapour density: a supercritical fluid is formed.

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Using the C-C equation The vapour pressure of mercury is 160 mPa at 20°C.

What is its vapour pressure at 50°C given that its enthalpy of vapourisation is 59.3 kJ/mol?

The vapour pressure of pyridine is 50.0 kPa at 365.7 K and the normal boiling point is 388.4 K. What is the enthalpy of vapourisation of pyridine?

Estimate the normal and standard boiling point of benzene given that its vapour pressure is 20.0kPa at 35°C and 50.0kPa at 58.8°C.

Remember: BP: temperature at which the vapour pressure of the

liquid is equal to the prevailing atmospheric pressure. At 1atm pressure: Normal Boiling Point (100°C for water) At 1bar pressure: Standard Boiling Point (99.6°C for

water; 1bar=0.987atm, 1atm = 1.01325bar)

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Phase Rule

Can more than 3 phases co-exist (for a single substance)?

Gibbs energies are equal:Gm(1)=Gm (2) Gm(2)=Gm(3) Gm(3)=Gm(4)

All a function of p and T. Need to solve 3 equations for 2 unknowns: impossible!

F = C-P+2

Phase rule

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CO2

Dry ice fog-special effects

Supercritical fluidsCaffeine extraction from coffee beans

Dry-cleaningPolymerisationsChromatography

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WaterIce I structure

Solid-liquid boundary slopes to the left with increasing pressure

volume decreases when ice melts, liquid is denser that solid at 273 K

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Introduction to mixtures

Homogeneous mixtures of a solvent (major component) and solute (minor component).

Introduce partial molar property: contribution that a substance makes to overall property.

V = nAVA + nBVB

Note: can be negative, if adding solute to solvent results in decrease in total volume (eg MgSO4 in

water)

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The chemical potential,

We can extend the concept of partial molar properties to state functions, such as Gibbs energy, G.

This is so important that it is given a special name and symbol, the chemical potential, .

G = nAGA + nBGB

G = nAA + nBB

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The chemical potential of perfect gases in a mixture

Recall that

Gm(pf) = Gm(pi) + RT ln (pf/pi)At standard pressure

Gm(p) = Gm° + RT ln (p/p°)

Therefore, for a mixture of gases

J = J° + RT ln (pJ/p°)More simply (at p° = 1 bar)

J = J° + RT ln pJ

System is at equilibrium when

for each substance has the same value in every phase

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Spontaneous mixingto be presented in lecture

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Gas mixtures

CompareGmix = nRT {xAln xA+ xB ln

xB}

G = H – TS

ThereforeH =

Smix = − nR {xAln xA+ xB ln xB}

Perfect gases mix spontaneously in all proportions

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Ideal Liquid Solutions

pJ = xJpJ*

Due to effect of solute on entropy of solution

Raoult’s Law

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Real Solutions

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Chemical potential of a solvent

At equilibrium A(g) = A(l)

A(l)= A°(g) + RT ln pA

A(l)= A°(g) + RT ln xApA*

A(l)= A°(g) + RT ln pA* + RT ln xA

└────────────────┘

A*

A(l)= A*+ RT ln xA

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Is solution formation spontaneous?

G = nAA + nBB

Can show that

Gmix = nRT {xAln xA+ xB ln xB}

and

H = Smix = −nR {xAln xA+ xB ln xB}

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Ideal-dilute solutions Raoult’s law generally describes well solvent vapour

pressure when solution is dilute, but not the solute vapour pressure

Experimentally found (by Henry) that vp of solute is proportional to its mole fraction, but proportionality constant is not the vp of pure solute.

Henry’s Law

pB = xBKB

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Gas solubilityHenry’s law constants for gases dissolved in water at 25°C

Concentration of 4 mg/L of oxygen is required to support aquatic life, what partial pressure of oxygen

can achieve this?

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Application-diving

Table 1Increasing severity of nitrogen narcosis symptoms with depth in feet and pressures in

atmospheres.

Depth P Total P N2 Symptoms

100 4.0 3.0 Reasoning measurably slowed.

150 5.5 4.3 Joviality; reflexes slowed; idea fixation.

200 7.1 5.5Euphoria; impaired concentration; drowsiness.

250 8.3 6.4Mental confusion; inaccurate observations.

300 10. 7.9Stupefaction; loss of perceptual faculties.

Gas narcosis caused by nitrogen in normal air dissolving into nervous tissue during dives of more than 120 feet [35 m]

Pain due to expanding or contracting trapped gases, potentially leading to Barotrauma. Can occur either during ascent or descent, but are potentially most severe when gases are expanding. Decompression sickness due to evolution of inert gas bubbles.

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Real Solutions-ActivitiesJ = J° + RT ln aJ

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Colligative propertiesProperties of solutions that are a result of

changes in the disorder of the solvent, and rely only on the number of solute particles present

Lowering of vp of pure liquid is one colligative

property

Freezing point depression

Boiling point elevation

Osmotic pressure

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Colligative properties Chemical potential of a solution (but

not vapour or solid) decreases by a factor (RTlnxA) in the presence of solute

Molecular interpretation is based on an enhanced molecular randomness of the solution

Get empirical relationship for FP and BP (related to enthalpies of transition)

mKT

mKT

bb

ff

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Cryoscopic and ebullioscopic constants

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Osmotic pressure

Van’t Hoff equation

MRT

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Phase diagrams of mixtures

We will focus on two-component systems (F = 4 ─ P), at constant pressure of 1 atm (F’ = 3 ─ P), depicted as temperature-composition diagrams.

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Fractional Distillation-volatile liquids

Important in oil refining

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Exceptions-azeotropesAzeotrope: boiling without changing

High-boiling and Low-boiling

Favourable interactions between components reduce vp of mixture

Trichloromethane/propanoneHCl/water (max at 80% water,

108.6°C)

Unfavourable interactions between components increase vp of mixture

Ethanol/water (min at 4% water, 78°C)

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Liquid-Liquid (partially miscible)

Hexane/nitrobenzene as example

Relative abundances in 2 phases given by Lever Rule

n’l’ = n’’l’’ Upper critical Temperature is

limit at which phase separation occurs. In thermodynamic terms the Gibbs energy of mixing becomes negative above this temperature

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Other examples

Water/triethylamineWeak complex at low temperature

disrupted at higher T.

Nicotine/waterWeak complex at low temperature

disrupted at higher T. Thermal motion homogenizes mixture

again at higher T.

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Liquid-solid phase diagrams