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Entropy & Spontaneity
Chapter 17
Review
• Enthalpy – ∆H=q - heat of reaction
• Exothermic vs. endothermic
• Exothermic is generally favored in nature
• Kinetics – rates of reaction – how fast or slow
• System refers to the reactants and products
• Surroundings - everything around it
• Heat flows from one to the other
• Laws of thermodynamics:
• First Law = conservation of energy = energy in universe is constant
• Second Law = universe is constantly increasing in disorder
(randomness) = increasing in entropy
• Third Law = entropy of a perfect crystal is zero at 0K = (absolute
entropy can be determined for any temp higher than 0K)
Spontaneous
• Means it occurs without outside intervention - on its own.
• Does not mean fast.
• Must follow the laws of thermodynamics
• Tells us about direction but not speed
• Helps predict if the process will occur but not how it will
• Alternate way to describe spontaneous process is to say it is
thermodynamically favored.
• Common characteristic of spontaneous processes is entropy
• Entropy = measure of molecular disorder or randomness
• Driving force behind processes
Entropy
• Represented as S
• ∆S = change in entropy (final – initial)
• ∆S can be positive or negative
• Atoms love going to lower energy states
• Atoms love to get all messed up (move around randomly)
• Things naturally tend to get messy unless you keep them in check.
• Entropy is closely associated with probability (likelihood)
• The more ways a state/condition can be achieved the more likely
(probable) it is to occur.
• Spontaneous processes proceed toward states that have highest
probability of existing.
• Larger number of arrangements or energy levels available to a
system
• More disorder or randomness = more entropy
Entropy
• Think about states of matter
•
•
•
•
•
Solids – tightly packed, rigid structure (lots of order)
Liquids – ability to flow, move a little
Gases - spread out, move far apart (little to no order)
Solids have lowest entropy; gases have highest entropy
Prefer to go to state with less order = more entropy
• What about mixtures/solutions?
• Tendency of materials to mix is due to increased volume available
to the particles of each component of a mixture
• More complex the molecule = generally more entropy
• EX: When 2 liquids are mixed, the molecules of each liquid have
more available total volume, therefore more available
positions/interactions available.
Relating entropy & temperature
∆Ssurr = -
∆𝐻
𝑇
• The sign of ∆S depends directly on direction of heat flow
• whether endothermic or exothermic reaction is important
• Endothermic (positive) q > 0; exothermic (negative) q < 0
• The magnitude of ∆S depends inversely on the temperature
• Units: J/K
• If reaction is exothermic, ∆Ssurr = positive
• If reaction is endothermic, ∆Ssurr = negative
• ∆Ssurr = positive is favored
Entropy Changes in Reactions
• Whether a reaction will occur spontaneously can be
determined by looking at ∆S and ∆H.
• Table 17.5, p798
• Also look at the number of molecules/moles of each reactant
and product in the equation
• Fewer molecules means fewer possible configurations = lower
entropy
• More molecules/moles on product side = entropy increases
• More molecules/moles on reactant side = entropy decreases
• Standard entropy - ∆S° - listed in Appendix 4
∆S°reaction = ∑np∆S°products - ∑nr∆S°reactants
Free Energy
• Symbol – G
• G = H – TS
∆G = ∆H – T∆S
∆G° = ∆H° – T∆S°
• Remember this ° indicates in standard states
• Calculating ∆G° is just like determining ∆H° and ∆S°
• ∆G°reaction = ∑np∆G°products - ∑nr∆G°reactants
• ∆G = ∆G° + RT ln Q
• ∆G° = -RT ln K (system at equilibrium so ∆G = 0)
• ∆G° = - nFE° (F = faradays constant; E° = standard voltage)
Summary
∆G positive = not spontaneous
∆G negative = spontaneous
∆H
Negative
Positive
Negative
Positive
∆S
positive
positive
negative
negative
Result
spontaneous at all temperatures
spontaneous at high temperatures
spontaneous at low temperatures
not spontaneous, ever
∆G
0
Negative
Positive
K
at equilibrium; K = 1
> 1; products favored
< 1; reactants favored