1. Entropy
The entropy of any system may be found, at least theoretically, using the relationship:
S = (Boltzman Constant)*Ln(microstates)
Where “microstates” measure the # of possible position and energy states of the particles making up the system. This is a probability. The book shows, for a volume change, ΔS = nRLn(Vf/Vi) & earlier we saw:
qrev= nRTLn(Vf/Vi), so ΔS = qrev/T

2. Entropy ΔS = nRLn(Vf/Vi) qrev= nRTLn(Vf/Vi) ΔS = qrev/T
&, at ΔP = 0 & ΔT >< 0
ΔS = nCPLn(Tf/Ti), or, if ΔV = 0
ΔS = nCVLn(Tf/Ti),

3. Entropy ΔS = qrev/T To melt one mole of a solid at its melting point:
Qrev = ΔHfusion and T is the MP in K.
The same relationship holds for any change of state.
Therefore, ΔS = ΔHstate change T
IF ΔE is used only to change S

4. Depends on magnitude of system vs. surroundings
Entropy ΔS
Spontaneous?
sys
sur
univ +
yes - No
+/-
-/+ ?
Depends on magnitude of
system vs. surroundings

5. Gibbs Free Energy, G ΔG = ΔH – TΔS ΔG = 0 for a system at equilibrium
The Free Energy is the amount of energy available to/from a system.
ΔG = ΔH – TΔS
ΔG = 0 for a system at equilibrium
ΔG > 0 for an endothermic process
ΔG < 0 for an exothermic process

6. Gibbs Free Energy, G For the reaction: C(graphite)+ O2  CO2(g)
ΔHo = kJ & ΔSo = 3.05J/K
ΔGo = kJ – 298K*3.05J/K
ΔGo = 394.4kJ

7. Gibbs Free Energy Maximum useful work, w = ΔG.
If we combine this with what we know about ΔE, ΔH and ΔG
ΔE = ΔH – PΔV, or ΔH = ΔE + PΔV and
ΔG = ΔH – TΔS we could show:
qP = ΔH if wusefull = 0, or
qP = ΔS if wusefull  0

8. Gibbs Free Energy ΔG if ΔP  0 we can show:
ΔG = ΔGo + RTLn(P), or, in general,
ΔG = ΔGo + RTLn(Q) where “Q” is the mass expression.
Q becomes K & ΔG = 0 at equilibrium, so:
ΔGo = RTLn(K)
(remember, “ΔG = 0” is the definition of a system at equilibrium.)