I. Entropy
A. Entropy is a measure of the number of microstates of a system (the number of ways the system can be
arranged).
Microstates: Why Entropy Happens--Probability
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Entropy is a state function that can be related to the number of
microstates for a system (the number of ways the system can be
arranged) and to the ratio of reversible heat to kelvin temperature. It
may be interpreted as a measure of the dispersal or distribution of
matter and/or energy in a system, and it is often described
erroneously as representing the “disorder” of the system.
Entropy is simply a measure how much the energy of atoms and molecules become more spread out in a
process and can be defined in terms of statistical probabilities of a system or in terms of the other
thermodynamic quantities.
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B. The Entropy Scale. The Third law of Thermodynamics states that the entropy of a pure, perfectly ordered
crystal substance at 0 K is 0.
1.
2.
3.
4.
This gives us an absolute starting place from which to measure entropy.
There are no negative values for entropy because nothing is more ordered than a pure, perfectly
ordered crystalline substance at 0K.
Further, elements in their standard state DO NOT have entropy values of 0!!!!
The symbol for entropy is S where So indicates the entropy of a substance at standard temperature
(25oC).
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C. Relative entropies.
The 2nd Law of Thermodynamics
How does the reaction contribute to the randomness of the universe? This is summarized by the equation:
∆SUniverse = ∆SSystem + ∆SSurroundings
1. There are more ways to arrange the particles in a gas, than in a liquid, so Sgas >> Sliquid ≈ Saqueous
2. There are more available microstates for the particles in a liquid than a solid, so Sliquid > Ssolid
3. Aqueous substances have more entropy than liquid, so Saqueous > Sliquid
4. Elements of higher atomic mass have more entropy than elements of lower atomic mass.
5. The greater the complexity of the molecule, the greater the entropy. (This seems counterintuitive, but
with more bonds and more atoms, there are more ways that the bonds can rotate and vibrate. Think of
bonds more like springs rather than sticks.)
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Molecular vibration - Wikipedia
Substance
and State
(J/K mol)
Iodine
I2(s)
I2(g)
I2(aq)
I(g)
I-(aq)
ICl(g)
116
261
137
181
106
248
Example: Which has more entropy?
a. H2O(l) or H2O(g)
b. H2(g) or H2O(g)
c. NaCl(s) or NaCl(l)
d. Cu(NO3)2 (aq) or Cu(NO3)2 (s)
e. Cu(NO3)2 (aq) or CuNO3 (aq)
f. N2(g) or N2(l)
g. N2 (g) or N2H6 (g)
h. F2 (g) or Cl2 (g)
Tip: When predicting whether a reaction increases in entropy or decreases in entropy, you should first consider
states of matter. If states of matter are the same on both sides, then you should consider how many particles
are on each side of the equation (the side with more particles has more entropy).
Example: Does entropy of the SYSTEM increase or decrease?
A. Boiling water, H2O (l) à H2O (g)
B. Dissolving a sugar cube in water, C12H22O11 (s) à C12H22O11 (aq)
C. Stalactites being formed by: CO2 (g) + CaO (s) à CaCO3 (s)
D. O2 (g) (1 atm, 25oC) à O2 (g) (0.1 atm, 25oC)
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E. A bottle of wine being chilled: CH3CH2OH (l) (30oC) à CH3CH2OH (l) (20oC)
F. Diluting tea that is too strong
G. Making diamonds from graphite: C (gr) à C (diamond)
H. Opening a can of Diet Coke
I. Baking cookies
J. 2 H2 (g) à 4 H (g)
K. 2H2 (g) + O2 (g) à 2 H2O (g)
L. 2 NH3 (g) à N2 (g) + 3 H2 (g)
M. Ba(NO3)2 (aq) + CuSO4 (aq) à BaSO4 (s) + Cu(NO3)2 (aq)
N. HCl (aq) + NaOH (aq) à NaCl (aq) + H2O (l)
O. 2 HNO2 (aq) + CuCO3 (aq) à H2O (l) + CO2 (g) + Cu(NO2)2 (aq)
D. Calculations of Entropy Changes: Entropy was originally defined as the change in energy in a process
divided by the temperature at which it occurs.
The standard entropy change in a chemical or physical process is the change in entropy that accompanies the
conversion of reactants to products.
For a chemical reaction:
Example: Nitrogen dioxide is the red-brown gas that you can sometimes see in bottles of nitric acid and in
polluted air. Predict the sign of the entropy change when nitrogen dioxide is formed from its elements in their
standard state. Determine the standard entropy change, So, involved in the formation of nitrogen dioxide at
25oC.
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E. Spontaneity - Two Factors: Enthalpy and Entropy
CH4(g) + 2O2(g)→ CO2(g) + 2 H2O(l)
Enthalpy:
Entropy:
∆H = -802 kJ
H2O(s)→ H2O(l)
Enthalpy:
Entropy:
∆H = 6.03 kJ
NaOH(s)→ Na+(aq) + OH-(aq)
Enthalpy:
Entropy:
∆H = exo
4 Al(s) + 3O2(g)→ 2 Al2O3(s)
Enthalpy:
Entropy:
∆H = - 3351 Kj
F. Calculations using Enthalpy and Entropy
∆SUniverse =
∆Ssystem + ∆SSurrounding
∆SSurroundings = -∆H/T
∆SUniverse =
∆Ssystem + -∆H/T
H2O(l) → H2O(s)
Is the above process spontaneous at:
1. -10 °C (263 K)
2. +10 °C (283 K)
Solving for ∆SSurroundings = -∆H/T
-10 °C (263 K)
-(-6010 J mol-1 )/263 K = 22.9 J K-1mol-1
+10 °C (283 K)
-(-6010 J mol-1 )/283 K = 21.2 J K-1mol -1
Solving for ∆SSystem = -22.0 J K-1 mol-1
∆SUniverse =
-10 °C :
∆Ssystem + ∆SSurrounding
-22.0 J K-1 mol-1 + 22.9 J K-1mol-1 = 0.9 J K-1mol-1
+10 °C:
-22.0 J K-1 mol-1 + 21.2 J K-1mol -1 = -0.8 J K-1mol-1
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