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1
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
3
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)
5
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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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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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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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?
26
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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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
32
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.
34
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)
35
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
36
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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