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Law of Disorder
the disorder (or entropy) of a system tends to increase
ENTROPY (S)
•Entropy is a measure of disorder
• Low entropy (S) = low disorder
•High entropy (S) = greater disorder
•Operates at the level of atoms and molecules
• hot metal block tends to cool
• gas spreads out as much as possible
Factors affecting Entropy
A. Entropy increase as matter moves from a solid to a liquid to a gas
Increasing Entropy
B. Entropy increases when a substance is divided into parts
Increasing Entropy
C. Entropy tends to increase in reactions in which the number of molecules increases
Increasing Entropy
D. Entropy increase with an increase in temperature
Entropy Changes in the System (∆Ssys)
aA + bB cC + dD
DS0
rxndS0(D)cS0(C)= [ + ] - bS0(B)aS0(A)[ + ]
DS0
rxnnS0(products)= S mS0(reactants)S-
The standard entropy of reaction (∆ S0 ) is the entropy change for a reaction carried out at 1 atm and 250C.
rxn
What is the standard entropy change for the following reaction at 250C? 2CO (g) + O2 (g) 2CO2 (g)
S0(CO) = 197.9 J/K•mol
S0(O2) = 205.0 J/K•mol
S0(CO2) = 213.6 J/K•mol
DS0
rxn = 2 x S0(CO2) – [2 x S0(CO) + S0 (O2)]
DS0
rxn = 427.2 – [395.8 + 205.0] = -173.6 J/K•mol
Entropy Changes in the System (∆Ssys)
When gases are produced (or consumed)
• If a reaction produces more gas molecules than it consumes, ∆S0 > 0.
• If the total number of gas molecules diminishes, ∆ S0 < 0.
• If there is no net change in the total number of gas molecules, then ∆ S0 may be positive or negative BUT ∆ S0 will be a small number.
What is the sign of the entropy change for the following reaction? 2Zn (s) + O2
(g) 2ZnO (s)
The total number of gas molecules goes down, ∆ S is negative.
DSuniv = DSsys + DSsurr > 0Spontaneous process:
DSuniv = DSsys + DSsurr = 0Equilibrium process:
Gibbs Free Energy
For a constant-temperature process:
DG = DHsys -TDSsys
Gibbs free energy (G)
DG < 0 The reaction is spontaneous in the forward direction.
DG > 0 reaction is spontaneous in the reverse direction. The reaction is non-spontaneous as written. The
DG = 0 The reaction is at equilibrium.
aA + bB cC + dD
DG0
rxndDG0 (D)
fcDG0 (C)
f= [ + ] - bDG0 (B)f
aDG0 (A)f
[ + ]
DG0
rxnnDG0 (products)
f= S mDG0 (reactants)f
S-
The standard free-energy of reaction (∆ G0 ) is the free-energy change for a reaction when it occurs under standard-state conditions.
rxn
Standard free energy of formation (∆ G0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states.
f
DG0 of any element in its stable form is zero.
f
f
2C6H6 (l) + 15O2 (g) 12CO2 (g) + 6H2O (l)
DG0
rxnnDG0 (products)
f= S mDG0 (reactants)f
S-
What is the standard free-energy change for the following reaction at 25 0C?
DG0
rxn6DG0 (H2O)
f12DG0 (CO2)f= [ + ] - 2DG0 (C6H6)f
[ ]
DG0
rxn = [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ
Is the reaction spontaneous at 25 0C?
DG0 = -6405 kJ < 0
spontaneous
Recap: Signs of Thermodynamic Values
Negative PositiveEnthalpy (ΔH)
Exothermic Endothermic
Entropy (ΔS)
Less disorder
More disorder
Gibbs Free Energy (ΔG)
Spontaneous
Not spontaneous
Gibbs Free Energy and Chemical Equilibrium
DG = DG0 + RT lnQ
R is the gas constant (8.314 J/K•mol)
T is the absolute temperature (K)Q is the reaction quotient
At Equilibrium
DG = 0 Q = K
0 = DG0 + RT lnK
DG0 = - RT lnK