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# Free Energy & Thermodynamics

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## Joe Christopher

on 25 March 2018

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#### Transcript of Free Energy & Thermodynamics

Gibbs Free Energy
We know that shows the relationship between the
enthalpy
change of a system and the
entropy
change of the surroundings
deltaS(univ)= deltaS(sys) + deltaS(surr)
Calculating entropy changes for a reaction
Standard entropy change for a reaction- the change in S for a process in which all reactants are in their standard state.
for a gas - 1 atm
for liquid or solid-the most stable form at 1 atm and temperature of interest
for solution - 1 M concenctration
Calculating Free Energy changes in Reactions
Energy & Entropy
What is the
Chemical Potential
?
Enthalpy? No! Not Enthalpy alone.
Spontaneous processes occur because they release energy from the system.
Most spontaneous processes proceed from higher potential energy to lower potential energy. - Exothermic, -deltaH
There are some spontaneous processes that proceed from lower potential energy to higher potential energy. - Endothermic, +deltaH
How can something absorb potential energy, yet have a net release of energy?
Heat Transfer and Entropy
delta
S
universe = delta
S
sys. + delta
S
surround.
What If the entropy of the system decreases? Then the entropy of the surroundings must increase by a larger amount.
Processes like heat flow from hot to cold, water vapor condensing or water freezing are spontaneous, even though entropy decrease. How?
The entropy increase of the surroundings must come from heat released by the system; the process must be exothermic!
Energy
The first law of thermodynamics is that energy cannot be created or destroyed.
two ways energy is “lost” from a system
deltaE = q + w
deltaE = deltaH + P(deltaV)
deltaE is a state function.
Every energy transition results in a “loss” of energy. (Heat Tax)
No Perpetual Motion!
Free Energy & Thermodynamics
Entropy
Entropy (
S
) is a thermodynamic function that increases as the number of energetically equivalent ways of arranging the components increases.
Units - J/K*mol
S =
k
ln W
k = Boltzmann constant = 1.38 × 10^-23 J/K
W
is the number of energetically equivalent ways a system can exist. Unitless
Practice
C3H8(g) + 5 O2(g) --> 3 CO2(g) + 4 H2O(g)
1. deltaG(rxn) = deltaH(rxn) - TdeltaS(rxn)
estimate at any temperature
2. Using free energy of formation values
deltaG(rxn) = deltaG(prod) - deltaG(react)
only at 25 C ( 298K)
3. For a stepwise reaction (Hess's Law)
Spontaneity
A fundamental goal of
Thermodynamics
is to predict spontaneity or processes.
Spontaneous
- Processes that will occur without outside intervention.
Nonspontaneous processes require energy input to go.
determined by looking at a
chemical potential
that predicts direction of change.
Spontaneous processes are
irreversible
.
Any
reversible
process is at equilibrium.
If this
potential
energy after reaction < before the reaction, the reaction is thermodynamically favorable.
Spontaneity
does not equal
fast or slow
More freedom of motion increases the randomness of the system. When systems become more random, energy is released. We call this energy,
entropy
A - 1 microstate
B - 1 microstate
C - 6 microstates
Therefore, state C has higher entropy than either state A or B.
energy more dispersed over 6 possibilities.
Macrostates
There are two factors that determine whether a reaction is spontaneous.
enthalpy change
and
entropy change
of the system.
The enthalpy change is favorable for exothermic reactions and unfavorable for endothermic reactions
deltaS = Sfinal - Sinitial (a state function)
Entropy change is favorable when the result is a more random system. deltaS is positive.
Some changes that increase the entropy are:
Reactions whose products are in a more random state
Solid more ordered than liquid; liquid more ordered than gas
Reactions that have larger numbers of product molecules than reactant molecules
Increase in temperature
Solids dissociating into ions upon dissolving
The second law of thermodynamics
- for a spontaneous process the total entropy change of the
universe
must be positive
For reversible process deltaSuniv = 0
A chemical system proceeds in the direction that increases the entropy of the universe.
Change is temperature dependent (units J/K)
delta
S
surr = deltaHsys/T
Kinetics - Speed of a reaction-How Fast (Chapter 13)
Looks at how long it takes for a reaction to reach equilibrium. The kinetics of a process is effected by:
Concentration of reactants
Temperature
Use of a catalyst
Mechanism of the reaction
Equilibrium – the extent of a reaction
Looks at how far a reaction proceeds toward products before the rate of the forward process equals the rate of the reverse process. The equilibrium expression and equilibrium constant (Keq) describes mathematically the extent of reaction.
Thermodynamics
– used to predict the
spontaneity
of a reaction. (
Why They Occur
)
Involves the study of changes in the system and surroundings of:
Enthalpy - H (Chapter 6)
Entropy - S
Free energy - G (a combination of H and S).
Looking Back
Catalyst?
Using q(sys) to quantify deltaS(surr)
-q(sys) --> +deltaS(surr)
entropy change of surrounding inversely related to temperature -
deltaS(surr) --> -q(sys)/T
at constant P
q(sys) = deltaH(sys)
so at
constant P & T
deltaS(surr) = - deltaH(sys)/T

So an exothermic system will lead to an increase in entropy of the surrounding that is inversely related to temperature

deltaH(rxn) = -2044KJ
a. calculate the entropy change in the surroundings associated with this reaction at 25 degrees C.
b. Determine the sign of the entropy change for the system.
c. Determine the sign of the entropy change for the universe. Will the reaction be spontaneous?
deltaS(univ)= deltaS(sys) - deltaH(sys)/T
(-T)deltaS(univ)= (-T)deltaS(sys) + (T)deltaH(sys)/T
(-T)deltaS(univ)= deltaH(sys) - (T)deltaS(sys)
the right side of this equation is the thermodynamic function
Gibbs Free Energy(G)

G = H -TS
the change in free energy:

deltaG = deltaH - T(deltaS)
deltaG = -TdeltaS(univ)
Since deltaS(univ) is a basis for spontaneity, So deltaG must also be an indicator of spontaneity.
Gibbs free energy is the
chemical potential
we have been looking for.
It represents the maximum Useful work available from a reaction
Chemical systems tend toward
lower free energy
- deltaG - indicates a spontaneous process
+ deltaG indicates a nonspontaneous process
CCl4(g) --> C (s, graphite) + 2 Cl2(g) deltaH = +95.7KJ, deltaS = +142.2 J/K
Calculate deltaG at 25 C. Is it spontaneous?
Practice:
C2H4(g) + H2(g) --> C2H6(g) deltaH = -137.5 KJ, deltaS = -120.5 J/K
Calculate deltaG at 25 C. Is it spontaneous?
At constant P and T
endothermic processes
like Melting favored at high T
decreasing entropy processes
like freezing favored at low T
deltaS(rxn)
deltaS(rxn) = S(prod) - S(react)
Third law of thermodynamics
- The entropy of a perfect crystal at absolute zero (0 K) is zero.
Standard molar entropy
values are measured against this
Calculate deltaS(rxn) for the following equation.
4 NH3(g) + 5 O2(g) --> 4 NO(g) + 6 H2O(g)
The change if Free energy of a chemical reaction represents the maximum amount of energy available, or
Free
, to do useful work (if deltaG is negative).
this is often less then the change in enthalpy
deltaG represents the
theoretical
limit of how much work can be done by the reaction.
In
Rea
l
reactions the available energy is even
less
then deltaG because of additional energy loss (heat tax)
deltaS = -80.5 KJ
"Free" Energy
If deltaG is positive it represents the theoretical minimum amount of energy required to make the reaction occur
slower current will reduce loss
recharging will also take more energy
Free Energy for Nonstandard States
Why?
H20(l) <-> H2O(g)
At standard state:
deltaG = +8.59 kJ/mol
Standard state - P(H2O) = 1 atm
Normal state - P(H2O) << 1 atm
normal conditions not standard conditions!
not spontaneous
deltaG @ nonstandard conditions-
deltaG = deltaG(stand) +
RT
ln
Q
Q
- reaction quotient
@ standard conditions
Q
= 1
@equilibrium at 298K
Q
=
K
=0.0313 and deltaG = 0
other nonstandard - plug in
Q
lower P(H2O) = evaporation
higher P(H2O) = condense
Standard Free Energy and Equilibrium
Spontaneity [delta G(stand)] and the equilibrium constant (K) and connected.
if a forward process occurs with a large negative deltaG then the K value will be large
if a forward process occurs with a large positive deltaG then the K value will be small
@ equilibrium DeltaG =0
deltaG(rxn) = -
RT
lnK
Temperature dependence and K
deltaG(rxn) = deltaH -TdeltaS
ln(K2/K1) = (-deltaH(rxn)/R)(1/T2 - 1/T1)
Can use to find deltaH from K at 2 temperatures or find K at a temperature if we know K at another temp and deltaH
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