# Thermodynamics Gibbs Free Energy by t0231232

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```									Thermodynamics : Gibbs Free Energy
Gibbs Free Energy (G) - The energy associated with a chemical reaction that can be
used to do work. The free energy of a system is the sum of its enthalpy (H) plus the
product of the temperature (Kelvin) and the entropy (S) of the system:

Free energy of reaction ( G)
 The change in the enthalpy ( H) of the system minus the product of the temperature
(Kelvin) and the change in the entropy ( S) of the system:

Standard-state free energy of reaction ( G )
 The free energy of reaction at standard state conditions:

Standard-state conditions

 The partial pressures of any gases involved in the reaction is 1 Atm
 The concentrations of all aqueous solutions are 1 M.
Measurements are also generally taken at a temperature of 25 C (298 K)

Standard-State Free Energy of Formation ( Gf )
 The change in free energy that occurs when a compound is formed form its elements in
their most thermodynamically stable states at standard-state conditions. In other words, it
is the difference between the free energy of a substance and the free energies of its
elements in their most thermodynamically stable states at standard-state conditions.

o   The standard-state free energy of reaction can be calculated from the
standard-state free energies of formation as well. It is the sum of the free
energies of formation of the products minus the sum of the free energies of
formation of the reactants:

Recall from the enthalpy notes that reactions can be classified according to the
change in enthalpy (heat):
o   Endothermic - absorbs heat, H > 0
o   Exothermic - releases heat, H < 0

Reactions can also be classified according to the change in the free energy of the
reaction:

o   Endergonic - NON-SPONTANEOUS, G > 0
o   Exergonic - SPONTANEOUS, G < 0

Summary
Favorable Unfavorable
Conditions Conditions
H <0           H >0
S >0           S <0

SPONTANEOUS: G is negative ( G < 0)
NON-SPONTANEOUS: G is positive ( G > 0)
EQUILIBRIUM: G = 0
o   If a reaction is favorable for both enthalpy (     H < 0 ) and entropy

( S > 0), then the reaction will be SPONTANEOUS (             G < 0 ) at any
temperature.

o   If a reaction is unfavorable for both enthalpy (     H > 0 ) and entropy

( S < 0 ), then the reaction will be NONSPONTANEOUS (              G >0)
at any temperature.

o   If a reaction is favorable for only one of either entropy or enthalpy, the
standard-state free energy equation must be used to determine whether the
reaction is spontaneous or not.

Sample free energy calculation
Compound        Hf        S
NH4NO3(s)     -365.56   151.08
NH4+(aq)      -132.51   113.4
NO3-(aq)      -205.0    146.4
Calculate H , S , and G for the above reaction to determine whether
the reaction is spontaneous or not.

First let's calculate Hf . Note that in the above reaction, one mole of NH4NO3
dissociates in water to give one mole each of NH4+ and NO3-:

Next, let's calculate   S:

Now we can plug in these values we've calculated into the free energy equation.

 NOTE: The units of Hf is kJ and the units of S is J/K. Since G is generally
reported in kJ, we can divide S by 1000 to convert it to units of kJ/K
 NOTE: The temperature in the free energy equation must be in Kelvin, so we must
convert the given temperature in Celsius to Kelvin by adding 273.15.
Temperature and Free Energy
   If a reaction is favorable for enthalpy ( H < 0 ), but unfavorable for
entropy ( S < 0 ), then the reaction becomes LESS SPONTANEOUS as
temperature increases.
o WHY? - The standard-state free energy equation states that:

If entropy is unfavorable, the S is negative. Subtracting a
negative number is the same as adding the respective positive
number. As the temperature increases, the T S factor (which is
ADDED to the enthalpy if the entropy is unfavorable) increases as
well. Eventually, the T S factor becomes larger than H
and G becomes positive, i.e. the reaction is no longer
spontaneous.

Sample Calculations
Compound      Hf       S
N2(g)         0      191.61
H2(g)         0      130.68
NH3(g)      -46.11   192.45
1) Calculate H and S for the above reaction. Explain what each of the
signs mean.

H is negative which is favorable.

S is negative which is unfavorable.

2) Predict whether the above reaction is spontaneous at 25 C.
G is negative, so the reaction is SPONTANEOUS.

3) Predict whether the above reaction is spontaneous at 500 C.

G is positive, so the reaction is NOT SPONTANEOUS.

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