Helmholtz and Gibbs (free) Energies

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Helmholtz and Gibbs (free) Energies

• Lecture Note 12
• Physical Chemistry II, 2008
• KAIST

Ann6 Quiz(11/14 25min)
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• ds0 for an isolated system too restrictive to
  predict spontaneous process, then what can be
  used to determine the direction of a spontaneous
  process?
• Free energies, Helmholtz and Gibbs

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22-1 Helmholtz energy A determines direction at
constant V and T (decreasing A, spontaneous)

• ds0 cannot be used at constant V and T (dV0,
  dT0) because ?
• Lets start with the 1st law to find a proper
  criterion

Lets define a new thermodynamic state function
by A U TS then
dA 0 (constant T and V) for a
spontaneous process.
Equality for reversible, nonequality for
irreversible
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Equality for reversible, nonequality for
irreversible
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Some observations on ?A
Maximum work Done Minimum work To be done
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22-2 Gibbs energy G determines the direction at
constant P and T (decreasing G, spontaneous)

• Recall why we defined H in addition to U
• Most chemical reactions at constant P
• Start from the 1st law

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G U TS PV, ?G0 (constant T and P,
spontaneous)
H and S change competing, at low T, H more
effective at high T, S more effective
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Most important eq. of the semester!
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?vap G 0 at T 373.15 K, liquid and vapor in
equilibrium 1.10 kJmol-1 at T
363.15 K no vaporization -1.08
kJmol-1 at T 383.15 K vaporization spontaneous
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?G maximum work obtainable from a process at
constant T and P
?G lt 0 ?nonPV is the maximum work that can be
done by the system in most practical
cases the quantity of work will be less ?G gt 0
process is not spontaneous. ?nonPV is the minimum
work to be done to make this process
happen
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NonPV work example
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Maxwell relations are useful thermodynamic
formulas (to obtain unmeasurable or
difficult-to-calculate quantities)
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Maxwell relation to calculate entropy change from
equation of state
If P-V-T data is known, entropy can be calculated
as a function of density or volume.
Ideal gas EOS for large V limit
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Same as example 20-2, but dU0 is not assumed here
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Unlike ideal gas, energy of real gas may depend
on T and other state variables use a Maxwell
relation to get U(T,V) and more
One example of thermodynamic equation of state
Now, P-V-T data can be used to calculate U at the
given P
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R
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Enthalpy is independent of pressure if the second
(and higher) virial coefficients are 0