Notes On Entropy and Gibbs Energy
Berthelot (1860's)--rxns with negative H were spontaneous
J Willard Gibbs (late 1800's)--negative H not only criteria, but entropy also important
A Brief Review of Enthalpy:
Most, but NOT all spontaneous rxns evolve energy
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For a rxn to be exothermic: Hrxn = Hf(prod) - Hf(reactants) must be less than 0
Hrxn is called Standard Enthalpy Change
Thermodynamic standard states = 1 atm, 1 M for sol'ns, 25 oC (298 K)
Hrxn = Hf(prod) - Hf(reactants) and is approximately equal to Urxn
Standard enthalpy change is approximately equal to the Standard energy
change
Enthalpy is relatively independent of pressure and temperature.
 Spontaneous- a process that takes place w/o imput of energy from external source.
 Natural tendency --------> decrease in energy
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Examples
water flows downhill, a spring
unwinds
CH4(g) + 2O2(g) ------> C02(g) +
2H2O(g)
Hrxn = - 802 kJ
4Fe(s) + 3O2(g) -----> 2Fe2O3(s)
Hrxn = -1648kJ
Zn(s) + 2HCl(aq) -----> H2(g) +
ZnC12(aq)
Hrxn = -150kJ
These rxns do not occur spontaneously in the reverse direction.
Some endothermic rxns do occur spontaneously, however.
At any temperature greater than 0, ice will melt
H2O(s) -----> H2O(l)
Hfus = +6.0 kJ
NaCl(s) -----> Na+(aq) + Cl-(aq)
Hsol'n = + 64 kJ
Ba(OH)2(s) + 2NH4NO3(s) -----> Ba(NO3)2(s) + 2H2O(l) + 2NH3(g)
Clearly then, having H greater than zero is not a general criterion of spontaneity.
2nd Law of Thermodynamics: Entropy
(Remember, the lst Law is Conservation of Energy: Etot = Ek + Ep = constant)
Spontaneous, unidirectional processes often are referred to as irreversible processes.
ex. scrambled eggs--don't unscramble
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System--that part of the universe where the change of interest occurs
Surroundings--the rest of the universe
When any kind of process has occurred--the system and its surroundings cannot be changed to be
exactly like they were before.
Carnot (1824) studied operation of heat engines (steam & internal combustion)
Heat engines are designed to convert heat into work
Carnot showed:
1. why the engines must be operated at a higher temp than surroundings
2. why all the energy cannot be converted into work
3. how ratio of work output to heat input ratio depends on temperature difference between
system and surroundings
Entropy has the symbol S
S = qsystem / Tsystem
2nd Law can also be written as q = TS
q -- energy transfered to or from a system
T -- Kelvin Temperature
if Tsys = Tsurroundings, and no heat is lost due to friction, then S = q
system
/ T system
if irreversible, then the inequality sign appears
S greater than 0 when q for the system is positive (heat in)
S less than 0 when q for the system is negative (heat out)
Unit for S is J/K
The total entropy change (S) for a spontaneous process must be positive. This includes surroundings,
as well as system.
Entropy, unlike energy, need not be conserved--entropy increases when a natural process occurs.
Carnot Cycle
In a Carnot cycle, the system traverses two isothermal and two adiabatic paths to return to the original
state. Each of the paths is carried out reversibly.
A to B: isothermal expansion, (temp, Th)
wAB = -qAB = -nRThln(VB / VA)
B to C: adiabatic expansion,
qBC = 0
wBC = nCv ( Tl - Th) = -nCv ( Tl - Th)
C to D: isothermal compresssion, (temp, Tl)
wCD = -qCD =-nRTlln(VD / VC)
= nRTlln(VC / VD)
D back to A: adiabatic compression
qDA = 0
wDA = nCv ( Th - Tl) = - nCv ( Tl - Th)
 Isothermal process--carried out at a constant temperature
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Adiabatic process--one for which there is no transfer of heat into or out of the system (q = 0)
Net work in one passage around the Carnot cycle is
Wnet = -nRT(Th-Tl)ln(VB/VA)
Entropy--measure of disorder or randomness of a system
There are two types of disorder in a substance:
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positional disorder--refers to the distribution of the particles in space
thermal disorder--refers to the distribution of the available energy among the particles
Any process that produces a more random distribution of the particles in space gives rise to an increase
in the total entropy of the substance. So does any constant pressure process that increases the
temperature of the particles.
3rd Law of Thermodynamics--the entropy of a perfect
crystalline substance is zero at absolute zero
There is an increase in entropy on melting & vaporization
Phase transition, e.g. melting at constant P
At normal freezing temp, Tf, an infinitesimally small change in external conditions (e.g.-lowering of the
temp) serves to reverse the process.
q = H fusion
S fusion = qrev/Tm = H fus/Tm---called molar entropy of fusion
Entropy increases when a solid melts and decreases when it freezes
Svap = Hvap / Tb
Molar entropies of gases & solutions depends on concentrations--due to change in positional disorder.
This differs from enthalpy which is relatively free from effects of pressure or concentrations.
Generally, the more atoms of a given type there are in a molecule, the greater the capacity of the
molecule to take up energy and thus the greater the entropy. For molecules with approx. the same
molecular masses, the more compact the molecule, the smaller the entropy.
Standard Entropy Change is given by: Srxn = S(prod) - S(reactants)
In general, the greater the difference between the total number of moles of gaseous products and the
total number of moles of gaseous reactants, the greater the value of Srxn.
Tendency in nature -----> higher entropy
Process that are both energy favored and entropy favored will be spontaneous.
H less than 0 and S greater than 0
Many reactions have values of H and S that are opposite to each other
1. H greater than 0 and S greater than 0---rxn is endo- and has (+) S
2. H less than 0 and S less than 0---rxn is exo- and has (-) S
1) entropy favored
2) energy favored
these reactions may or may not be spontaneous: depends on temperature and relative sizes of H & S
Gibbs energy
Gibbs energy relates the energy that can be obtained as work from a process to the change in
enthalpy, change in entropy and absolute temperature.
Gibbs-Helmholtz Equation: Grxn = Hrxn - TSrxn
Criteria for spontaniety:
1. if Grxn is less than 0, then rxn is spontaneous
2. if Grxn greater than 0, then rxn is not spontaneous
3. if Grxn = 0, then rxn is at equilibrium, no net change occurs.
ΔG maybe positive or negative under certain conditions.
4. ΔG = ΔH - TΔS
Enthalpy
Entropy
change ΔH
change ΔS
positive
Gibbs free energy ΔG
Spontaneity
positive
depends on T, may be + or -
yes, if the temperature is high enough
negative
positive
always negative
always spontaneous
negative
negative
depends on T, may be + or -
yes, if the temperature is low enough
positive
negative
always positive
never spontaneous