Equilibrium and Kinetics
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Transcript of Equilibrium and Kinetics
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Equilibrium and Kinetics
Chapter 2
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Fig. 2.1
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metastable
unstable
stable
Activation barrier
Fig. 2.2
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Otherwise Unstable
Minimum Energy – STABLE EQUILIBRIUM
Maximum Energy – UNSTABLE EQUILIBRIUM
Global Minimum - Most STABLE
Local Minimum - METASTABLE
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Intensive PropertiesPressureTemperature
Extensive Properties
Internal Energy E
Enthalpy H = E + PV
Eqn. (2.3)
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Gibbs Free Energy
TSHG
Condition for equilibrium
≡ minimization of G
Local minimum ≡ metastable equilibrium
Global minimum ≡ stable equilibrium
(2.6)
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G = GfinalGinitial
G = 0 reversible change
G < 0 irreversible or spontaneous change
G > 0 impossible
(2.7)
(2.8)
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Josiah Willard Gibbs
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Atomic
or
statistical
interpretation of entropy
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Boltzmann’s Tomb
Central Cemetery,
Vienna, Austria
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Boltzmann’s Epitaph
WkS lnW is the number of microstates corresponding to a given macrostate
(2.5)
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N=16, n=8, W=12,870
)!(!
!
nNn
NCW n
N
(2.9)
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Stirling’s Approximation
)ln()(lnln[ nNnNnnNNk nnnn ln!lnnnnn ln!ln
93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
100!=
(2.11)
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)ln()(lnln[ nNnNnnNNk WkS ln
)!(!
!ln
nNn
Nk
)]ln()(lnln[ nNnNnnNNk nnnn ln!ln (2.10)
(2.12)
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Thermal energy
Average thermal energy per atom per mode of oscillation is kT
Average thermal energy per mole of atoms per mode of oscillation is NkT=RT
(2.13)
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Maxwell-Boltzmann Distribution
kT
E
N
nexp WkS lnFraction of atoms having an energy E
at temperature T
(2.14)
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KINETICSSvante Augustus
Arrhenius
1859-1927
Nobel 1903
RT
QArate exp
(2.15)
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R
Qslope
RT
QArate exp
ln (rate)
T
1
Fig. 2.4
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A + BC AB + C
A + BC (ABC)* AB + C
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Configuration
Fre
e E
nerg
y
A + BC
(ABC)*
AB + C
ΔG*
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The three laws of thermodynamics
First Law: You cannot win, you can only break even.
Second Law: You can break even only at absolute zero.
Third Law: You can’t reach absolute zero.